* algebra/Makefile.in (oa_strap_0_sources): Don't include OM.

	(axiom_algebra_layer_0): Don't include OM, OMCONN, OMDEV.
	(axiom_algebra_layer_4): Don't include OMENC.
	(axiom_algebra_layer_14): Don't include OMPKG.
	(axiom_algebra_layer_19): Don't include OMERR, OMERRK.
	(axiom_algebra_layer_20): Don't include OMEXPR.
	* algebra/omcat.spad.pamphlet: Remove.
	* algebra/omdev.spad.pamphlet: Remove.
	* algebra/omerror.spad.pamphlet: Remove.
	* algebra/omserver.spad.pamphlet: Remove.
	* algebra/openmath.spad.pamphlet: Remove.

13 files changed, 17838 insertions, 19108 deletions

diff --git a/src/ChangeLog b/src/ChangeLog
index d1101fc5..da585f8b 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,17 @@
+2011-08-10  Gabriel Dos Reis  <gdr@cs.tamu.edu>
+
+	* algebra/Makefile.in (oa_strap_0_sources): Don't include OM.
+	(axiom_algebra_layer_0): Don't include OM, OMCONN, OMDEV.
+	(axiom_algebra_layer_4): Don't include OMENC.
+	(axiom_algebra_layer_14): Don't include OMPKG.
+	(axiom_algebra_layer_19): Don't include OMERR, OMERRK.
+	(axiom_algebra_layer_20): Don't include OMEXPR.
+	* algebra/omcat.spad.pamphlet: Remove.
+	* algebra/omdev.spad.pamphlet: Remove.
+	* algebra/omerror.spad.pamphlet: Remove.
+	* algebra/omserver.spad.pamphlet: Remove.
+	* algebra/openmath.spad.pamphlet: Remove.
+
 2011-08-09  Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
 	* interp/setvart.boot: Remoe OpenMath description.
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 0f52ada6..bb7f11e7 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -113,7 +113,7 @@ oa_strap_0_sources = \
 	RNG SRING RING ORDRING LMODULE RMODULE BMODULE \
 	COMRING ENTIRER ALGEBRA MODULE DIVRING FIELD \
 	DIFFSPC DIFFDOM DIFRING LINEXP PATMAB CFCAT REAL \
-	INTDOM GCDDOM PID UFD OINTDOM INS OM \
+	INTDOM GCDDOM PID UFD OINTDOM INS \
 	CHARZ CHARNZ STEP IEVALAB EVALAB \
 	AGG HOAGG CLAGG ELTAB ELTAGG IXAGG LNAGG \
 	FLAGG ELAGG RCAGG URAGG STAGG LSAGG A1AGG \
@@ -259,9 +259,8 @@ strap-0/FPATMAB.$(FASLEXT): strap-0/PATMAB.$(FASLEXT)
 strap-0/BOOLEAN.$(FASLEXT): strap-0/ORDFIN.$(FASLEXT) \
 	strap-0/PROPLOG.$(FASLEXT) strap-0/KONVERT.$(FASLEXT)
 
-strap-0/OM.$(FASLEXT): strap-0/TYPE.$(FASLEXT)
 strap-0/INT.$(FASLEXT): strap-0/INS.$(FASLEXT) \
-	strap-0/KONVERT.$(FASLEXT) strap-0/OM.$(FASLEXT)
+	strap-0/KONVERT.$(FASLEXT)
 
 strap-0/NNI.$(FASLEXT): strap-0/INT.$(FASLEXT)
 strap-0/PI.$(FASLEXT): strap-0/NNI.$(FASLEXT)
@@ -617,9 +616,8 @@ SPADFILES= \
  ${OUTSRC}/numode.spad ${OUTSRC}/numquad.spad ${OUTSRC}/numsolve.spad \
  ${OUTSRC}/numtheor.spad \
  ${OUTSRC}/oct.spad ${OUTSRC}/odealg.spad ${OUTSRC}/odeef.spad \
- ${OUTSRC}/oderf.spad ${OUTSRC}/omcat.spad ${OUTSRC}/omdev.spad \
- ${OUTSRC}/omerror.spad ${OUTSRC}/omserver.spad ${OUTSRC}/opalg.spad \
- ${OUTSRC}/openmath.spad ${OUTSRC}/op.spad ${OUTSRC}/ore.spad \
+ ${OUTSRC}/oderf.spad ${OUTSRC}/opalg.spad \
+ ${OUTSRC}/op.spad ${OUTSRC}/ore.spad \
  ${OUTSRC}/outform.spad ${OUTSRC}/out.spad \
  ${OUTSRC}/pade.spad ${OUTSRC}/padiclib.spad ${OUTSRC}/padic.spad \
  ${OUTSRC}/paramete.spad ${OUTSRC}/partperm.spad ${OUTSRC}/patmatch1.spad \
@@ -819,7 +817,7 @@ axiom_algebra_layer_0 = \
   AHYP     ATTREG   CFCAT    ELTAB    KOERCE   KONVERT  \
   KRCFROM  KVTFROM  IEVALAB  IEVALAB- EVALAB   EVALAB-  \
   RETRACT  RETRACT- SETCAT   SETCAT-  VOID     SEGCAT   \
-  MSYSCMD  FINITE   OM       OMCONN   OMDEV    OUT      \
+  MSYSCMD  FINITE                              OUT      \
   PRIMCAT  PRINT    PTRANFN  SPFCAT   TYPE     UTYPE    \
   BMODULE           BASTYPE  BASTYPE- STEP     LMODULE  \
   RMODULE  ALGEBRA  ALGEBRA- SGROUP   SGROUP-  ABELSG   \
@@ -969,7 +967,7 @@ $(OUT)/PALETTE.$(FASLEXT): $(OUT)/COLOR.$(FASLEXT)
 axiom_algebra_layer_4 = \
   ANON     OSI      COMM     COMPPROP ESCONT1  EXIT     \
   FAMONC   FORMULA1 IDPC              NONE     NUMINT   \
-  ODECAT   COLOR    OMENC    ONECOMP2 OPTCAT            \
+  ODECAT   COLOR             ONECOMP2 OPTCAT            \
   PALETTE  PARPCURV PARPC2   PARSCURV PARSC2   PARSURF  \
   PARSU2            PATRES2  PATTERN1 PDECAT            \
   REPSQ    REPDB    RFDIST   RIDIST   SPACEC   SPLNODE  \
@@ -1225,7 +1223,7 @@ axiom_algebra_layer_14 = \
   MPC2     MPC3     MPOLY    MPRFF    \
   MRATFAC  MULTSQFR NORMRETR NPCOEF   \
   NSUP     NTPOLFN  ODP      ODEPRIM  \
-  ODEPRRIC OMPKG             PADEPAC  \
+  ODEPRRIC                   PADEPAC  \
   PADICRAT PADICRC  PCOMP    PDECOMP  \
   PF       PFBR     PFBRU    PFOTOOLS \
   PFRPAC   PGCD     PINTERPA PLEQN    \
@@ -1325,7 +1323,6 @@ axiom_algebra_layer_18_objects = \
 $(OUT)/TSETCAT.$(FASLEXT): $(OUT)/PSETCAT.$(FASLEXT) $(OUT)/RPOLCAT.$(FASLEXT)
 $(OUT)/FPARFRAC.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT)
 $(OUT)/FEXPR.$(FASLEXT): $(OUT)/EXPR.$(FASLEXT)
-$(OUT)/OMERR.$(FASLEXT): $(OUT)/OMERRK.$(FASLEXT)
 
 axiom_algebra_layer_19 = \
   ACPLOT   ANTISYM           ATTRBUT \
@@ -1344,7 +1341,7 @@ axiom_algebra_layer_19 = \
   NAGC06   NAGD03   NAGE01   NAGE02  \
   NAGE04   NAGF07   NAGS     NAGSP   \
   NREP     NUMFMT   OC       OC-     \
-  ODEPACK  ODERAT   OMERR    OMERRK  \
+  ODEPACK  ODERAT                    \
   OPTPACK           PATTERN  OVAR    \
   PMKERNEL PMSYM             PRIMELT \
   QALGSET2 QEQUAT   RECLOS   REP1    \
@@ -1385,7 +1382,7 @@ axiom_algebra_layer_20 = \
   INTAF    INTALG   INTEF    INTG0    \
   INTHERAL INTPAF   INTPM    INTTOOLS \
   ITRIGMNP JORDAN   KOVACIC  LF       \
-  LIE      LODOF    LSQM     OMEXPR   \
+  LIE      LODOF    LSQM              \
   MCMPLX   MULTFACT NAGD01   NAGD02   \
   NAGF01   NAGF02   NAGF04   NCEP     \
   NLINSOL  NSMP     NUMERIC  OCT      \
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index 2b24b303..97cdea86 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -145,7 +145,6 @@
   (|ExpressionFunctions2| . EXPR2)
   (|ExpressionSpaceFunctions2| . ES2)
   (|ExpressionSpaceODESolver| . EXPRODE)
-  (|ExpressionToOpenMath| . OMEXPR)
   (|ExpressionToUnivariatePowerSeries| . EXPR2UPS)
   (|Factored| . FR)
   (|FactoredFunctions2| . FR2)
@@ -287,13 +286,6 @@
   (|OneDimensionalArrayFunctions2| . ARRAY12)
   (|OnePointCompletion| . ONECOMP)
   (|OnePointCompletionFunctions2| . ONECOMP2)
-  (|OpenMathConnection| . OMCONN)
-  (|OpenMathDevice| . OMDEV)
-  (|OpenMathEncoding| . OMENC)
-  (|OpenMathError| . OMERR)
-  (|OpenMathErrorKind| . OMERRK)
-  (|OpenMathPackage| . OMPKG)
-  (|OpenMathServerPackage| . OMSERVER)
   (|OperationsQuery| . OPQUERY)
   (|OrderedCompletion| . ORDCOMP)
   (|OrderedCompletionFunctions2| . ORDCOMP2)
@@ -722,7 +714,6 @@
   (|Object| . OBJECT)
   (|OctonionCategory| . OC)
   (|OneDimensionalArrayAggregate| . A1AGG)
-  (|OpenMath| . OM)
   (|OperatorCategory| . OPERCAT)
   (|OrderedAbelianGroup| . OAGROUP)
   (|OrderedAbelianMonoid| . OAMON)
diff --git a/src/algebra/omcat.spad.pamphlet b/src/algebra/omcat.spad.pamphlet
deleted file mode 100644
index 638aa325..00000000
--- a/src/algebra/omcat.spad.pamphlet
+++ /dev/null
@@ -1,85 +0,0 @@
-\documentclass{article}
-\usepackage{open-axiom}
-\begin{document}
-\title{\$SPAD/src/algebra omcat.spad}
-\author{Mike Dewar, Vilya Harvey}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{category OM OpenMath}
-<<category OM OpenMath>>=
-)abbrev category OM OpenMath
-++ Author: Mike Dewar & Vilya Harvey
-++ Basic Functions: OMwrite
-++ Related Constructors: 
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description:
-++ \spadtype{OpenMath} provides operations for exporting an object
-++ in OpenMath format.
-
-OpenMath(): Category == with
-  OMwrite  : % -> String
-  ++ OMwrite(u) returns the OpenMath XML encoding of \axiom{u} as a
-  ++ complete OpenMath object.
-  OMwrite  : (%, Boolean) -> String
-  ++ OMwrite(u, true) returns the OpenMath XML encoding of \axiom{u}
-  ++ as a complete OpenMath object; OMwrite(u, false) returns the
-  ++ OpenMath XML encoding of \axiom{u} as an OpenMath fragment.
-  OMwrite  : (OpenMathDevice, %) -> Void
-  ++ OMwrite(dev, u) writes the OpenMath form of \axiom{u} to the
-  ++ OpenMath device \axiom{dev} as a complete OpenMath object.
-  OMwrite  : (OpenMathDevice, %, Boolean) -> Void
-  ++ OMwrite(dev, u, true) writes the OpenMath form of \axiom{u} to
-  ++ the OpenMath device \axiom{dev} as a complete OpenMath object;
-  ++ OMwrite(dev, u, false) writes the object as an OpenMath fragment.
-
-@
-\section{License}
-<<license>>=
---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
---All rights reserved.
---
---Redistribution and use in source and binary forms, with or without
---modification, are permitted provided that the following conditions are
---met:
---
---    - Redistributions of source code must retain the above copyright
---      notice, this list of conditions and the following disclaimer.
---
---    - Redistributions in binary form must reproduce the above copyright
---      notice, this list of conditions and the following disclaimer in
---      the documentation and/or other materials provided with the
---      distribution.
---
---    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
---      names of its contributors may be used to endorse or promote products
---      derived from this software without specific prior written permission.
---
---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-@
-<<*>>=
-<<license>>
-
-<<category OM OpenMath>>
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}
diff --git a/src/algebra/omdev.spad.pamphlet b/src/algebra/omdev.spad.pamphlet
deleted file mode 100644
index d2897a37..00000000
--- a/src/algebra/omdev.spad.pamphlet
+++ /dev/null
@@ -1,397 +0,0 @@
-\documentclass{article}
-\usepackage{open-axiom}
-\begin{document}
-\title{\$SPAD/src/algebra omdev.spad}
-\author{Vilya Harvey}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{domain OMENC OpenMathEncoding}
-<<domain OMENC OpenMathEncoding>>=
-)abbrev domain OMENC OpenMathEncoding
-++ Author: Vilya Harvey
-++ Date Created:
-++ Date Last Updated:
-++ Basic Functions: 
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description:
-++ \spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.
-OpenMathEncoding(): SetCategory with
-  OMencodingUnknown : () -> %
-  ++ OMencodingUnknown() is the constant for unknown encoding types. If this 
-  ++ is used on an input device, the encoding will be autodetected.
-  ++ It is invalid to use it on an output device.
-  OMencodingXML     : () -> %
-  ++ OMencodingXML() is the constant for the OpenMath XML encoding.
-  OMencodingSGML    : () -> %
-  ++ OMencodingSGML() is the constant for the deprecated OpenMath SGML encoding.
-  OMencodingBinary  : () -> %
-  ++ OMencodingBinary() is the constant for the OpenMath binary encoding.
- == add
-  Rep := SingleInteger
-
-  =(u,v) == (u=v)$Rep
-
-  import Rep
-
-  coerce(u) ==
-    u::Rep = 0$Rep => "Unknown"::OutputForm
-    u::Rep = 1$Rep => "Binary"::OutputForm
-    u::Rep = 2::Rep => "XML"::OutputForm
-    u::Rep = 3::Rep => "SGML"::OutputForm
-    error "Bogus OpenMath Encoding Type"
-
-  OMencodingUnknown(): % == 0::Rep
-  OMencodingBinary(): % == 1::Rep
-  OMencodingXML(): % == 2::Rep
-  OMencodingSGML(): % == 3::Rep
-
-@
-\section{domain OMDEV OpenMathDevice}
-<<domain OMDEV OpenMathDevice>>=
-import Void
-import String
-import Integer
-import DoubleFloat
-import String
-import Symbol
-import OpenMathEncoding
-)abbrev domain OMDEV OpenMathDevice
-++ Author: Vilya Harvey
-++ Date Created:
-++ Date Last Updated:
-++ Basic Functions:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description: \spadtype{OpenMathDevice} provides support for reading
-++ and writing openMath objects to files, strings etc.  It also provides
-++ access to low-level operations from within the interpreter.
-
-
-OpenMathDevice(): with
-  OMopenFile    : (String, String, OpenMathEncoding) -> %
-  ++ OMopenFile(f,mode,enc) opens file \axiom{f} for reading or writing
-  ++ OpenMath objects (depending on \axiom{mode} which can be "r", "w"
-  ++ or "a" for read, write and append respectively), in the encoding
-  ++ \axiom{enc}.
-  OMopenString  : (String, OpenMathEncoding) -> %
-  ++ OMopenString(s,mode) opens the string \axiom{s} for reading or writing 
-  ++ OpenMath objects in encoding \axiom{enc}.
-  OMclose       : % -> Void
-  ++ OMclose(dev) closes \axiom{dev}, flushing output if necessary.
-  OMsetEncoding : (%, OpenMathEncoding) -> Void
-  ++ OMsetEncoding(dev,enc) sets the encoding used for reading or writing
-  ++ OpenMath objects to or from \axiom{dev} to \axiom{enc}.
-  OMputApp      : % -> Void
-  ++ OMputApp(dev) writes a begin application token to \axiom{dev}.
-  OMputAtp      : % -> Void
-  ++ OMputAtp(dev) writes a begin attribute pair token to \axiom{dev}.
-  OMputAttr     : % -> Void
-  ++ OMputAttr(dev) writes a begin attribute token to \axiom{dev}.
-  OMputBind     : % -> Void
-  ++ OMputBind(dev) writes a begin binder token to \axiom{dev}.
-  OMputBVar     : % -> Void
-  ++ OMputBVar(dev) writes a begin bound variable list token to \axiom{dev}.
-  OMputError    : % -> Void
-  ++ OMputError(dev) writes a begin error token to \axiom{dev}.
-  OMputObject   : % -> Void
-  ++ OMputObject(dev) writes a begin object token to \axiom{dev}.
-  OMputEndApp   : % -> Void
-  ++ OMputEndApp(dev) writes an end application token to \axiom{dev}.
-  OMputEndAtp   : % -> Void
-  ++ OMputEndAtp(dev) writes an end attribute pair token to \axiom{dev}.
-  OMputEndAttr  : % -> Void
-  ++ OMputEndAttr(dev) writes an end attribute token to \axiom{dev}.
-  OMputEndBind  : % -> Void
-  ++ OMputEndBind(dev) writes an end binder token to \axiom{dev}.
-  OMputEndBVar  : % -> Void
-  ++ OMputEndBVar(dev) writes an end bound variable list token to \axiom{dev}.
-  OMputEndError : % -> Void
-  ++ OMputEndError(dev) writes an end error token to \axiom{dev}.
-  OMputEndObject: % -> Void
-  ++ OMputEndObject(dev) writes an end object token to \axiom{dev}.
-  OMputInteger  : (%, Integer) -> Void
-  ++ OMputInteger(dev,i) writes the integer \axiom{i} to \axiom{dev}.
-  OMputFloat    : (%, DoubleFloat) -> Void
-  ++ OMputFloat(dev,i) writes the float \axiom{i} to \axiom{dev}.
-  OMputVariable : (%, Symbol) -> Void
-  ++ OMputVariable(dev,i) writes the variable \axiom{i} to \axiom{dev}.
-  OMputString   : (%, String) -> Void
-  ++ OMputString(dev,i) writes the string \axiom{i} to \axiom{dev}.
-  OMputSymbol   : (%, String, String) -> Void
-  ++ OMputSymbol(dev,cd,s) writes the symbol \axiom{s} from CD \axiom{cd}
-  ++ to \axiom{dev}.
-
-  OMgetApp      : % -> Void
-  ++ OMgetApp(dev) reads a begin application token from \axiom{dev}.
-  OMgetAtp      : % -> Void
-  ++ OMgetAtp(dev) reads a begin attribute pair token from \axiom{dev}.
-  OMgetAttr     : % -> Void
-  ++ OMgetAttr(dev) reads a begin attribute token from \axiom{dev}.
-  OMgetBind     : % -> Void
-  ++ OMgetBind(dev) reads a begin binder token from \axiom{dev}.
-  OMgetBVar     : % -> Void
-  ++ OMgetBVar(dev) reads a begin bound variable list token from \axiom{dev}.
-  OMgetError    : % -> Void
-  ++ OMgetError(dev) reads a begin error token from \axiom{dev}.
-  OMgetObject   : % -> Void
-  ++ OMgetObject(dev) reads a begin object token from \axiom{dev}.
-  OMgetEndApp   : % -> Void
-  ++ OMgetEndApp(dev) reads an end application token from \axiom{dev}.
-  OMgetEndAtp   : % -> Void
-  ++ OMgetEndAtp(dev) reads an end attribute pair token from \axiom{dev}.
-  OMgetEndAttr  : % -> Void
-  ++ OMgetEndAttr(dev) reads an end attribute token from \axiom{dev}.
-  OMgetEndBind  : % -> Void
-  ++ OMgetEndBind(dev) reads an end binder token from \axiom{dev}.
-  OMgetEndBVar  : % -> Void
-  ++ OMgetEndBVar(dev) reads an end bound variable list token from \axiom{dev}.
-  OMgetEndError : % -> Void
-  ++ OMgetEndError(dev) reads an end error token from \axiom{dev}.
-  OMgetEndObject: % -> Void
-  ++ OMgetEndObject(dev) reads an end object token from \axiom{dev}.
-  OMgetInteger  : % -> Integer
-  ++ OMgetInteger(dev) reads an integer from \axiom{dev}.
-  OMgetFloat    : % -> DoubleFloat
-  ++ OMgetFloat(dev) reads a float from \axiom{dev}.
-  OMgetVariable : % -> Symbol
-  ++ OMgetVariable(dev) reads a variable from \axiom{dev}.
-  OMgetString   : % -> String
-  ++ OMgetString(dev) reads a string from \axiom{dev}.
-  OMgetSymbol   : % -> Record(cd:String, name:String)
-  ++ OMgetSymbol(dev) reads a symbol from \axiom{dev}.
-
-  OMgetType     : % -> Symbol
-  ++ OMgetType(dev) returns the type of the next object on \axiom{dev}.
- == add
-  OMopenFile(fname: String, fmode: String, enc: OpenMathEncoding): % ==
-    OM_-OPENFILEDEV(fname, fmode, enc)$Lisp
-  OMopenString(str: String, enc: OpenMathEncoding): % ==
-    OM_-OPENSTRINGDEV(str, enc)$Lisp
-  OMclose(dev: %): Void ==
-    OM_-CLOSEDEV(dev)$Lisp
-  OMsetEncoding(dev: %, enc: OpenMathEncoding): Void ==
-    OM_-SETDEVENCODING(dev, enc)$Lisp
-
-  OMputApp(dev: %): Void == OM_-PUTAPP(dev)$Lisp
-  OMputAtp(dev: %): Void == OM_-PUTATP(dev)$Lisp
-  OMputAttr(dev: %): Void == OM_-PUTATTR(dev)$Lisp
-  OMputBind(dev: %): Void == OM_-PUTBIND(dev)$Lisp
-  OMputBVar(dev: %): Void == OM_-PUTBVAR(dev)$Lisp
-  OMputError(dev: %): Void == OM_-PUTERROR(dev)$Lisp
-  OMputObject(dev: %): Void == OM_-PUTOBJECT(dev)$Lisp
-  OMputEndApp(dev: %): Void == OM_-PUTENDAPP(dev)$Lisp
-  OMputEndAtp(dev: %): Void == OM_-PUTENDATP(dev)$Lisp
-  OMputEndAttr(dev: %): Void == OM_-PUTENDATTR(dev)$Lisp
-  OMputEndBind(dev: %): Void == OM_-PUTENDBIND(dev)$Lisp
-  OMputEndBVar(dev: %): Void == OM_-PUTENDBVAR(dev)$Lisp
-  OMputEndError(dev: %): Void == OM_-PUTENDERROR(dev)$Lisp
-  OMputEndObject(dev: %): Void == OM_-PUTENDOBJECT(dev)$Lisp
-  OMputInteger(dev: %, i: Integer): Void == OM_-PUTINT(dev, i)$Lisp
-  OMputFloat(dev: %, f: DoubleFloat): Void == OM_-PUTFLOAT(dev, f)$Lisp
-  --OMputByteArray(dev: %, b: Array Byte): Void == OM_-PUTBYTEARRAY(dev, b)$Lisp
-  OMputVariable(dev: %, v: Symbol): Void == OM_-PUTVAR(dev, v)$Lisp
-  OMputString(dev: %, s: String): Void == OM_-PUTSTRING(dev, s)$Lisp
-  OMputSymbol(dev: %, cd: String, nm: String): Void == OM_-PUTSYMBOL(dev, cd, nm)$Lisp
-
-  OMgetApp(dev: %): Void == OM_-GETAPP(dev)$Lisp
-  OMgetAtp(dev: %): Void == OM_-GETATP(dev)$Lisp
-  OMgetAttr(dev: %): Void == OM_-GETATTR(dev)$Lisp
-  OMgetBind(dev: %): Void == OM_-GETBIND(dev)$Lisp
-  OMgetBVar(dev: %): Void == OM_-GETBVAR(dev)$Lisp
-  OMgetError(dev: %): Void == OM_-GETERROR(dev)$Lisp
-  OMgetObject(dev: %): Void == OM_-GETOBJECT(dev)$Lisp
-  OMgetEndApp(dev: %): Void == OM_-GETENDAPP(dev)$Lisp
-  OMgetEndAtp(dev: %): Void == OM_-GETENDATP(dev)$Lisp
-  OMgetEndAttr(dev: %): Void == OM_-GETENDATTR(dev)$Lisp
-  OMgetEndBind(dev: %): Void == OM_-GETENDBIND(dev)$Lisp
-  OMgetEndBVar(dev: %): Void == OM_-GETENDBVAR(dev)$Lisp
-  OMgetEndError(dev: %): Void == OM_-GETENDERROR(dev)$Lisp
-  OMgetEndObject(dev: %): Void == OM_-GETENDOBJECT(dev)$Lisp
-  OMgetInteger(dev: %): Integer == OM_-GETINT(dev)$Lisp
-  OMgetFloat(dev: %): DoubleFloat == OM_-GETFLOAT(dev)$Lisp
-  --OMgetByteArray(dev: %): Array Byte == OM_-GETBYTEARRAY(dev)$Lisp
-  OMgetVariable(dev: %): Symbol == OM_-GETVAR(dev)$Lisp
-  OMgetString(dev: %): String == OM_-GETSTRING(dev)$Lisp
-  OMgetSymbol(dev: %): Record(cd:String, name:String) == OM_-GETSYMBOL(dev)$Lisp
-
-  OMgetType(dev: %): Symbol == OM_-GETTYPE(dev)$Lisp
-
-@
-\section{domain OMCONN OpenMathConnection}
-<<domain OMCONN OpenMathConnection>>=
-import Void
-import Boolean
-import SingleInteger
-import String
-import OpenMathDevice
-)abbrev domain OMCONN OpenMathConnection
-++ Author: Vilya Harvey
-++ Date Created:
-++ Date Last Updated:
-++ Basic Functions:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description: \spadtype{OpenMathConnection} provides low-level functions
-++ for handling connections to and from \spadtype{OpenMathDevice}s.
-
-
-OpenMathConnection(): with
-  OMmakeConn    : SingleInteger -> % ++ \spad{OMmakeConn}
-  OMcloseConn   : % -> Void ++ \spad{OMcloseConn}
-  OMconnInDevice: %-> OpenMathDevice ++ \spad{OMconnInDevice:}
-  OMconnOutDevice: %-> OpenMathDevice ++ \spad{OMconnOutDevice:}
-  OMconnectTCP  : (%, String, SingleInteger) -> Boolean ++ \spad{OMconnectTCP}
-  OMbindTCP     : (%, SingleInteger) -> Boolean ++ \spad{OMbindTCP}
- == add
-  OMmakeConn(timeout: SingleInteger): % == OM_-MAKECONN(timeout)$Lisp
-  OMcloseConn(conn: %): Void == OM_-CLOSECONN(conn)$Lisp
-
-  OMconnInDevice(conn: %): OpenMathDevice ==
-    OM_-GETCONNINDEV(conn)$Lisp
-  OMconnOutDevice(conn: %): OpenMathDevice ==
-    OM_-GETCONNOUTDEV(conn)$Lisp
-
-  OMconnectTCP(conn: %, host: String, port: SingleInteger): Boolean ==
-    OM_-CONNECTTCP(conn, host, port)$Lisp
-  OMbindTCP(conn: %, port: SingleInteger): Boolean ==
-    OM_-BINDTCP(conn, port)$Lisp
-
-@
-\section{package OMPKG OpenMathPackage}
-<<package OMPKG OpenMathPackage>>=
-)abbrev package OMPKG OpenMathPackage
-++ Author: Vilya Harvey
-++ Date Created:
-++ Date Last Updated:
-++ Basic Functions:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description: \spadtype{OpenMathPackage} provides some simple utilities 
-++ to make reading OpenMath objects easier.
-
-OpenMathPackage(): with
-  OMread            : OpenMathDevice -> Any
-  ++ OMread(dev) reads an OpenMath object from \axiom{dev} and passes it
-  ++ to AXIOM.
-  OMreadFile        : String -> Any
-  ++ OMreadFile(f) reads an OpenMath object from \axiom{f} and passes it
-  ++ to AXIOM.
-  OMreadStr         : String -> Any
-  ++ OMreadStr(f) reads an OpenMath object from \axiom{f} and passes it
-  ++ to AXIOM.
-  OMlistCDs         : () -> List(String)
-  ++ OMlistCDs() lists all the CDs supported by AXIOM.
-  OMlistSymbols     : String -> List(String)
-  ++ OMlistSymbols(cd) lists all the symbols in \axiom{cd}.
-  OMsupportsCD?      : String -> Boolean
-  ++ OMsupportsCD?(cd) returns true if AXIOM supports \axiom{cd}, false 
-  ++ otherwise.
-  OMsupportsSymbol? : (String, String) -> Boolean
-  ++ OMsupportsSymbol?(s,cd) returns true if AXIOM supports symbol \axiom{s}
-  ++ from CD \axiom{cd}, false otherwise.
-  OMunhandledSymbol : (String, String) -> Exit
-  ++ OMunhandledSymbol(s,cd) raises an error if AXIOM reads a symbol which it
-  ++ is unable to handle.  Note that this is different from an unexpected
-  ++ symbol.
- == add
-  import OpenMathEncoding
-  import OpenMathDevice
-  import String
-
-  OMunhandledSymbol(u,v) ==
-    error concat ["AXIOM is unable to process the symbol ",u," from CD ",v,"."]
-
-  OMread(dev: OpenMathDevice): Any ==
-    interpret(OM_-READ(dev)$Lisp :: InputForm)
-
-  OMreadFile(filename: String): Any ==
-    dev := OMopenFile(filename, "r", OMencodingUnknown())
-    res: Any := interpret(OM_-READ(dev)$Lisp :: InputForm)
-    OMclose(dev)
-    res
-
-  OMreadStr(str: String): Any ==
-    strp := OM_-STRINGTOSTRINGPTR(str)$Lisp
-    dev := OMopenString(strp pretend String, OMencodingUnknown())
-    res: Any := interpret(OM_-READ(dev)$Lisp :: InputForm)
-    OMclose(dev)
-    res
-
-  OMlistCDs(): List(String) ==
-    OM_-LISTCDS()$Lisp pretend List(String)
-
-  OMlistSymbols(cd: String): List(String) ==
-    OM_-LISTSYMBOLS(cd)$Lisp pretend List(String)
-
-  import SExpression
-
-  OMsupportsCD?(cd: String): Boolean ==
-    not null? OM_-SUPPORTSCD(cd)$Lisp 
-
-  OMsupportsSymbol?(cd: String, name: String): Boolean ==
-    not null? OM_-SUPPORTSSYMBOL(cd, name)$Lisp
-
-@
-\section{License}
-<<license>>=
---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
---All rights reserved.
---
---Redistribution and use in source and binary forms, with or without
---modification, are permitted provided that the following conditions are
---met:
---
---    - Redistributions of source code must retain the above copyright
---      notice, this list of conditions and the following disclaimer.
---
---    - Redistributions in binary form must reproduce the above copyright
---      notice, this list of conditions and the following disclaimer in
---      the documentation and/or other materials provided with the
---      distribution.
---
---    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
---      names of its contributors may be used to endorse or promote products
---      derived from this software without specific prior written permission.
---
---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-@
-<<*>>=
-<<license>>
-
-<<domain OMENC OpenMathEncoding>>
-<<domain OMDEV OpenMathDevice>>
-<<domain OMCONN OpenMathConnection>>
-<<package OMPKG OpenMathPackage>>
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}
diff --git a/src/algebra/omerror.spad.pamphlet b/src/algebra/omerror.spad.pamphlet
deleted file mode 100644
index 50843010..00000000
--- a/src/algebra/omerror.spad.pamphlet
+++ /dev/null
@@ -1,150 +0,0 @@
-\documentclass{article}
-\usepackage{open-axiom}
-\begin{document}
-\title{\$SPAD/src/algebra omerror.spad}
-\author{Vilya Harvey}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{domain OMERRK OpenMathErrorKind}
-<<domain OMERRK OpenMathErrorKind>>=
-)abbrev domain OMERRK OpenMathErrorKind
-++ Author: Vilya Harvey
-++ Date Created:
-++ Date Last Updated:
-++ Basic Functions:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description: \spadtype{OpenMathErrorKind} represents different kinds
-++ of OpenMath errors: specifically parse errors, unknown CD or symbol 
-++ errors, and read errors.
-OpenMathErrorKind() : SetCategory with
-  coerce           : Symbol -> %
-  ++ coerce(u) creates an OpenMath error object of an appropriate type if
-  ++ \axiom{u} is one of \axiom{OMParseError}, \axiom{OMReadError},
-  ++ \axiom{OMUnknownCD} or \axiom{OMUnknownSymbol}, otherwise it
-  ++ raises a runtime error.
-  OMParseError?    : % -> Boolean
-  ++ OMParseError?(u) tests whether u is an OpenMath parsing error.
-  OMUnknownCD?     : % -> Boolean
-  ++ OMUnknownCD?(u) tests whether u is an OpenMath unknown CD error.
-  OMUnknownSymbol? : % -> Boolean
-  ++ OMUnknownSymbol?(u) tests whether u is an OpenMath unknown symbol error.
-  OMReadError?     : % -> Boolean
-  ++ OMReadError?(u) tests whether u is an OpenMath read error.
- == add
-  Rep := Union(parseError:"OMParseError", unknownCD:"OMUnknownCD", 
-               unknownSymbol:"OMUnknownSymbol",readError:"OMReadError")
-
-  OMParseError?(u) == (u case parseError)$Rep
-  OMUnknownCD?(u) == (u case unknownCD)$Rep
-  OMUnknownSymbol?(u) == (u case unknownSymbol)$Rep
-  OMReadError?(u) == (u case readError)$Rep
-
-  coerce(s:Symbol):% == 
-    s = OMParseError    => ["OMParseError"]$Rep
-    s = OMUnknownCD     => ["OMUnknownCD"]$Rep
-    s = OMUnknownSymbol => ["OMUnknownSymbol"]$Rep
-    s = OMReadError     => ["OMReadError"]$Rep
-    error concat(string s, " is not a valid OpenMathErrorKind.")
-
-  a = b == (a=b)$Rep
-
-  coerce(e:%):OutputForm == coerce(e)$Rep
-
-@
-\section{domain OMERR OpenMathError}
-<<domain OMERR OpenMathError>>=
-)abbrev domain OMERR OpenMathError
-++ Author: Vilya Harvey
-++ Date Created:
-++ Date Last Updated:
-++ Basic Functions:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description: \spadtype{OpenMathError} is the domain of OpenMath errors.
-OpenMathError() : SetCategory with
-  errorKind : % -> OpenMathErrorKind
-  ++ errorKind(u) returns the type of error which u represents.
-  errorInfo : % -> List Symbol
-  ++ errorInfo(u) returns information about the error u.
-  omError   : (OpenMathErrorKind, List Symbol) -> % 
-  ++ omError(k,l) creates an instance of OpenMathError.
- == add
-  Rep := Record(err:OpenMathErrorKind, info:List Symbol)
-
-  import List String
-
-  coerce(e:%):OutputForm ==
-    OMParseError? e.err => message "Error parsing OpenMath object"
-    infoSize := #(e.info)
-    OMUnknownCD? e.err => 
-      not one? infoSize => error "Malformed info list in OMUnknownCD"
-      message concat("Cannot handle CD ",string first e.info)
-    OMUnknownSymbol? e.err =>
-      not 2=infoSize => error "Malformed info list in OMUnknownSymbol"
-      message concat ["Cannot handle Symbol ",
-                      string e.info.2, " from CD ", string e.info.1]
-    OMReadError? e.err =>
-      message "OpenMath read error"
-    error "Malformed OpenMath Error"
-
-  omError(e:OpenMathErrorKind,i:List Symbol):% == [e,i]$Rep
-
-  errorKind(e:%):OpenMathErrorKind == e.err
-  errorInfo(e:%):List Symbol == e.info
-
-@
-\section{License}
-<<license>>=
---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
---All rights reserved.
---
---Redistribution and use in source and binary forms, with or without
---modification, are permitted provided that the following conditions are
---met:
---
---    - Redistributions of source code must retain the above copyright
---      notice, this list of conditions and the following disclaimer.
---
---    - Redistributions in binary form must reproduce the above copyright
---      notice, this list of conditions and the following disclaimer in
---      the documentation and/or other materials provided with the
---      distribution.
---
---    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
---      names of its contributors may be used to endorse or promote products
---      derived from this software without specific prior written permission.
---
---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-@
-<<*>>=
-<<license>>
-
-<<domain OMERRK OpenMathErrorKind>>
-<<domain OMERR OpenMathError>>
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}
diff --git a/src/algebra/omserver.spad.pamphlet b/src/algebra/omserver.spad.pamphlet
deleted file mode 100644
index cd09ad27..00000000
--- a/src/algebra/omserver.spad.pamphlet
+++ /dev/null
@@ -1,122 +0,0 @@
-\documentclass{article}
-\usepackage{open-axiom}
-\begin{document}
-\title{\$SPAD/src/algebra omserver.spad}
-\author{Vilya Harvey}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{package OMSERVER OpenMathServerPackage}
-<<package OMSERVER OpenMathServerPackage>>=
-)abbrev package OMSERVER OpenMathServerPackage
-++ Author: Vilya Harvey
-++ Date Created:
-++ Date Last Updated:
-++ Basic Functions:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description: \spadtype{OpenMathServerPackage} provides the necessary
-++ operations to run AXIOM as an OpenMath server, reading/writing objects
-++ to/from a port.  Please note the facilities available here are very basic.
-++ The idea is that a user calls e.g. \axiom{Omserve(4000,60)} and then
-++ another process sends OpenMath objects to port 4000 and reads the result.
-
-OpenMathServerPackage(): with
-  OMreceive : OpenMathConnection -> Any
-  ++ OMreceive(c) reads an OpenMath object from connection \axiom{c} and
-  ++ returns the appropriate AXIOM object.
-  OMsend    : (OpenMathConnection, Any) -> Void
-  ++ OMsend(c,u) attempts to output \axiom{u} on \aciom{c} in OpenMath.
-  OMserve   : (SingleInteger, SingleInteger) -> Void
-  ++ OMserve(portnum,timeout) puts AXIOM into server mode on port number
-  ++ \axiom{portnum}.  The parameter \axiom{timeout} specifies the timeout
-  ++ period for the connection.
- == add
-  import OpenMathDevice
-  import OpenMathConnection
-  import OpenMathPackage
-  import OpenMath
-
-
-
-  OMreceive(conn: OpenMathConnection): Any ==
-    dev: OpenMathDevice := OMconnInDevice(conn)
-    OMsetEncoding(dev, OMencodingUnknown());
-    OMread(dev)
-
-  OMsend(conn: OpenMathConnection, value: Any): Void ==
-    dev: OpenMathDevice := OMconnOutDevice(conn)
-    OMsetEncoding(dev, OMencodingXML());
-    --retractable?(value)$AnyFunctions1(Expression Integer) =>
-    --  OMwrite(dev, retract(value)$AnyFunctions1(Expression Integer), true)
-    retractable?(value)$AnyFunctions1(Integer) =>
-      OMwrite(dev, retract(value)$AnyFunctions1(Integer), true)
-    retractable?(value)$AnyFunctions1(Float) =>
-      OMwrite(dev, retract(value)$AnyFunctions1(Float), true)
-    retractable?(value)$AnyFunctions1(SingleInteger) =>
-      OMwrite(dev, retract(value)$AnyFunctions1(SingleInteger), true)
-    retractable?(value)$AnyFunctions1(DoubleFloat) =>
-      OMwrite(dev, retract(value)$AnyFunctions1(DoubleFloat), true)
-    retractable?(value)$AnyFunctions1(String) =>
-      OMwrite(dev, retract(value)$AnyFunctions1(String), true)
-
-  OMserve(portNum: SingleInteger, timeout: SingleInteger): Void ==
-    conn: OpenMathConnection := OMmakeConn(timeout)
-    OMbindTCP(conn, portNum)
-    val: Any
-    while true repeat
-      val := OMreceive(conn)
-      OMsend(conn, val)
-
-@
-\section{License}
-<<license>>=
---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
---All rights reserved.
--- Copyright (C) 2007-2010, Gabriel Dos Reis.
--- All rights reserved.
---
---Redistribution and use in source and binary forms, with or without
---modification, are permitted provided that the following conditions are
---met:
---
---    - Redistributions of source code must retain the above copyright
---      notice, this list of conditions and the following disclaimer.
---
---    - Redistributions in binary form must reproduce the above copyright
---      notice, this list of conditions and the following disclaimer in
---      the documentation and/or other materials provided with the
---      distribution.
---
---    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
---      names of its contributors may be used to endorse or promote products
---      derived from this software without specific prior written permission.
---
---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-@
-<<*>>=
-<<license>>
-
-<<package OMSERVER OpenMathServerPackage>>
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}
diff --git a/src/algebra/openmath.spad.pamphlet b/src/algebra/openmath.spad.pamphlet
index 24a53ae4..e69de29b 100644
--- a/src/algebra/openmath.spad.pamphlet
+++ b/src/algebra/openmath.spad.pamphlet
@@ -1,331 +0,0 @@
-\documentclass{article}
-\usepackage{open-axiom}
-\begin{document}
-\title{\$SPAD/src/algebra openmath.spad}
-\author{Mike Dewar, Vilya Harvey}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{package OMEXPR ExpressionToOpenMath}
-<<package OMEXPR ExpressionToOpenMath>>=
-)abbrev package OMEXPR ExpressionToOpenMath
-++ Author: Mike Dewar & Vilya Harvey
-++ Date Created:
-++ Date Last Updated:
-++ Basic Functions:
-++ Related Constructors:
-++ Also See:
-++ AMS Classifications:
-++ Keywords:
-++ References:
-++ Description: \spadtype{ExpressionToOpenMath} provides support for
-++ converting objects of type \spadtype{Expression} into OpenMath.
-ExpressionToOpenMath(R: Join(OpenMath, Ring)): with
-  OMwrite  : Expression R -> String
-  OMwrite  : (Expression R, Boolean) -> String
-  OMwrite  : (OpenMathDevice, Expression R) -> Void
-  OMwrite  : (OpenMathDevice, Expression R, Boolean) -> Void
- == add
-  import Expression R
-  SymInfo ==> Record(cd:String, name:String)
-  import SymInfo
-  import Record(key: Symbol, entry: SymInfo)
-  import AssociationList(Symbol, SymInfo)
-  import OMENC
-
-  ----------------------------
-  -- Local translation tables.
-  ----------------------------
-
-  nullaryFunctionAList : AssociationList(Symbol, SymInfo) := construct [_
-    [pi, ["nums1", "pi"]] ]
-
-  unaryFunctionAList : AssociationList(Symbol, SymInfo) := construct [_
-    [exp,  ["transc1", "exp"]],_
-    [log,  ["transc1", "ln"]],_
-    [sin,  ["transc1", "sin"]],_
-    [cos,  ["transc1", "cos"]],_
-    [tan,  ["transc1", "tan"]],_
-    [cot,  ["transc1", "cot"]],_
-    [sec,  ["transc1", "sec"]],_
-    [csc,  ["transc1", "csc"]],_
-    [asin, ["transc1", "arcsin"]],_
-    [acos, ["transc1", "arccos"]],_
-    [atan, ["transc1", "arctan"]],_
-    [acot, ["transc1", "arccot"]],_
-    [asec, ["transc1", "arcsec"]],_
-    [acsc, ["transc1", "arccsc"]],_
-    [sinh, ["transc1", "sinh"]],_
-    [cosh, ["transc1", "cosh"]],_
-    [tanh, ["transc1", "tanh"]],_
-    [coth, ["transc1", "coth"]],_
-    [sech, ["transc1", "sech"]],_
-    [csch, ["transc1", "csch"]],_
-    [asinh, ["transc1", "arcsinh"]],_
-    [acosh, ["transc1", "arccosh"]],_
-    [atanh, ["transc1", "arctanh"]],_
-    [acoth, ["transc1", "arccoth"]],_
-    [asech, ["transc1", "arcsech"]],_
-    [acsch, ["transc1", "arccsch"]],_
-    [factorial, ["integer1", "factorial"]],_
-    [abs, ["arith1", "abs"]] ]
-
-    -- Still need the following unary functions:
-    --  digamma
-    --  Gamma
-    --  airyAi
-    --  airyBi
-    --  erf
-    --  Ei
-    --  Si
-    --  Ci
-    --  li
-    --  dilog
-
-    -- Still need the following binary functions:
-    --      Gamma(a, x)
-    --      Beta(x,y) 
-    --      polygamma(k,x)
-    --      besselJ(v,x)
-    --      besselY(v,x)
-    --      besselI(v,x)
-    --      besselK(v,x)
-    --      permutation(n, m)
-    --      summation(x:%, n:Symbol) : as opposed to "definite" sum
-    --      product(x:%, n:Symbol)   : ditto
-
-  ------------------------
-  -- Forward declarations.
-  ------------------------
-
-  outputOMExpr  : (OpenMathDevice, Expression R) -> Void
-
-  -------------------------
-  -- Local helper functions
-  -------------------------
-
-  outputOMArith1(dev: OpenMathDevice, sym: String, args: List Expression R): Void ==
-    OMputApp(dev)
-    OMputSymbol(dev, "arith1", sym)
-    for arg in args repeat
-      OMwrite(dev, arg, false)
-    OMputEndApp(dev)
-
-  outputOMLambda(dev: OpenMathDevice, ex: Expression R, var: Expression R): Void ==
-    OMputBind(dev)
-    OMputSymbol(dev, "fns1", "lambda")
-    OMputBVar(dev)
-    OMwrite(dev, var, false)
-    OMputEndBVar(dev)
-    OMwrite(dev, ex, false)
-    OMputEndBind(dev)
-
-  outputOMInterval(dev: OpenMathDevice, lo: Expression R, hi: Expression R): Void ==
-    OMputApp(dev)
-    OMputSymbol(dev, "interval1", "interval")
-    OMwrite(dev, lo, false)
-    OMwrite(dev, hi, false)
-    OMputEndApp(dev)
-
-  outputOMIntInterval(dev: OpenMathDevice, lo: Expression R, hi: Expression R): Void ==
-    OMputApp(dev)
-    OMputSymbol(dev, "interval1", "integer__interval")
-    OMwrite(dev, lo, false)
-    OMwrite(dev, hi, false)
-    OMputEndApp(dev)
-
-  outputOMBinomial(dev: OpenMathDevice, args: List Expression R): Void ==
-    not #args=2 => error "Wrong number of arguments to binomial"
-    OMputApp(dev)
-    OMputSymbol(dev, "combinat1", "binomial")
-    for arg in args repeat
-      OMwrite(dev, arg, false)
-    OMputEndApp(dev)
-
-  outputOMPower(dev: OpenMathDevice, args: List Expression R): Void ==
-    not #args=2 => error "Wrong number of arguments to power"
-    outputOMArith1(dev, "power", args)
-
-  outputOMDefsum(dev: OpenMathDevice, args: List Expression R): Void ==
-    #args ~= 5 => error "Unexpected number of arguments to a defsum"
-    OMputApp(dev)
-    OMputSymbol(dev, "arith1", "sum")
-    outputOMIntInterval(dev, args.4, args.5)
-    outputOMLambda(dev, eval(args.1, args.2, args.3), args.3)
-    OMputEndApp(dev)
-
-  outputOMDefprod(dev: OpenMathDevice, args: List Expression R): Void ==
-    #args ~= 5 => error "Unexpected number of arguments to a defprod"
-    OMputApp(dev)
-    OMputSymbol(dev, "arith1", "product")
-    outputOMIntInterval(dev, args.4, args.5)
-    outputOMLambda(dev, eval(args.1, args.2, args.3), args.3)
-    OMputEndApp(dev)
-
-  outputOMDefint(dev: OpenMathDevice, args: List Expression R): Void ==
-    #args ~= 5 => error "Unexpected number of arguments to a defint"
-    OMputApp(dev)
-    OMputSymbol(dev, "calculus1", "defint")
-    outputOMInterval(dev, args.4, args.5)
-    outputOMLambda(dev, eval(args.1, args.2, args.3), args.3)
-    OMputEndApp(dev)
-
-  outputOMInt(dev: OpenMathDevice, args: List Expression R): Void ==
-    #args ~= 3 => error "Unexpected number of arguments to a defint"
-    OMputApp(dev)
-    OMputSymbol(dev, "calculus1", "int")
-    outputOMLambda(dev, eval(args.1, args.2, args.3), args.3)
-    OMputEndApp(dev)
-
-  outputOMFunction(dev: OpenMathDevice, op: Symbol, args: List Expression R): Void ==
-    nargs := #args
-    zero? nargs =>
-      omOp: Union(SymInfo, "failed") := search(op, nullaryFunctionAList)
-      omOp case "failed" =>
-        msg := concat ["No OpenMath definition for nullary function ", string op]
-        error msg
-      OMputSymbol(dev, omOp.cd, omOp.name)
-    one? nargs =>
-      omOp: Union(SymInfo, "failed") := search(op, unaryFunctionAList)
-      omOp case "failed" =>
-        msg := concat ["No OpenMath definition for unary function ", string op]
-        error msg
-      OMputApp(dev)
-      OMputSymbol(dev, omOp.cd, omOp.name)
-      for arg in args repeat
-        OMwrite(dev, arg, false)
-      OMputEndApp(dev)
-    -- Most of the binary operators cannot be handled trivialy like the
-    -- unary ones since they have bound variables of one kind or another.
-    -- The special functions should be straightforward, but we don't have
-    -- a CD for them yet :-)
-    op = %defint  => outputOMDefint(dev, args)
-    op = integral => outputOMInt(dev, args)
-    op = %defsum  => outputOMDefsum(dev, args)
-    op = %defprod => outputOMDefprod(dev, args)
-    op = %power   => outputOMPower(dev, args)
-    op = binomial => outputOMBinomial(dev, args)
-    msg := concat ["No OpenMath definition for function ", string op]
-    error msg
- 
-  outputOMExpr(dev: OpenMathDevice, ex: Expression R): Void ==
-    ground? ex => OMwrite(dev, ground ex, false)
-    not((v := retractIfCan(ex)@Union(Symbol,"failed")) case "failed") =>
-      OMputVariable(dev, v)
-    not((w := isPlus ex) case "failed") => outputOMArith1(dev, "plus", w)
-    not((w := isTimes ex) case "failed") => outputOMArith1(dev, "times", w)
-    --not((y := isMult ex) case "failed") =>
-    --  outputOMArith("times", [OMwrite(y.coef)$Integer,
-    --          OMwrite(coerce y.var)])
-    -- At the time of writing we don't need both isExpt and isPower
-    -- here but they may be relevent when we integrate this stuff into
-    -- the main Expression code.  Note that if we don't check that
-    -- the exponent is non-trivial we get thrown into an infinite recursion.
-    not (((x := isExpt ex) case "failed") or one? x.exponent) =>
-      not((s := symbolIfCan(x.var)@Union(Symbol,"failed")) case "failed") =>
-        --outputOMPower(dev, [s::Expression(R), (x.exponent)::Expression(R)])
-        OMputApp(dev)
-        OMputSymbol(dev, "arith1", "power")
-        OMputVariable(dev, s)
-        OMputInteger(dev, x.exponent)
-        OMputEndApp(dev)
-      -- TODO: add error handling code here...
-    not (((z := isPower ex) case "failed") or one? z.exponent) =>
-      outputOMPower(dev, [ z.val, z.exponent::Expression R ])
-      --OMputApp(dev)
-      --OMputSymbol(dev, "arith1", "power")
-      --outputOMExpr(dev, z.val)
-      --OMputInteger(dev, z.exponent)
-      --OMputEndApp(dev)
-    -- Must only be one top-level Kernel by this point
-    k : Kernel Expression R := first kernels ex
-    outputOMFunction(dev, name operator k, argument k)
-
-
-  ----------
-  -- Exports
-  ----------
-
-  OMwrite(ex: Expression R): String ==
-    s: String := ""
-    sp := OM_-STRINGTOSTRINGPTR(s)$Lisp
-    dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML())
-    OMputObject(dev)
-    outputOMExpr(dev, ex)
-    OMputEndObject(dev)
-    OMclose(dev)
-    s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String
-    s
-
-  OMwrite(ex: Expression R, wholeObj: Boolean): String ==
-    s: String := ""
-    sp := OM_-STRINGTOSTRINGPTR(s)$Lisp
-    dev: OpenMathDevice := OMopenString(sp pretend String, OMencodingXML())
-    if wholeObj then
-      OMputObject(dev)
-    outputOMExpr(dev, ex)
-    if wholeObj then
-      OMputEndObject(dev)
-    OMclose(dev)
-    s := OM_-STRINGPTRTOSTRING(sp)$Lisp pretend String
-    s
-
-  OMwrite(dev: OpenMathDevice, ex: Expression R): Void ==
-    OMputObject(dev)
-    outputOMExpr(dev, ex)
-    OMputEndObject(dev)
-
-  OMwrite(dev: OpenMathDevice, ex: Expression R, wholeObj: Boolean): Void ==
-    if wholeObj then
-      OMputObject(dev)
-    outputOMExpr(dev, ex)
-    if wholeObj then
-      OMputEndObject(dev)
-
-@
-\section{License}
-<<license>>=
---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
---All rights reserved.
---
---Redistribution and use in source and binary forms, with or without
---modification, are permitted provided that the following conditions are
---met:
---
---    - Redistributions of source code must retain the above copyright
---      notice, this list of conditions and the following disclaimer.
---
---    - Redistributions in binary form must reproduce the above copyright
---      notice, this list of conditions and the following disclaimer in
---      the documentation and/or other materials provided with the
---      distribution.
---
---    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
---      names of its contributors may be used to endorse or promote products
---      derived from this software without specific prior written permission.
---
---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-@
-<<*>>=
-<<license>>
-
-<<package OMEXPR ExpressionToOpenMath>>
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index f40ffcf2..c2b51aa4 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(2287954 . 3521929246)       
+(2277097 . 3521934608)       
 (-18 A S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
 NIL 
 NIL 
 (-19 S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
 (-20 S) 
 ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) 
@@ -38,7 +38,7 @@ NIL
 NIL 
 (-27) 
 ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-28 S R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
@@ -46,7 +46,7 @@ NIL
 NIL 
 (-29 R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4499 . T) (-4497 . T) (-4496 . T) ((-4504 "*") . T) (-4495 . T) (-4500 . T) (-4494 . T)) 
+((-4422 . T) (-4420 . T) (-4419 . T) ((-4427 "*") . T) (-4418 . T) (-4423 . T) (-4417 . T)) 
 NIL 
 (-30) 
 ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
@@ -56,14 +56,14 @@ NIL
 ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -3572) 
+(-32 R -3495) 
 ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) 
 (-33 S) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4502))) 
+((|HasAttribute| |#1| (QUOTE -4425))) 
 (-34) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
@@ -74,7 +74,7 @@ NIL
 NIL 
 (-36 |Key| |Entry|) 
 ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table.	It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) 
-((-4502 . T) (-4503 . T)) 
+((-4425 . T) (-4426 . T)) 
 NIL 
 (-37 S R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
@@ -82,20 +82,20 @@ NIL
 NIL 
 (-38 R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-39 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -3572 UP UPUP -3090) 
+(-40 -3495 UP UPUP -3013) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-4495 |has| (-419 |#2|) (-376)) (-4500 |has| (-419 |#2|) (-376)) (-4494 |has| (-419 |#2|) (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-4034 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206)))))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -927) (QUOTE (-1206)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-4034 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -927) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206)))))) 
-(-41 R -3572) 
+((-4418 |has| (-419 |#2|) (-376)) (-4423 |has| (-419 |#2|) (-376)) (-4417 |has| (-419 |#2|) (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-3957 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198)))))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -919) (QUOTE (-1198)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-3957 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198)))))) 
+(-41 R -3495) 
 ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -433) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -433) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -106,31 +106,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-319)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) 
-((-4499 |has| |#1| (-569)) (-4497 . T) (-4496 . T)) 
+((-4422 |has| |#1| (-569)) (-4420 . T) (-4419 . T)) 
 ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) 
 (-45 |Key| |Entry|) 
 ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) 
-((-4502 . T) (-4503 . T)) 
-((-4034 (-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869)))) (-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))))) 
+((-4425 . T) (-4426 . T)) 
+((-3957 (-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861)))) (-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))))) 
 (-46 S R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| $ (QUOTE (-1078))) (|HasCategory| $ (|%list| (QUOTE -1067) (QUOTE (-558))))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (|%list| (QUOTE -1059) (QUOTE (-558))))) 
 (-49) 
 ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) 
 NIL 
 NIL 
 (-50 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-51) 
 ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) 
@@ -144,7 +144,7 @@ NIL
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-54 |Base| R -3572) 
+(-54 |Base| R -3495) 
 ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) 
 NIL 
 NIL 
@@ -158,77 +158,77 @@ NIL
 NIL 
 (-57 R |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) 
-((-4502 . T) (-4503 . T)) 
+((-4425 . T) (-4426 . T)) 
 NIL 
 (-58 S) 
 ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-59 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
 NIL 
 NIL 
 (-60 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray's."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-61 -4047) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-61 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim}      DOUBLE PRECISION FUNCTION F(X)      DOUBLE PRECISION X      F=DSIN(X)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-62 -4047) 
+(-62 -3970) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-63 -4047) 
+(-63 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim}      SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO)      DOUBLE PRECISION ELAM,FINFO(15)      INTEGER MAXIT,IFLAG      IF(MAXIT.EQ.-1)THEN        PRINT*,\"Output from Monit\"      ENDIF      PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) 
 NIL 
 NIL 
-(-64 -4047) 
+(-64 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim}      SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC)      DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N)      INTEGER M,N,LJC      INTEGER I,J      DO 25003 I=1,LJC        DO 25004 J=1,N          FJACC(I,J)=0.0D025004   CONTINUE25003 CONTINUE      FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/(     &XC(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/(     &XC(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)*     &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)*     &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+     &XC(2))      FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714     &286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666     &6667D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3)     &+XC(2))      FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      FJACC(1,1)=1.0D0      FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(2,1)=1.0D0      FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(3,1)=1.0D0      FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/(     &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)     &**2)      FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666     &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2)      FJACC(4,1)=1.0D0      FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(5,1)=1.0D0      FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399     &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999     &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(6,1)=1.0D0      FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/(     &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)     &**2)      FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333     &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2)      FJACC(7,1)=1.0D0      FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/(     &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)     &**2)      FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428     &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2)      FJACC(8,1)=1.0D0      FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(9,1)=1.0D0      FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(10,1)=1.0D0      FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(11,1)=1.0D0      FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,1)=1.0D0      FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(13,1)=1.0D0      FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(14,1)=1.0D0      FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,1)=1.0D0      FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-65 -4047) 
+(-65 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim}      SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX)      DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH)      INTEGER JTHCOL,N,NROWH,NCOLH      HX(1)=2.0D0*X(1)      HX(2)=2.0D0*X(2)      HX(3)=2.0D0*X(4)+2.0D0*X(3)      HX(4)=2.0D0*X(4)+2.0D0*X(3)      HX(5)=2.0D0*X(5)      HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6))      HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6))      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-66 -4047) 
+(-66 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim}      SUBROUTINE FUNCT1(N,XC,FC)      DOUBLE PRECISION FC,XC(N)      INTEGER N      FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5     &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X     &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+     &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC(     &2)+10.0D0*XC(1)**4+XC(1)**2      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-67 -4047) 
+(-67 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim}      FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1     &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W(     &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1     &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W(     &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8))     &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7)     &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0.     &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3     &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W(     &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-68 -4047) 
+(-68 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK      W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00     &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554     &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365     &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z(     &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0.     &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050     &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z     &(1)      W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010     &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136     &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D     &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8)     &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532     &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056     &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1     &))      W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0     &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033     &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502     &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D     &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(-     &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961     &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917     &D0*Z(1))      W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0.     &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688     &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315     &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z     &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0     &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802     &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0*     &Z(1)      W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+(     &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014     &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966     &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352     &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6))     &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718     &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851     &6D0*Z(1)      W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048     &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323     &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730     &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z(     &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583     &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700     &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1)      W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0     &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843     &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017     &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z(     &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136     &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015     &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1     &)      W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05     &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338     &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869     &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8)     &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056     &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544     &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z(     &1)      W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(-     &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173     &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441     &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8     &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23     &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773     &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z(     &1)      W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0     &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246     &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609     &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8     &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032     &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688     &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z(     &1)      W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0     &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830     &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D     &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8)     &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493     &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054     &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1)      W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(-     &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162     &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889     &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8     &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0.     &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226     &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763     &75D0*Z(1)      W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+(     &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169     &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453     &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z(     &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05     &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277     &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0     &*Z(1)      W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15))     &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236     &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278     &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D     &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0     &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660     &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903     &02D0*Z(1)      W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0     &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325     &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556     &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D     &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0.     &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122     &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z     &(1)      W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0.     &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669     &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114     &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z     &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0     &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739     &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0*     &Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-69 -4047) 
+(-69 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      DOUBLE PRECISION D(K),F(K)      INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE      CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) 
 NIL 
 NIL 
-(-70 -4047) 
+(-70 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK)      INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE      DOUBLE PRECISION A(5,5)      EXTERNAL F06PAF      A(1,1)=1.0D0      A(1,2)=0.0D0      A(1,3)=0.0D0      A(1,4)=-1.0D0      A(1,5)=0.0D0      A(2,1)=0.0D0      A(2,2)=1.0D0      A(2,3)=0.0D0      A(2,4)=0.0D0      A(2,5)=-1.0D0      A(3,1)=0.0D0      A(3,2)=0.0D0      A(3,3)=1.0D0      A(3,4)=-1.0D0      A(3,5)=0.0D0      A(4,1)=-1.0D0      A(4,2)=0.0D0      A(4,3)=-1.0D0      A(4,4)=4.0D0      A(4,5)=-1.0D0      A(5,1)=0.0D0      A(5,2)=-1.0D0      A(5,3)=0.0D0      A(5,4)=-1.0D0      A(5,5)=4.0D0      IF(MODE.EQ.1)THEN        CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1)      ELSEIF(MODE.EQ.2)THEN        CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1)      ENDIF      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-71 -4047) 
+(-71 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE PEDERV(X,Y,PW)      DOUBLE PRECISION X,Y(*)      DOUBLE PRECISION PW(3,3)      PW(1,1)=-0.03999999999999999D0      PW(1,2)=10000.0D0*Y(3)      PW(1,3)=10000.0D0*Y(2)      PW(2,1)=0.03999999999999999D0      PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2))      PW(2,3)=-10000.0D0*Y(2)      PW(3,1)=0.0D0      PW(3,2)=60000000.0D0*Y(2)      PW(3,3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-72 -4047) 
+(-72 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim}      SUBROUTINE REPORT(X,V,JINT)      DOUBLE PRECISION V(3),X      INTEGER JINT      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) 
 NIL 
 NIL 
-(-73 -4047) 
+(-73 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N)      INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOUBLE PRECISION W1(3),W2(3),MS(3,3)      IFLAG=-1      MS(1,1)=2.0D0      MS(1,2)=1.0D0      MS(1,3)=0.0D0      MS(2,1)=1.0D0      MS(2,2)=2.0D0      MS(2,3)=1.0D0      MS(3,1)=0.0D0      MS(3,2)=1.0D0      MS(3,3)=2.0D0      CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG)      IFLAG=-IFLAG      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-74 -4047) 
+(-74 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)      INTEGER LDFJAC,N,IFLAG      IF(IFLAG.EQ.1)THEN        FVEC(1)=(-1.0D0*X(2))+X(1)        FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2)        FVEC(3)=3.0D0*X(3)      ELSEIF(IFLAG.EQ.2)THEN        FJAC(1,1)=1.0D0        FJAC(1,2)=-1.0D0        FJAC(1,3)=0.0D0        FJAC(2,1)=0.0D0        FJAC(2,2)=2.0D0        FJAC(2,3)=-1.0D0        FJAC(3,1)=0.0D0        FJAC(3,2)=0.0D0        FJAC(3,3)=3.0D0      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-75 -4047) 
+(-75 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim}      DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X)      DOUBLE PRECISION X(NDIM)      INTEGER NDIM      FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0*     &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
@@ -240,51 +240,51 @@ NIL
 ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives wrt \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim}      SUBROUTINE G(EPS,YA,YB,BC,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BC(N)      INTEGER N      BC(1)=YA(1)      BC(2)=YA(2)      BC(3)=YB(2)-1.0D0      RETURN      END      SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N)      DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N)      INTEGER N      AJ(1,1)=1.0D0      AJ(1,2)=0.0D0      AJ(1,3)=0.0D0      AJ(2,1)=0.0D0      AJ(2,2)=1.0D0      AJ(2,3)=0.0D0      AJ(3,1)=0.0D0      AJ(3,2)=0.0D0      AJ(3,3)=0.0D0      BJ(1,1)=0.0D0      BJ(1,2)=0.0D0      BJ(1,3)=0.0D0      BJ(2,1)=0.0D0      BJ(2,2)=0.0D0      BJ(2,3)=0.0D0      BJ(3,1)=0.0D0      BJ(3,2)=1.0D0      BJ(3,3)=0.0D0      RETURN      END      SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N)      INTEGER N      BCEP(1)=0.0D0      BCEP(2)=0.0D0      BCEP(3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-78 -4047) 
+(-78 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER)      DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*)      INTEGER N,IUSER(*),MODE,NSTATE      OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7)     &+(-1.0D0*X(2)*X(6))      OBJGRD(1)=X(7)      OBJGRD(2)=-1.0D0*X(6)      OBJGRD(3)=X(8)+(-1.0D0*X(7))      OBJGRD(4)=X(9)      OBJGRD(5)=-1.0D0*X(8)      OBJGRD(6)=-1.0D0*X(2)      OBJGRD(7)=(-1.0D0*X(3))+X(1)      OBJGRD(8)=(-1.0D0*X(5))+X(3)      OBJGRD(9)=X(4)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-79 -4047) 
+(-79 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE LSFUN1(M,N,XC,FVECC)      DOUBLE PRECISION FVECC(M),XC(N)      INTEGER I,M,N      FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X     &C(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666     &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X     &C(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC     &(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X     &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142     &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999     &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2))      FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999     &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666     &67D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999     &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2))      FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-80 -4047) 
+(-80 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER     &,USER)      DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*)      INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE      IF(NEEDC(1).GT.0)THEN        C(1)=X(6)**2+X(1)**2        CJAC(1,1)=2.0D0*X(1)        CJAC(1,2)=0.0D0        CJAC(1,3)=0.0D0        CJAC(1,4)=0.0D0        CJAC(1,5)=0.0D0        CJAC(1,6)=2.0D0*X(6)      ENDIF      IF(NEEDC(2).GT.0)THEN        C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2        CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1)        CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1))        CJAC(2,3)=0.0D0        CJAC(2,4)=0.0D0        CJAC(2,5)=0.0D0        CJAC(2,6)=0.0D0      ENDIF      IF(NEEDC(3).GT.0)THEN        C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2        CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1)        CJAC(3,2)=2.0D0*X(2)        CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1))        CJAC(3,4)=0.0D0        CJAC(3,5)=0.0D0        CJAC(3,6)=0.0D0      ENDIF      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-81 -4047) 
+(-81 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N)      INTEGER N,IFLAG      FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0      FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1.     &0D0      FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1.     &0D0      FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1.     &0D0      FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1.     &0D0      FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1.     &0D0      FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1.     &0D0      FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1.     &0D0      FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-82 -4047) 
+(-82 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim}      SUBROUTINE FCN(X,Z,F)      DOUBLE PRECISION F(*),X,Z(*)      F(1)=DTAN(Z(3))      F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2)     &**2))/(Z(2)*DCOS(Z(3)))      F(3)=-0.03199999999999999D0/(X*Z(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-83 -4047) 
+(-83 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI)      DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI      ALPHA=DSIN(X)      BETA=Y      GAMMA=X*Y      DELTA=DCOS(X)*DSIN(Y)      EPSOLN=Y+X      PHI=X      PSI=Y      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-84 -4047) 
+(-84 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE BNDY(X,Y,A,B,C,IBND)      DOUBLE PRECISION A,B,C,X,Y      INTEGER IBND      IF(IBND.EQ.0)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(X)      ELSEIF(IBND.EQ.1)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.2)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.3)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(Y)      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-85 -4047) 
+(-85 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNF(X,F)      DOUBLE PRECISION X      DOUBLE PRECISION F(2,2)      F(1,1)=0.0D0      F(1,2)=1.0D0      F(2,1)=0.0D0      F(2,2)=-10.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-86 -4047) 
+(-86 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNG(X,G)      DOUBLE PRECISION G(*),X      G(1)=0.0D0      G(2)=0.0D0      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-87 -4047) 
+(-87 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim}      SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD)      DOUBLE PRECISION Y(N),RESULT(M,N),XSOL      INTEGER M,N,COUNT      LOGICAL FORWRD      DOUBLE PRECISION X02ALF,POINTS(8)      EXTERNAL X02ALF      INTEGER I      POINTS(1)=1.0D0      POINTS(2)=2.0D0      POINTS(3)=3.0D0      POINTS(4)=4.0D0      POINTS(5)=5.0D0      POINTS(6)=6.0D0      POINTS(7)=7.0D0      POINTS(8)=8.0D0      COUNT=COUNT+1      DO 25001 I=1,N        RESULT(COUNT,I)=Y(I)25001 CONTINUE      IF(COUNT.EQ.M)THEN        IF(FORWRD)THEN          XSOL=X02ALF()        ELSE          XSOL=-X02ALF()        ENDIF      ELSE        XSOL=POINTS(COUNT)      ENDIF      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-88 -4047) 
+(-88 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR)      DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3)      YL(1)=XL      YL(2)=2.0D0      YR(1)=1.0D0      YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM))      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-89 -4047) 
+(-89 -3970) 
 ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim}      DOUBLE PRECISION FUNCTION G(X,Y)      DOUBLE PRECISION X,Y(*)      G=X+Y(1)      RETURN      END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
@@ -294,8 +294,8 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-376)))) 
 (-91 S) 
 ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-92 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -318,15 +318,15 @@ NIL
 NIL 
 (-97) 
 ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) 
-((-4502 . T)) 
+((-4425 . T)) 
 NIL 
 (-98) 
 ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) 
-((-4502 . T) ((-4504 "*") . T) (-4503 . T) (-4499 . T) (-4497 . T) (-4496 . T) (-4495 . T) (-4500 . T) (-4494 . T) (-4493 . T) (-4492 . T) (-4491 . T) (-4490 . T) (-4498 . T) (-4501 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4489 . T)) 
+((-4425 . T) ((-4427 "*") . T) (-4426 . T) (-4422 . T) (-4420 . T) (-4419 . T) (-4418 . T) (-4423 . T) (-4417 . T) (-4416 . T) (-4415 . T) (-4414 . T) (-4413 . T) (-4421 . T) (-4424 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4412 . T)) 
 NIL 
 (-99 R) 
 ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-100 R UP) 
 ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) 
@@ -342,15 +342,15 @@ NIL
 NIL 
 (-103 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-104 R UP M |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE (-4504 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4427 "*")))) 
 (-105) 
 ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) 
-((-4502 . T)) 
+((-4425 . T)) 
 NIL 
 (-106 A S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) 
@@ -358,23 +358,23 @@ NIL
 NIL 
 (-107 S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) 
-((-4503 . T)) 
+((-4426 . T)) 
 NIL 
 (-108) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-558) (QUOTE (-937))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1049))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869))) (-4034 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869)))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1181))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1206)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (|HasCategory| (-558) (QUOTE (-147))))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-558) (QUOTE (-929))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1041))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861))) (-3957 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861)))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1173))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (|HasCategory| (-558) (QUOTE (-147))))) 
 (-109) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
 NIL 
 (-110) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| (-114) (QUOTE (-1130))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-869))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-114) (QUOTE (-1130))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-114) (QUOTE (-102)))) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| (-114) (QUOTE (-1122))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-861))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-114) (QUOTE (-1122))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-114) (QUOTE (-102)))) 
 (-111 R S) 
 ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
 (-112 S) 
 ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) 
@@ -396,22 +396,22 @@ NIL
 ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-117 -3572 UP) 
+(-117 -3495 UP) 
 ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) 
 NIL 
 NIL 
 (-118 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-119 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-118 |#1|) (QUOTE (-937))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-118 |#1|) (QUOTE (-1049))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-869))) (-4034 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-869)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-1181))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -526) (QUOTE (-1206)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-937)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-118 |#1|) (QUOTE (-929))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-118 |#1|) (QUOTE (-1041))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-861))) (-3957 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-861)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-1173))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -526) (QUOTE (-1198)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-929)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) 
 (-120 A S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4503))) 
+((|HasAttribute| |#1| (QUOTE -4426))) 
 (-121 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
@@ -422,15 +422,15 @@ NIL
 NIL 
 (-123 S) 
 ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-124 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-125) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
 (-126 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -438,24 +438,24 @@ NIL
 NIL 
 (-127 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-4502 . T) (-4503 . T)) 
+((-4425 . T) (-4426 . T)) 
 NIL 
 (-128 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-129 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-130) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) 
 NIL 
 NIL 
 (-131) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| (-130) (QUOTE (-869))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-4034 (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| (-130) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| (-130) (QUOTE (-869))) (|HasCategory| (-130) (QUOTE (-1130)))) (|HasCategory| (-130) (QUOTE (-869))) (-4034 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-869))) (|HasCategory| (-130) (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-3957 (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| (-130) (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-130) (QUOTE (-861))) (-3957 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1122))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) 
 (-132) 
 ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) 
 NIL 
@@ -474,13 +474,13 @@ NIL
 NIL 
 (-136) 
 ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-4504 "*") . T)) 
+(((-4427 "*") . T)) 
 NIL 
-(-137 |minix| -3097 R) 
+(-137 |minix| -3020 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
-(-138 |minix| -3097 S T$) 
+(-138 |minix| -3020 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
@@ -502,8 +502,8 @@ NIL
 NIL 
 (-143) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) 
-((-4502 . T) (-4492 . T) (-4503 . T)) 
-((-4034 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
+((-4425 . T) (-4415 . T) (-4426 . T)) 
+((-3957 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
 (-144 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
@@ -518,7 +518,7 @@ NIL
 NIL 
 (-147) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-148 R) 
 ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) 
@@ -526,9 +526,9 @@ NIL
 NIL 
 (-149) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
-(-150 -3572 UP UPUP) 
+(-150 -3495 UP UPUP) 
 ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) 
 NIL 
 NIL 
@@ -539,14 +539,14 @@ NIL
 (-152 A S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasAttribute| |#1| (QUOTE -4502))) 
+((|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasAttribute| |#1| (QUOTE -4425))) 
 (-153 S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
 NIL 
 (-154 |n| K Q) 
 ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) 
-((-4497 . T) (-4496 . T) (-4499 . T)) 
+((-4420 . T) (-4419 . T) (-4422 . T)) 
 NIL 
 (-155) 
 ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) 
@@ -568,7 +568,7 @@ NIL
 ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) 
 NIL 
 NIL 
-(-160 R -3572) 
+(-160 R -3495) 
 ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) 
 NIL 
 NIL 
@@ -599,10 +599,10 @@ NIL
 (-167 S R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-1232))) (|HasCategory| |#2| (QUOTE (-1089))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4498)) (|HasAttribute| |#2| (QUOTE -4501)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569)))) 
+((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4421)) (|HasAttribute| |#2| (QUOTE -4424)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569)))) 
 (-168 R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
-((-4495 -4034 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-937)))) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4498 |has| |#1| (-6 -4498)) (-4501 |has| |#1| (-6 -4501)) (-1498 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 -3957 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-929)))) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4421 |has| |#1| (-6 -4421)) (-4424 |has| |#1| (-6 -4424)) (-1490 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-169 RR PR) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) 
@@ -614,8 +614,8 @@ NIL
 NIL 
 (-171 R) 
 ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) 
-((-4495 -4034 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-937)))) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4498 |has| |#1| (-6 -4498)) (-4501 |has| |#1| (-6 -4501)) (-1498 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
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+((-4418 -3957 (|has| |#1| (-569)) (-12 (|has| |#1| (-319)) (|has| |#1| (-929)))) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4421 |has| |#1| (-6 -4421)) (-4424 |has| |#1| (-6 -4424)) (-1490 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-3957 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-376)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-929)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-929))))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1224)))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1224)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-929))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-376)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasAttribute| |#1| (QUOTE -4421)) (|HasAttribute| |#1| (QUOTE -4424)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-363)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
 (-172 R S) 
 ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) 
 NIL 
@@ -630,7 +630,7 @@ NIL
 NIL 
 (-175) 
 ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) 
-(((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-176) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
@@ -638,7 +638,7 @@ NIL
 NIL 
 (-177 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) 
-(((-4504 "*") . T) (-4495 . T) (-4500 . T) (-4494 . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") . T) (-4418 . T) (-4423 . T) (-4417 . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-178) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -655,7 +655,7 @@ NIL
 (-181 R S CS) 
 ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
-((|HasCategory| (-973 |#2|) (|%list| (QUOTE -909) (|devaluate| |#1|)))) 
+((|HasCategory| (-965 |#2|) (|%list| (QUOTE -901) (|devaluate| |#1|)))) 
 (-182 R) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
@@ -692,7 +692,7 @@ NIL
 ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) 
 NIL 
 NIL 
-(-191 R -3572) 
+(-191 R -3495) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -804,23 +804,23 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) 
 NIL 
 NIL 
-(-219 -3572 UP UPUP R) 
+(-219 -3495 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) 
 NIL 
 NIL 
-(-220 -3572 FP) 
+(-220 -3495 FP) 
 ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
 (-221) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-558) (QUOTE (-937))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1049))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869))) (-4034 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869)))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1181))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1206)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (|HasCategory| (-558) (QUOTE (-147))))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-558) (QUOTE (-929))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1041))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861))) (-3957 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861)))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1173))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (|HasCategory| (-558) (QUOTE (-147))))) 
 (-222) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-223 R -3572) 
+(-223 R -3495) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -834,19 +834,19 @@ NIL
 NIL 
 (-226 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-227 |CoefRing| |listIndVar|) 
 ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
-(-228 R -3572) 
+(-228 R -3495) 
 ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) 
 NIL 
 NIL 
 (-229) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4277 . T) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4200 . T) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-230) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) 
@@ -854,19 +854,19 @@ NIL
 NIL 
 (-231 R) 
 ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4504 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4427 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-232 A S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
 NIL 
 NIL 
 (-233 S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
-((-4503 . T)) 
+((-4426 . T)) 
 NIL 
 (-234 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-235 S T$) 
 ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -878,7 +878,7 @@ NIL
 NIL 
 (-237 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
 (-238 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) 
@@ -890,33 +890,33 @@ NIL
 NIL 
 (-240) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-241 A S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4502))) 
+((|HasAttribute| |#1| (QUOTE -4425))) 
 (-242 S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
-((-4503 . T)) 
+((-4426 . T)) 
 NIL 
 (-243) 
 ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) 
 NIL 
 NIL 
-(-244 S -3097 R) 
+(-244 S -3020 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-869))) (|HasAttribute| |#3| (QUOTE -4499)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (QUOTE (-1130)))) 
-(-245 -3097 R) 
+((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4422)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (QUOTE (-1122)))) 
+(-245 -3020 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
-((-4496 |has| |#2| (-1078)) (-4497 |has| |#2| (-1078)) (-4499 |has| |#2| (-6 -4499)) (-4502 . T)) 
+((-4419 |has| |#2| (-1070)) (-4420 |has| |#2| (-1070)) (-4422 |has| |#2| (-6 -4422)) (-4425 . T)) 
 NIL 
-(-246 -3097 R) 
+(-246 -3020 R) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) 
-((-4496 |has| |#2| (-1078)) (-4497 |has| |#2| (-1078)) (-4499 |has| |#2| (-6 -4499)) (-4502 . T)) 
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(QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-4034 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-4034 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| 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+(-247 -3020 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
@@ -930,7 +930,7 @@ NIL
 NIL 
 (-250) 
 ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) 
-((-4495 . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-251 S) 
 ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) 
@@ -938,20 +938,20 @@ NIL
 NIL 
 (-252 S) 
 ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-253 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
 NIL 
 (-254 R) 
 ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
 (-255 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4504 "*") |has| |#2| (-175)) (-4495 |has| |#2| (-569)) (-4500 |has| |#2| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#2| (QUOTE (-937))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(((-4427 "*") |has| |#2| (-175)) (-4418 |has| |#2| (-569)) (-4423 |has| |#2| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#2| (QUOTE (-929))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
 (-256) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 
 NIL 
@@ -966,23 +966,23 @@ NIL
 NIL 
 (-259 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-4499 -4034 (-3038 (|has| |#4| (-1078)) (|has| |#4| (-240))) (|has| |#4| (-6 -4499)) (-3038 (|has| |#4| (-1078)) (|has| |#4| (-925 (-1206))))) (-4496 |has| |#4| (-1078)) (-4497 |has| |#4| (-1078)) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-240))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-746))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-815))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-869))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1130))) 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(-12 (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#4| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#4| (|%list| (QUOTE -925) (QUOTE (-1206)))))) (|HasCategory| |#4| (|%list| (QUOTE -925) (QUOTE (-1206)))) (-4034 (|HasCategory| |#4| (QUOTE (-240))) (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (|%list| (QUOTE -925) (QUOTE (-1206))))) (|HasCategory| |#4| (QUOTE (-240))) (-4034 (|HasCategory| |#4| (QUOTE (-240))) (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (QUOTE (-1078))))) (-4034 (-12 (|HasCategory| |#4| (QUOTE (-1078))) (|HasCategory| |#4| (|%list| (QUOTE -927) (QUOTE (-1206))))) (|HasCategory| |#4| (|%list| (QUOTE -925) (QUOTE (-1206))))) (|HasCategory| |#4| (QUOTE (-1130))) (-4034 (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#4| (QUOTE (-175))) (|HasCategory| |#4| (|%list| 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(|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1078)))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -925) (QUOTE (-1206))))) (|HasAttribute| |#3| (QUOTE -4499)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1078))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1078)))) (-12 (|HasCategory| |#3| (QUOTE (-1078))) (|HasCategory| |#3| (|%list| (QUOTE -927) (QUOTE (-1206))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) 
+((-4422 -3957 (-2961 (|has| |#3| (-1070)) (|has| |#3| (-240))) (|has| |#3| (-6 -4422)) (-2961 (|has| |#3| (-1070)) (|has| |#3| (-917 (-1198))))) (-4419 |has| |#3| (-1070)) (-4420 |has| |#3| (-1070)) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))))) (|HasCategory| |#3| (QUOTE (-376))) (-3957 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1070)))) (-3957 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (QUOTE (-815))) (-3957 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-861)))) (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (QUOTE (-381))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))) (-3957 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#3| (QUOTE (-240))) (-3957 (|HasCategory| |#3| (QUOTE (-240))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1070))))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -919) (QUOTE (-1198))))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#3| (QUOTE (-1122))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1070)))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558)))))) (|HasCategory| (-558) (QUOTE (-861))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -658) (QUOTE (-558))))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -919) (QUOTE (-1198)))))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1070))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasAttribute| |#3| (QUOTE -4422)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1070))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -919) (QUOTE (-1198))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) 
 (-261 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-240)))) 
 (-262 R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
 NIL 
 (-263 S) 
 ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) 
-((-4502 . T) (-4503 . T)) 
+((-4425 . T) (-4426 . T)) 
 NIL 
 (-264 |Ex|) 
 ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
@@ -1023,15 +1023,15 @@ NIL
 (-273 S R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-239)))) 
 (-274 R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
 NIL 
 (-275 R S V) 
 ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-929))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
 (-276 A S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
@@ -1076,11 +1076,11 @@ NIL
 ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) 
 NIL 
 NIL 
-(-287 R -3572) 
+(-287 R -3495) 
 ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the	inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) 
 NIL 
 NIL 
-(-288 R -3572) 
+(-288 R -3495) 
 ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) 
 NIL 
 NIL 
@@ -1103,10 +1103,10 @@ NIL
 (-293 A S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130)))) 
+((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122)))) 
 (-294 S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
-((-4503 . T)) 
+((-4426 . T)) 
 NIL 
 (-295 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
@@ -1127,18 +1127,18 @@ NIL
 (-299 S |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4503))) 
+((|HasAttribute| |#1| (QUOTE -4426))) 
 (-300 |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
 NIL 
-(-301 S R |Mod| -2255 -4015 |exactQuo|) 
+(-301 S R |Mod| -2247 -3938 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-302) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-4495 . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-303) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) 
@@ -1150,16 +1150,16 @@ NIL
 NIL 
 (-305 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) 
-((-4499 -4034 (|has| |#1| (-1078)) (|has| |#1| (-485))) (-4496 |has| |#1| (-1078)) (-4497 |has| |#1| (-1078))) 
-((|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1078)))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (-4034 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1078)))) (-4034 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-746)))) (|HasCategory| |#1| (QUOTE (-485))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-4034 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1141)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-310))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-485)))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746)))) (-4034 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-746)))) 
+((-4422 -3957 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4419 |has| |#1| (-1070)) (-4420 |has| |#1| (-1070))) 
+((|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (-3957 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3957 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-746)))) (|HasCategory| |#1| (QUOTE (-485))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-3957 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-310))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-485)))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746)))) (-3957 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-746)))) 
 (-306 S R) 
 ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) 
 NIL 
 NIL 
 (-307 |Key| |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) 
 (-308) 
 ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) 
 NIL 
@@ -1167,16 +1167,16 @@ NIL
 (-309 S) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1078)))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1070)))) 
 (-310) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
 NIL 
-(-311 -3572 S) 
+(-311 -3495 S) 
 ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) 
 NIL 
 NIL 
-(-312 E -3572) 
+(-312 E -3495) 
 ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) 
 NIL 
 NIL 
@@ -1206,7 +1206,7 @@ NIL
 NIL 
 (-319) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-320 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
@@ -1216,7 +1216,7 @@ NIL
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-322 -3572) 
+(-322 -3495) 
 ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) 
 NIL 
 NIL 
@@ -1230,12 +1230,12 @@ NIL
 NIL 
 (-325 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-1049))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-869))) (-4034 (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-869)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-1181))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -526) (QUOTE (-1206)) (|%list| (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-147))))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
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 (-326 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
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+((-4422 -3957 (-12 (|has| |#1| (-569)) (-3957 (|has| |#1| (-1070)) (|has| |#1| (-485)))) (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) ((-4427 "*") |has| |#1| (-569)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-569)) (-4417 |has| |#1| (-569))) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-21))) (-3957 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-1070))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))))) (-3957 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1070)))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-21)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-25)))) (-3957 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (|%list| (QUOTE -1059) (QUOTE (-558))))) 
 (-327 R S) 
 ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) 
 NIL 
@@ -1244,7 +1244,7 @@ NIL
 ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) 
 NIL 
 NIL 
-(-329 R -3572) 
+(-329 R -3495) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) 
 NIL 
 NIL 
@@ -1254,8 +1254,8 @@ NIL
 NIL 
 (-331 FE |var| |cen|) 
 ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
 (-332 M) 
 ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
@@ -1266,8 +1266,8 @@ NIL
 NIL 
 (-334 S) 
 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) 
-((-4497 . T) (-4496 . T)) 
-((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| (-558) (QUOTE (-814)))) 
+((-4420 . T) (-4419 . T)) 
+((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-558) (QUOTE (-814)))) 
 (-335 S E) 
 ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
@@ -1282,19 +1282,19 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175)))) 
 (-338 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-339 S) 
 ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-340 S -3572) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-340 S -3495) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-381)))) 
-(-341 -3572) 
+(-341 -3495) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-342) 
 ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) 
@@ -1312,7 +1312,7 @@ NIL
 ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) 
 NIL 
 NIL 
-(-346 -3572 UP UPUP R) 
+(-346 -3495 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
@@ -1320,37 +1320,37 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-348 S -3572 UP UPUP R) 
+(-348 S -3495 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-349 -3572 UP UPUP R) 
+(-349 -3495 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
 (-350 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-351 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-352 |basicSymbols| |subscriptedSymbols| R) 
 ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function \\spad{LOG10}")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -1067) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1078))) (|HasCategory| $ (|%list| (QUOTE -1067) (QUOTE (-558))))) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (|%list| (QUOTE -1059) (QUOTE (-558))))) 
 (-353 |p| |n|) 
 ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| (-933 |#1|) (QUOTE (-147))) (|HasCategory| (-933 |#1|) (QUOTE (-381)))) (|HasCategory| (-933 |#1|) (QUOTE (-149))) (|HasCategory| (-933 |#1|) (QUOTE (-381))) (|HasCategory| (-933 |#1|) (QUOTE (-147)))) 
-(-354 S -3572 UP UPUP) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| (-925 |#1|) (QUOTE (-147))) (|HasCategory| (-925 |#1|) (QUOTE (-381)))) (|HasCategory| (-925 |#1|) (QUOTE (-149))) (|HasCategory| (-925 |#1|) (QUOTE (-381))) (|HasCategory| (-925 |#1|) (QUOTE (-147)))) 
+(-354 S -3495 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) 
-(-355 -3572 UP UPUP) 
+(-355 -3495 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
-((-4495 |has| (-419 |#2|) (-376)) (-4500 |has| (-419 |#2|) (-376)) (-4494 |has| (-419 |#2|) (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 |has| (-419 |#2|) (-376)) (-4423 |has| (-419 |#2|) (-376)) (-4417 |has| (-419 |#2|) (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-356 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) 
@@ -1358,16 +1358,16 @@ NIL
 NIL 
 (-357 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| (-933 |#1|) (QUOTE (-147))) (|HasCategory| (-933 |#1|) (QUOTE (-381)))) (|HasCategory| (-933 |#1|) (QUOTE (-149))) (|HasCategory| (-933 |#1|) (QUOTE (-381))) (|HasCategory| (-933 |#1|) (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| (-925 |#1|) (QUOTE (-147))) (|HasCategory| (-925 |#1|) (QUOTE (-381)))) (|HasCategory| (-925 |#1|) (QUOTE (-149))) (|HasCategory| (-925 |#1|) (QUOTE (-381))) (|HasCategory| (-925 |#1|) (QUOTE (-147)))) 
 (-358 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-359 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-360 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
 NIL 
@@ -1382,51 +1382,51 @@ NIL
 NIL 
 (-363) 
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-364 R UP -3572) 
+(-364 R UP -3495) 
 ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-365 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| (-933 |#1|) (QUOTE (-147))) (|HasCategory| (-933 |#1|) (QUOTE (-381)))) (|HasCategory| (-933 |#1|) (QUOTE (-149))) (|HasCategory| (-933 |#1|) (QUOTE (-381))) (|HasCategory| (-933 |#1|) (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| (-925 |#1|) (QUOTE (-147))) (|HasCategory| (-925 |#1|) (QUOTE (-381)))) (|HasCategory| (-925 |#1|) (QUOTE (-149))) (|HasCategory| (-925 |#1|) (QUOTE (-381))) (|HasCategory| (-925 |#1|) (QUOTE (-147)))) 
 (-366 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-367 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-368 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-369 GF) 
 ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) 
 NIL 
 NIL 
-(-370 -3572 GF) 
+(-370 -3495 GF) 
 ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-371 -3572 FP FPP) 
+(-371 -3495 FP FPP) 
 ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) 
 NIL 
 NIL 
 (-372 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) 
 (-373 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) 
 NIL 
 NIL 
 (-374 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-375 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1434,7 +1434,7 @@ NIL
 NIL 
 (-376) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-377 S) 
 ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
@@ -1450,7 +1450,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-569)))) 
 (-380 R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-4499 |has| |#1| (-569)) (-4497 . T) (-4496 . T)) 
+((-4422 |has| |#1| (-569)) (-4420 . T) (-4419 . T)) 
 NIL 
 (-381) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) 
@@ -1462,15 +1462,15 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-376)))) 
 (-383 R UP) 
 ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-384 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130)))) 
+((|HasAttribute| |#1| (QUOTE -4426)) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122)))) 
 (-385 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-4502 . T)) 
+((-4425 . T)) 
 NIL 
 (-386 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) 
@@ -1478,7 +1478,7 @@ NIL
 NIL 
 (-387 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4497 . T) (-4496 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4420 . T) (-4419 . T)) 
 NIL 
 (-388 S V) 
 ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) 
@@ -1494,7 +1494,7 @@ NIL
 NIL 
 (-391) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4485 . T) (-4493 . T) (-4277 . T) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4408 . T) (-4416 . T) (-4200 . T) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-392 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) 
@@ -1506,11 +1506,11 @@ NIL
 NIL 
 (-394 R S) 
 ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) 
-((-4497 . T) (-4496 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) 
+((-4420 . T) (-4419 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
 (-395 R S) 
 ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175)))) 
 (-396) 
 ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) 
@@ -1518,7 +1518,7 @@ NIL
 NIL 
 (-397 R |Basis|) 
 ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
 (-398) 
 ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
@@ -1531,10 +1531,10 @@ NIL
 (-400 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-869)))) 
+((|HasCategory| |#1| (QUOTE (-861)))) 
 (-401) 
 ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-402) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
@@ -1546,13 +1546,13 @@ NIL
 NIL 
 (-404 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
 (-405) 
 ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) 
 NIL 
 NIL 
-(-406 -3572 UP UPUP R) 
+(-406 -3495 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
@@ -1568,11 +1568,11 @@ NIL
 ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
 NIL 
 NIL 
-(-410 -4047 |returnType| -1545 |symbols|) 
+(-410 -3970 |returnType| -1537 |symbols|) 
 ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-411 -3572 UP) 
+(-411 -3495 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
@@ -1586,28 +1586,28 @@ NIL
 NIL 
 (-414) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-415 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4485)) (|HasAttribute| |#1| (QUOTE -4493))) 
+((|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4416))) 
 (-416) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
-((-4277 . T) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4200 . T) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-417 R) 
 ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1251))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1251)))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1243))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1243)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) 
 (-418 R S) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) 
 NIL 
 NIL 
 (-419 S) 
 ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
-((-4489 -12 (|has| |#1| (-6 -4500)) (|has| |#1| (-464)) (|has| |#1| (-6 -4489))) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1181))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4489)) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464)))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+((-4412 -12 (|has| |#1| (-6 -4423)) (|has| |#1| (-464)) (|has| |#1| (-6 -4412))) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1041))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464)))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
 (-420 A B) 
 ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) 
 NIL 
@@ -1618,28 +1618,28 @@ NIL
 NIL 
 (-422 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-423 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558))))) 
+((|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558))))) 
 (-424 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-425 R -3572 UP A) 
+(-425 R -3495 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-426 R1 F1 U1 A1 R2 F2 U2 A2) 
 ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-427 R -3572 UP A |ibasis|) 
+(-427 R -3495 UP A |ibasis|) 
 ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (|%list| (QUOTE -1067) (|devaluate| |#2|)))) 
+((|HasCategory| |#4| (|%list| (QUOTE -1059) (|devaluate| |#2|)))) 
 (-428 AR R AS S) 
 ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
@@ -1650,7 +1650,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-376)))) 
 (-430 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-4499 |has| |#1| (-569)) (-4497 . T) (-4496 . T)) 
+((-4422 |has| |#1| (-569)) (-4420 . T) (-4419 . T)) 
 NIL 
 (-431 R) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) 
@@ -1659,10 +1659,10 @@ NIL
 (-432 S R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1141))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) 
+((|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) 
 (-433 R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
-((-4499 -4034 (|has| |#1| (-1078)) (|has| |#1| (-485))) (-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) ((-4504 "*") |has| |#1| (-569)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-569)) (-4494 |has| |#1| (-569))) 
+((-4422 -3957 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) ((-4427 "*") |has| |#1| (-569)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-569)) (-4417 |has| |#1| (-569))) 
 NIL 
 (-434 R A S B) 
 ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) 
@@ -1679,36 +1679,36 @@ NIL
 (-437 A S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-381)))) 
+((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-381)))) 
 (-438 S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-4502 . T) (-4492 . T) (-4503 . T)) 
+((-4425 . T) (-4415 . T) (-4426 . T)) 
 NIL 
 (-439 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) 
 NIL 
 NIL 
-(-440 R -3572) 
+(-440 R -3495) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
 (-441 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) 
-((-4489 -12 (|has| |#1| (-6 -4489)) (|has| |#2| (-6 -4489))) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -4489)) (|HasAttribute| |#2| (QUOTE -4489)))) 
-(-442 R -3572) 
+((-4412 -12 (|has| |#1| (-6 -4412)) (|has| |#2| (-6 -4412))) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#2| (QUOTE -4412)))) 
+(-442 R -3495) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) 
 NIL 
 NIL 
-(-443 R -3572) 
+(-443 R -3495) 
 ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) 
 NIL 
 NIL 
-(-444 R -3572) 
+(-444 R -3495) 
 ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-27)))) 
-(-445 R -3572) 
+(-445 R -3495) 
 ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) 
 NIL 
 NIL 
@@ -1716,10 +1716,10 @@ NIL
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-447 R -3572 UP) 
+(-447 R -3495 UP) 
 ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-48))))) 
+((|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-48))))) 
 (-448) 
 ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) 
 NIL 
@@ -1748,7 +1748,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) 
 NIL 
 NIL 
-(-455 R UP -3572) 
+(-455 R UP -3495) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) 
 NIL 
 NIL 
@@ -1786,16 +1786,16 @@ NIL
 NIL 
 (-464) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-465 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) 
-((-4499 |has| (-419 (-973 |#1|)) (-569)) (-4497 . T) (-4496 . T)) 
-((|HasCategory| (-419 (-973 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-419 (-973 |#1|)) (QUOTE (-569)))) 
+((-4422 |has| (-419 (-965 |#1|)) (-569)) (-4420 . T) (-4419 . T)) 
+((|HasCategory| (-419 (-965 |#1|)) (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-419 (-965 |#1|)) (QUOTE (-569)))) 
 (-466 |vl| R E) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4504 "*") |has| |#2| (-175)) (-4495 |has| |#2| (-569)) (-4500 |has| |#2| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#2| (QUOTE (-937))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(((-4427 "*") |has| |#2| (-175)) (-4418 |has| |#2| (-569)) (-4423 |has| |#2| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#2| (QUOTE (-929))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
 (-467 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) 
 NIL 
@@ -1822,7 +1822,7 @@ NIL
 NIL 
 (-473 |vl| R IS E |ff| P) 
 ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
 (-474 E V R P Q) 
 ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1830,8 +1830,8 @@ NIL
 NIL 
 (-475 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
 (-476 S R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) 
 NIL 
@@ -1860,7 +1860,7 @@ NIL
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-483 |lv| -3572 R) 
+(-483 |lv| -3495 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1870,23 +1870,23 @@ NIL
 NIL 
 (-485) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-486 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
 (-487 |Key| |Entry| |Tbl| |dent|) 
 ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 
-((-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) 
+((-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) 
 (-488 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
 (-489) 
 ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-490) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) 
@@ -1894,29 +1894,29 @@ NIL
 NIL 
 (-491 |Key| |Entry| |hashfn|) 
 ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) 
-((-4502 . T) (-4503 . T)) 
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+((-4425 . T) (-4426 . T)) 
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 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) 
 NIL 
 NIL 
 (-493 |vl| R) 
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(QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) 
 (-495) 
 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) 
 NIL 
 NIL 
 (-496 S) 
 ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-497 -3572 UP UPUP R) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-497 -3495 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) 
 NIL 
 NIL 
@@ -1926,12 +1926,12 @@ NIL
 NIL 
 (-499) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-558) (QUOTE (-937))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1049))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869))) (-4034 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869)))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1181))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1206)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (|HasCategory| (-558) (QUOTE (-147))))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-558) (QUOTE (-929))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1041))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861))) (-3957 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861)))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1173))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (|HasCategory| (-558) (QUOTE (-147))))) 
 (-500 A S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4502)) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) 
+((|HasAttribute| |#1| (QUOTE -4425)) (|HasAttribute| |#1| (QUOTE -4426)) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) 
 (-501 S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1952,34 +1952,34 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-506 -3572 UP |AlExt| |AlPol|) 
+(-506 -3495 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-507) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| $ (QUOTE (-1078))) (|HasCategory| $ (|%list| (QUOTE -1067) (QUOTE (-558))))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (|%list| (QUOTE -1059) (QUOTE (-558))))) 
 (-508 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-509 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray's with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-510 K R UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) 
 NIL 
 NIL 
-(-511 R UP -3572) 
+(-511 R UP -3495) 
 ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-512 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| (-114) (QUOTE (-1130))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-869))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-114) (QUOTE (-1130))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-114) (QUOTE (-102)))) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| (-114) (QUOTE (-1122))) (|HasCategory| (-114) (|%list| (QUOTE -321) (QUOTE (-114))))) (|HasCategory| (-114) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-114) (QUOTE (-861))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-114) (QUOTE (-1122))) (|HasCategory| (-114) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-114) (QUOTE (-102)))) 
 (-513 K R UP L) 
 ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) 
 NIL 
@@ -1992,10 +1992,10 @@ NIL
 ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
 NIL 
-(-516 -3572 |Expon| |VarSet| |DPoly|) 
+(-516 -3495 |Expon| |VarSet| |DPoly|) 
 ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-1206))))) 
+((|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-1198))))) 
 (-517 |vl| |nv|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) 
 NIL 
@@ -2007,11 +2007,11 @@ NIL
 (-519 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
 (-520 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
 (-521 A S) 
 ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
@@ -2019,15 +2019,15 @@ NIL
 (-522 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
 (-523 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
 (-524 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) 
 (-525 S A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
@@ -2042,36 +2042,36 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-814)))) 
 (-528 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-529) 
 ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) 
 NIL 
 NIL 
 (-530 |p| |n|) 
 ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (|HasCategory| (-593 |#1|) (QUOTE (-147))) (|HasCategory| (-593 |#1|) (QUOTE (-381)))) (|HasCategory| (-593 |#1|) (QUOTE (-149))) (|HasCategory| (-593 |#1|) (QUOTE (-381))) (|HasCategory| (-593 |#1|) (QUOTE (-147)))) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((-3957 (|HasCategory| (-593 |#1|) (QUOTE (-147))) (|HasCategory| (-593 |#1|) (QUOTE (-381)))) (|HasCategory| (-593 |#1|) (QUOTE (-149))) (|HasCategory| (-593 |#1|) (QUOTE (-381))) (|HasCategory| (-593 |#1|) (QUOTE (-147)))) 
 (-531 R |mnRow| |mnCol| |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-532 S |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-533 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) 
 NIL 
-((|HasAttribute| |#3| (QUOTE -4503))) 
+((|HasAttribute| |#3| (QUOTE -4426))) 
 (-534 R |Row| |Col| M QF |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) 
 NIL 
-((|HasAttribute| |#7| (QUOTE -4503))) 
+((|HasAttribute| |#7| (QUOTE -4426))) 
 (-535 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4504 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4427 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-536) 
 ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) 
 NIL 
@@ -2103,8 +2103,8 @@ NIL
 (-543 |Varset|) 
 ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-791) (QUOTE (-1130))))) 
-(-544 K -3572 |Par|) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-791) (QUOTE (-1122))))) 
+(-544 K -3495 |Par|) 
 ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) 
 NIL 
 NIL 
@@ -2128,7 +2128,7 @@ NIL
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-550 K -3572 |Par|) 
+(-550 K -3495 |Par|) 
 ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) 
 NIL 
 NIL 
@@ -2158,11 +2158,11 @@ NIL
 NIL 
 (-557) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
-((-4500 . T) (-4501 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4423 . T) (-4424 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-558) 
 ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \\spad{nothing}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-4484 . T) (-4490 . T) (-4494 . T) (-4489 . T) (-4500 . T) (-4501 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4407 . T) (-4413 . T) (-4417 . T) (-4412 . T) (-4423 . T) (-4424 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-559) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
@@ -2182,13 +2182,13 @@ NIL
 NIL 
 (-563 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) 
-(-564 R -3572) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) 
+(-564 R -3495) 
 ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) 
 NIL 
 NIL 
-(-565 R0 -3572 UP UPUP R) 
+(-565 R0 -3495 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) 
 NIL 
 NIL 
@@ -2198,7 +2198,7 @@ NIL
 NIL 
 (-567 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-4277 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4200 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-568 S) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
@@ -2206,9 +2206,9 @@ NIL
 NIL 
 (-569) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-570 R -3572) 
+(-570 R -3495) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) 
 NIL 
 NIL 
@@ -2220,7 +2220,7 @@ NIL
 ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) 
 NIL 
 NIL 
-(-573 R -3572 L) 
+(-573 R -3495 L) 
 ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) 
 NIL 
 ((|HasCategory| |#3| (|%list| (QUOTE -678) (|devaluate| |#2|)))) 
@@ -2228,11 +2228,11 @@ NIL
 ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) 
 NIL 
 NIL 
-(-575 -3572 UP UPUP R) 
+(-575 -3495 UP UPUP R) 
 ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) 
 NIL 
 NIL 
-(-576 -3572 UP) 
+(-576 -3495 UP) 
 ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) 
 NIL 
 NIL 
@@ -2240,15 +2240,15 @@ NIL
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\tt numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\tt \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) 
 NIL 
 NIL 
-(-578 R -3572 L) 
+(-578 R -3495 L) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) 
 NIL 
 ((|HasCategory| |#3| (|%list| (QUOTE -678) (|devaluate| |#2|)))) 
-(-579 R -3572) 
+(-579 R -3495) 
 ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1168)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-647))))) 
-(-580 -3572 UP) 
+((-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1160)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-647))))) 
+(-580 -3495 UP) 
 ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) 
 NIL 
 NIL 
@@ -2256,27 +2256,27 @@ NIL
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-582 -3572) 
+(-582 -3495) 
 ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) 
 NIL 
 NIL 
 (-583 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) 
-((-4277 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4200 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-584) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) 
 NIL 
 NIL 
-(-585 R -3572) 
+(-585 R -3495) 
 ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-647))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-569)))) 
-(-586 -3572 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-647))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-569)))) 
+(-586 -3495 UP) 
 ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) 
 NIL 
 NIL 
-(-587 R -3572) 
+(-587 R -3495) 
 ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) 
 NIL 
 NIL 
@@ -2298,25 +2298,25 @@ NIL
 NIL 
 (-592 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-593 |p|) 
 ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) 
 (-594) 
 ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) 
 NIL 
 NIL 
-(-595 -3572) 
+(-595 -3495) 
 ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) 
-((-4497 . T) (-4496 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-1206))))) 
-(-596 E -3572) 
+((-4420 . T) (-4419 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-1198))))) 
+(-596 E -3495) 
 ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) 
 NIL 
 NIL 
-(-597 R -3572) 
+(-597 R -3495) 
 ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) 
 NIL 
 NIL 
@@ -2350,19 +2350,19 @@ NIL
 NIL 
 (-605 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings"))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4034 (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130)))) (|HasCategory| (-146) (QUOTE (-869))) (-4034 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-3957 (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122)))) (|HasCategory| (-146) (QUOTE (-861))) (-3957 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
 (-606 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
 (-607 |Coef|) 
 ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) 
 (-608 |Coef|) 
 ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-(((-4504 "*") |has| |#1| (-569)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-569)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 ((|HasCategory| |#1| (QUOTE (-569)))) 
 (-609) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) 
@@ -2376,7 +2376,7 @@ NIL
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) 
 NIL 
 NIL 
-(-612 R -3572 FG) 
+(-612 R -3495 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) 
 NIL 
 NIL 
@@ -2386,12 +2386,12 @@ NIL
 NIL 
 (-614 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-615 S |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-869))) (|HasAttribute| |#1| (QUOTE -4502)) (|HasCategory| |#3| (QUOTE (-1130)))) 
+((|HasAttribute| |#1| (QUOTE -4426)) (|HasCategory| |#2| (QUOTE (-861))) (|HasAttribute| |#1| (QUOTE -4425)) (|HasCategory| |#3| (QUOTE (-1122)))) 
 (-616 |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
@@ -2402,8 +2402,8 @@ NIL
 NIL 
 (-618 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) 
-((-4499 -4034 (-3038 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4497 . T) (-4496 . T)) 
-((-4034 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) 
+((-4422 -3957 (-2961 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4420 . T) (-4419 . T)) 
+((-3957 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) 
 (-619) 
 ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) 
 NIL 
@@ -2430,20 +2430,20 @@ NIL
 NIL 
 (-625 |Entry|) 
 ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (QUOTE (-1188))) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-1188) (QUOTE (-869))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1180))) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-102)))) 
 (-626 S |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
 NIL 
 NIL 
 (-627 |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
-((-4503 . T)) 
+((-4426 . T)) 
 NIL 
 (-628 S) 
 ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) 
+((|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) 
 (-629 R S) 
 ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) 
 NIL 
@@ -2456,7 +2456,7 @@ NIL
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-632 -3572 UP) 
+(-632 -3495 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) 
 NIL 
 NIL 
@@ -2474,24 +2474,24 @@ NIL
 NIL 
 (-636 A R S) 
 ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-868)))) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
 (-637 S R) 
 ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) 
 NIL 
 NIL 
 (-638 R) 
 ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
-(-639 R -3572) 
+(-639 R -3495) 
 ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) 
 NIL 
 NIL 
 (-640 R UP) 
 ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) 
-((-4497 . T) (-4496 . T) ((-4504 "*") . T) (-4495 . T) (-4499 . T)) 
-((|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) 
+((-4420 . T) (-4419 . T) ((-4427 "*") . T) (-4418 . T) (-4422 . T)) 
+((|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) 
 (-641 R E V P TS ST) 
 ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) 
 NIL 
@@ -2506,13 +2506,13 @@ NIL
 NIL 
 (-644 |VarSet| R |Order|) 
 ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-645 R |ls|) 
 ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) 
 NIL 
 NIL 
-(-646 R -3572) 
+(-646 R -3495) 
 ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) 
 NIL 
 NIL 
@@ -2520,25 +2520,25 @@ NIL
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-648 |lv| -3572) 
+(-648 |lv| -3495) 
 ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) 
 NIL 
 NIL 
 (-649) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
-((-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (QUOTE (-1188))) (|%list| (QUOTE |:|) (QUOTE -2294) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1188) (QUOTE (-869))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 (-51))) (QUOTE (-1130)))) 
+((-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1180))) (|%list| (QUOTE |:|) (QUOTE -2286) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1180) (QUOTE (-861))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 (-51))) (QUOTE (-1122)))) 
 (-650 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) 
-((-4499 -4034 (-3038 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4497 . T) (-4496 . T)) 
-((-4034 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) 
+((-4422 -3957 (-2961 (|has| |#2| (-380 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4420 . T) (-4419 . T)) 
+((-3957 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) 
 (-651 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-376)))) 
 (-652 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4497 . T) (-4496 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4420 . T) (-4419 . T)) 
 NIL 
 (-653 R FE) 
 ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) 
@@ -2555,18 +2555,18 @@ NIL
 (-656 S R) 
 ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((-3036 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) 
+((-2959 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) 
 (-657 K B) 
 ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) 
-((-4497 . T) (-4496 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-655 |#2|) (QUOTE (-1130))))) 
+((-4420 . T) (-4419 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-655 |#2|) (QUOTE (-1122))))) 
 (-658 R) 
 ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) 
 NIL 
 NIL 
 (-659 K B) 
 ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
 (-660 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) 
@@ -2574,8 +2574,8 @@ NIL
 NIL 
 (-661 S) 
 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-662 A B) 
 ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) 
 NIL 
@@ -2598,8 +2598,8 @@ NIL
 NIL 
 (-667 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-668 R) 
 ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) 
 NIL 
@@ -2611,40 +2611,40 @@ NIL
 (-670 A S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4503))) 
+((|HasAttribute| |#1| (QUOTE -4426))) 
 (-671 S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
 (-672 M R S) 
 ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 ((|HasCategory| |#1| (QUOTE (-812)))) 
-(-673 R -3572 L) 
+(-673 R -3495 L) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
-(-674 A -2896) 
+(-674 A -2888) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) 
 (-675 A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) 
 (-676 A M) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) 
 (-677 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-376)))) 
 (-678 A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-679 -3572 UP) 
+(-679 -3495 UP) 
 ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
@@ -2666,7 +2666,7 @@ NIL
 NIL 
 (-684 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4497 . T) (-4496 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4420 . T) (-4419 . T)) 
 ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-175)))) 
 (-685 A S) 
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
@@ -2674,13 +2674,13 @@ NIL
 NIL 
 (-686 S) 
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
-(-687 -3572 |Row| |Col| M) 
+(-687 -3495 |Row| |Col| M) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-688 -3572) 
+(-688 -3495) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
@@ -2690,8 +2690,8 @@ NIL
 NIL 
 (-690 |n| R) 
 ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) 
-((-4499 . T) (-4502 . T) (-4496 . T) (-4497 . T)) 
-((|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4504 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569))) (-4034 (|HasAttribute| |#2| (QUOTE (-4504 #1#))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) 
+((-4422 . T) (-4425 . T) (-4419 . T) (-4420 . T)) 
+((|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4427 #1="*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569))) (-3957 (|HasAttribute| |#2| (QUOTE (-4427 #1#))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) 
 (-691) 
 ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) 
 NIL 
@@ -2711,7 +2711,7 @@ NIL
 (-695 R) 
 ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) 
 NIL 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-696) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) 
 NIL 
@@ -2751,10 +2751,10 @@ NIL
 (-705 S R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
 NIL 
-((|HasAttribute| |#2| (QUOTE (-4504 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569)))) 
+((|HasAttribute| |#2| (QUOTE (-4427 "*"))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-569)))) 
 (-706 R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
-((-4502 . T) (-4503 . T)) 
+((-4425 . T) (-4426 . T)) 
 NIL 
 (-707 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
@@ -2766,8 +2766,8 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569)))) 
 (-709 R) 
 ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) 
-((-4502 . T) (-4503 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4504 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+((-4425 . T) (-4426 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4427 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
 (-710 R) 
 ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) 
 NIL 
@@ -2776,7 +2776,7 @@ NIL
 ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) 
 NIL 
 NIL 
-(-712 S -3572 FLAF FLAS) 
+(-712 S -3495 FLAF FLAS) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) 
 NIL 
 NIL 
@@ -2786,11 +2786,11 @@ NIL
 NIL 
 (-714) 
 ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) 
-((-4495 . T) (-4500 |has| (-719) (-376)) (-4494 |has| (-719) (-376)) (-1498 . T) (-4501 |has| (-719) (-6 -4501)) (-4498 |has| (-719) (-6 -4498)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
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+((-4418 . T) (-4423 |has| (-719) (-376)) (-4417 |has| (-719) (-376)) (-1490 . T) (-4424 |has| (-719) (-6 -4424)) (-4421 |has| (-719) (-6 -4421)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-719) (QUOTE (-149))) (|HasCategory| (-719) (QUOTE (-147))) (|HasCategory| (-719) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-719) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-719) (QUOTE (-381))) (|HasCategory| (-719) (QUOTE (-376))) (-3957 (|HasCategory| (-719) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-719) (QUOTE (-376)))) (|HasCategory| (-719) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-719) (QUOTE (-240))) (|HasCategory| (-719) (QUOTE (-239))) (-3957 (-12 (|HasCategory| (-719) (QUOTE (-376))) (|HasCategory| (-719) (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| (-719) (|%list| (QUOTE -919) (QUOTE (-1198))))) (-3957 (|HasCategory| (-719) (QUOTE (-376))) (|HasCategory| (-719) (QUOTE (-363)))) (|HasCategory| (-719) (QUOTE (-363))) (|HasCategory| (-719) (|%list| (QUOTE -298) (QUOTE (-719)) (QUOTE (-719)))) (|HasCategory| (-719) (|%list| (QUOTE -321) (QUOTE (-719)))) (|HasCategory| (-719) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-719)))) (|HasCategory| (-719) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-719) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-719) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-719) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (-3957 (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-376))) (|HasCategory| (-719) (QUOTE (-363)))) (|HasCategory| (-719) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-719) (QUOTE (-1041))) (|HasCategory| (-719) (QUOTE (-1224))) (-12 (|HasCategory| (-719) (QUOTE (-1023))) (|HasCategory| (-719) (QUOTE (-1224)))) (-3957 (-12 (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-929)))) (-12 (|HasCategory| (-719) (QUOTE (-363))) (|HasCategory| (-719) (QUOTE (-929)))) (|HasCategory| (-719) (QUOTE (-376)))) (-3957 (-12 (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-929)))) (-12 (|HasCategory| (-719) (QUOTE (-376))) (|HasCategory| (-719) (QUOTE (-929)))) (-12 (|HasCategory| (-719) (QUOTE (-363))) (|HasCategory| (-719) (QUOTE (-929))))) (|HasCategory| (-719) (QUOTE (-557))) (-12 (|HasCategory| (-719) (QUOTE (-1081))) (|HasCategory| (-719) (QUOTE (-1224)))) (|HasCategory| (-719) (QUOTE (-1081))) (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-929))) (-3957 (-12 (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-929)))) (|HasCategory| (-719) (QUOTE (-376)))) (-3957 (-12 (|HasCategory| (-719) (QUOTE (-240))) (|HasCategory| (-719) (QUOTE (-376)))) (|HasCategory| (-719) (QUOTE (-239)))) (-3957 (-12 (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-929)))) (|HasCategory| (-719) (QUOTE (-569)))) (-12 (|HasCategory| (-719) (QUOTE (-239))) (|HasCategory| (-719) (QUOTE (-376)))) (-12 (|HasCategory| (-719) (QUOTE (-376))) (|HasCategory| (-719) (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| (-719) (QUOTE (-240))) (|HasCategory| (-719) (QUOTE (-376)))) (-12 (|HasCategory| (-719) (QUOTE (-376))) (|HasCategory| (-719) (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| (-719) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-719) (QUOTE (-569))) (|HasAttribute| (-719) (QUOTE -4424)) (|HasAttribute| (-719) (QUOTE -4421)) (-12 (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-929)))) (|HasCategory| (-719) (|%list| (QUOTE -919) (QUOTE (-1198)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-929)))) (|HasCategory| (-719) (QUOTE (-147)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-719) (QUOTE (-319))) (|HasCategory| (-719) (QUOTE (-929)))) (|HasCategory| (-719) (QUOTE (-363))))) 
 (-715 S) 
 ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) 
-((-4503 . T)) 
+((-4426 . T)) 
 NIL 
 (-716 U) 
 ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) 
@@ -2800,13 +2800,13 @@ NIL
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) 
 NIL 
 NIL 
-(-718 OV E -3572 PG) 
+(-718 OV E -3495 PG) 
 ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) 
 NIL 
 NIL 
 (-719) 
 ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) 
-((-4277 . T) (-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4200 . T) (-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-720 R) 
 ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) 
@@ -2814,7 +2814,7 @@ NIL
 NIL 
 (-721) 
 ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) 
-((-4501 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4424 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-722 S D1 D2 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) 
@@ -2832,7 +2832,7 @@ NIL
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) 
 NIL 
 NIL 
-(-726 S -3147 I) 
+(-726 S -3070 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) 
 NIL 
 NIL 
@@ -2842,7 +2842,7 @@ NIL
 NIL 
 (-728 R) 
 ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-729 R1 UP1 UPUP1 R2 UP2 UPUP2) 
 ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) 
@@ -2852,25 +2852,25 @@ NIL
 ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 
 NIL 
 NIL 
-(-731 R |Mod| -2255 -4015 |exactQuo|) 
+(-731 R |Mod| -2247 -3938 |exactQuo|) 
 ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-732 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4498 |has| |#1| (-376)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1111) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1111) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1181))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4421 |has| |#1| (-376)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-1103) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-1103) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1103) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
 (-733 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
 (-734 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) 
+((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) 
-(-735 R |Mod| -2255 -4015 |exactQuo|) 
+(-735 R |Mod| -2247 -3938 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-736 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
@@ -2878,11 +2878,11 @@ NIL
 NIL 
 (-737 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
-(-738 -3572) 
+(-738 -3495) 
 ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
 (-739 S) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
@@ -2906,7 +2906,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381)))) 
 (-744 R UP) 
 ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) 
-((-4495 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 |has| |#1| (-376)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-745 S) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) 
@@ -2916,7 +2916,7 @@ NIL
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-747 -3572 UP) 
+(-747 -3495 UP) 
 ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
@@ -2934,8 +2934,8 @@ NIL
 NIL 
 (-751 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) 
-(((-4504 "*") |has| |#2| (-175)) (-4495 |has| |#2| (-569)) (-4500 |has| |#2| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#2| (QUOTE (-937))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-886 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(((-4427 "*") |has| |#2| (-175)) (-4418 |has| |#2| (-569)) (-4423 |has| |#2| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#2| (QUOTE (-929))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-929)))) (-3957 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-929)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-3957 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-878 |#1|) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
 (-752 E OV R PRF) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
@@ -2950,15 +2950,15 @@ NIL
 NIL 
 (-755 R M) 
 ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) 
-((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-869)))) 
+((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-861)))) 
 (-756 S) 
 ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) 
-((-4502 . T) (-4492 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+((-4425 . T) (-4415 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
 (-757 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-4492 . T) (-4503 . T)) 
+((-4415 . T) (-4426 . T)) 
 NIL 
 (-758) 
 ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) 
@@ -2970,7 +2970,7 @@ NIL
 NIL 
 (-760 |Coef| |Var|) 
 ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4497 . T) (-4496 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4420 . T) (-4419 . T) (-4422 . T)) 
 NIL 
 (-761 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) 
@@ -2986,7 +2986,7 @@ NIL
 NIL 
 (-764 R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
 (-765) 
 ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{\\spad{manpageXXc02}}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre's Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre's Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) 
@@ -3068,11 +3068,11 @@ NIL
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-785 -3572) 
+(-785 -3495) 
 ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) 
 NIL 
 NIL 
-(-786 P -3572) 
+(-786 P -3495) 
 ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) 
 NIL 
 NIL 
@@ -3080,7 +3080,7 @@ NIL
 NIL 
 NIL 
 NIL 
-(-788 UP -3572) 
+(-788 UP -3495) 
 ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) 
 NIL 
 NIL 
@@ -3094,9 +3094,9 @@ NIL
 NIL 
 (-791) 
 ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) 
-(((-4504 "*") . T)) 
+(((-4427 "*") . T)) 
 NIL 
-(-792 R -3572) 
+(-792 R -3495) 
 ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) 
 NIL 
 NIL 
@@ -3116,7 +3116,7 @@ NIL
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) 
 NIL 
 NIL 
-(-797 -3572 |ExtF| |SUEx| |ExtP| |n|) 
+(-797 -3495 |ExtF| |SUEx| |ExtP| |n|) 
 ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) 
 NIL 
 NIL 
@@ -3130,12 +3130,12 @@ NIL
 NIL 
 (-800 R |VarSet|) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) 
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+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
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 (-801 R) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4498 |has| |#1| (-376)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
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 (-802 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) 
 NIL 
@@ -3146,12 +3146,12 @@ NIL
 ((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) 
 (-804 R E V P) 
 ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
 (-805 S) 
 ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1078))) (|HasCategory| |#1| (QUOTE (-175)))) 
+((-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-175)))) 
 (-806) 
 ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) 
 NIL 
@@ -3199,10 +3199,10 @@ NIL
 (-817 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1089))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-381)))) 
+((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-381)))) 
 (-818 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 (-819) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
@@ -3210,9 +3210,9 @@ NIL
 NIL 
 (-820 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-4034 (|HasCategory| (-1025 |#1|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-1025 |#1|) (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1089))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1025 |#1|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1025 |#1|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) 
-(-821 -4034 R OS S) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-3957 (|HasCategory| (-1017 |#1|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-1017 |#1|) (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1017 |#1|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1017 |#1|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) 
+(-821 -3957 R OS S) 
 ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
@@ -3220,11 +3220,11 @@ NIL
 ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-823 R -3572 L) 
+(-823 R -3495 L) 
 ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-824 R -3572) 
+(-824 R -3495) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
@@ -3232,7 +3232,7 @@ NIL
 ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE's.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) 
 NIL 
 NIL 
-(-826 R -3572) 
+(-826 R -3495) 
 ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) 
 NIL 
 NIL 
@@ -3240,11 +3240,11 @@ NIL
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) 
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-(-828 -3572 UP UPUP R) 
+(-828 -3495 UP UPUP R) 
 ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) 
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-(-829 -3572 UP L LQ) 
+(-829 -3495 UP L LQ) 
 ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) 
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@@ -3252,41 +3252,41 @@ NIL
 ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
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-(-831 -3572 UP L LQ) 
+(-831 -3495 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) 
 NIL 
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-(-832 -3572 UP) 
+(-832 -3495 UP) 
 ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) 
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-(-833 -3572 L UP A LO) 
+(-833 -3495 L UP A LO) 
 ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) 
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-(-834 -3572 UP) 
+(-834 -3495 UP) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-835 -3572 LO) 
+(-835 -3495 LO) 
 ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) 
 NIL 
 NIL 
-(-836 -3572 LODO) 
+(-836 -3495 LODO) 
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-837 -3097 S |f|) 
+(-837 -3020 S |f|) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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+((|HasCategory| |#1| (QUOTE (-929))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-840 (-1198)) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-840 (-1198)) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-840 (-1198)) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-840 (-1198)) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-840 (-1198)) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
 (-839 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-4504 "*") |has| |#2| (-376)) (-4495 |has| |#2| (-376)) (-4500 |has| |#2| (-376)) (-4494 |has| |#2| (-376)) (-4499 . T) (-4497 . T) (-4496 . T)) 
+(((-4427 "*") |has| |#2| (-376)) (-4418 |has| |#2| (-376)) (-4423 |has| |#2| (-376)) (-4417 |has| |#2| (-376)) (-4422 . T) (-4420 . T) (-4419 . T)) 
 ((|HasCategory| |#2| (QUOTE (-376)))) 
 (-840 S) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) 
@@ -3295,1946 +3295,1914 @@ NIL
 (-841 S) 
 ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-869)))) 
+((|HasCategory| |#1| (QUOTE (-861)))) 
 (-842) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-843) 
-((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath XML encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath XML encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath XML encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) 
-NIL 
-NIL 
-(-844) 
-((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) 
-NIL 
-NIL 
-(-845) 
-((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,cd,s)} writes the symbol \\axiom{\\spad{s}} from CD \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,mode,enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \"r\",{} \"w\" or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) 
-NIL 
-NIL 
-(-846) 
-((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath XML encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) 
-NIL 
-NIL 
-(-847) 
-((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) 
-NIL 
-NIL 
-(-848) 
-((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown CD or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown CD error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) 
-NIL 
-NIL 
-(-849 R) 
-((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) 
-NIL 
-NIL 
-(-850 P R) 
+(-843 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-240)))) 
-(-851) 
-((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from CD \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the CDs supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) 
-NIL 
-NIL 
-(-852 S) 
+(-844 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-4502 . T) (-4492 . T) (-4503 . T)) 
+((-4425 . T) (-4415 . T) (-4426 . T)) 
 NIL 
-(-853 R) 
+(-845 R) 
 ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) 
-((-4499 |has| |#1| (-868))) 
-((|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (QUOTE (-21))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-868)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4034 (|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) 
-(-854 R S) 
+((-4422 |has| |#1| (-860))) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3957 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) 
+(-846 R S) 
 ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) 
 NIL 
 NIL 
-(-855 R) 
+(-847 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) 
+((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) 
-(-856 A S) 
+(-848 A S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-857 S) 
+(-849 S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-858) 
+(-850) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) 
 NIL 
 NIL 
-(-859) 
+(-851) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) 
 NIL 
 NIL 
-(-860) 
+(-852) 
 ((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-861) 
+(-853) 
 ((|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,start,lower,upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,start,lower,cons,upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information."))) 
 NIL 
 NIL 
-(-862) 
+(-854) 
 ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-863 R) 
+(-855 R) 
 ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-4499 |has| |#1| (-868))) 
-((|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (QUOTE (-21))) (-4034 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-868)))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4034 (|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) 
-(-864 R S) 
+((-4422 |has| |#1| (-860))) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3957 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (-3957 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-557)))) 
+(-856 R S) 
 ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) 
 NIL 
 NIL 
-(-865) 
+(-857) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-866 -3097 S) 
+(-858 -3020 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-867) 
+(-859) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-868) 
+(-860) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
-(-869) 
+(-861) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-870 T$ |f|) 
+(-862 T$ |f|) 
 ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) 
-(-871 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) 
+(-863 S) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-872) 
+(-864) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-873 S R) 
+(-865 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175)))) 
-(-874 R) 
+(-866 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-875 R C) 
+(-867 R C) 
 ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) 
-(-876 R |sigma| -3739) 
+(-868 R |sigma| -3662) 
 ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p, x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-877 |x| R |sigma| -3739) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-376)))) 
+(-869 |x| R |sigma| -3662) 
 ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-376)))) 
-(-878 R) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-376)))) 
+(-870 R) 
 ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) 
 NIL 
 ((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) 
-(-879) 
+(-871) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-880) 
+(-872) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) 
 NIL 
 NIL 
-(-881) 
+(-873) 
 ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) 
 NIL 
 NIL 
-(-882 S) 
+(-874 S) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-883) 
+(-875) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-884) 
+(-876) 
 ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-885) 
+(-877) 
 ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) 
 NIL 
 NIL 
-(-886 |VariableList|) 
+(-878 |VariableList|) 
 ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) 
 NIL 
 NIL 
-(-887) 
+(-879) 
 ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) 
 NIL 
 NIL 
-(-888 R |vl| |wl| |wtlevel|) 
+(-880 R |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) 
-((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) 
+((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-889 R PS UP) 
+(-881 R PS UP) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
 NIL 
 NIL 
-(-890 R |x| |pt|) 
+(-882 R |x| |pt|) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
 NIL 
 NIL 
-(-891 |p|) 
+(-883 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-892 |p|) 
+(-884 |p|) 
 ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-893 |p|) 
+(-885 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-891 |#1|) (QUOTE (-937))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-891 |#1|) (QUOTE (-147))) (|HasCategory| (-891 |#1|) (QUOTE (-149))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-891 |#1|) (QUOTE (-1049))) (|HasCategory| (-891 |#1|) (QUOTE (-842))) (|HasCategory| (-891 |#1|) (QUOTE (-869))) (-4034 (|HasCategory| (-891 |#1|) (QUOTE (-842))) (|HasCategory| (-891 |#1|) (QUOTE (-869)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-891 |#1|) (QUOTE (-1181))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-891 |#1|) (QUOTE (-239))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-891 |#1|) (QUOTE (-240))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -526) (QUOTE (-1206)) (|%list| (QUOTE -891) (|devaluate| |#1|)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -891) (|devaluate| |#1|)))) (|HasCategory| (-891 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -891) (|devaluate| |#1|)) (|%list| (QUOTE -891) (|devaluate| |#1|)))) (|HasCategory| (-891 |#1|) (QUOTE (-319))) (|HasCategory| (-891 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-891 |#1|) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-891 |#1|) (QUOTE (-937)))) (|HasCategory| (-891 |#1|) (QUOTE (-147))))) 
-(-894 |p| PADIC) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-883 |#1|) (QUOTE (-929))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-883 |#1|) (QUOTE (-147))) (|HasCategory| (-883 |#1|) (QUOTE (-149))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-883 |#1|) (QUOTE (-1041))) (|HasCategory| (-883 |#1|) (QUOTE (-842))) (|HasCategory| (-883 |#1|) (QUOTE (-861))) (-3957 (|HasCategory| (-883 |#1|) (QUOTE (-842))) (|HasCategory| (-883 |#1|) (QUOTE (-861)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-883 |#1|) (QUOTE (-1173))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| (-883 |#1|) (QUOTE (-239))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-883 |#1|) (QUOTE (-240))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -526) (QUOTE (-1198)) (|%list| (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -883) (|devaluate| |#1|)) (|%list| (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (QUOTE (-319))) (|HasCategory| (-883 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-883 |#1|) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-883 |#1|) (QUOTE (-929)))) (|HasCategory| (-883 |#1|) (QUOTE (-147))))) 
+(-886 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-869))) (-4034 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-869)))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1181))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
-(-895 S T$) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-861))) (-3957 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
+(-887 S T$) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))))) 
-(-896) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-1122))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))))) 
+(-888) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) 
 NIL 
 NIL 
-(-897) 
+(-889) 
 ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) 
 NIL 
 NIL 
-(-898) 
+(-890) 
 ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) 
 NIL 
 NIL 
-(-899 CF1 CF2) 
+(-891 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-900 |ComponentFunction|) 
+(-892 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) 
 NIL 
 NIL 
-(-901 CF1 CF2) 
+(-893 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-902 |ComponentFunction|) 
+(-894 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) 
 NIL 
 NIL 
-(-903) 
+(-895) 
 ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) 
 NIL 
 NIL 
-(-904 CF1 CF2) 
+(-896 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-905 |ComponentFunction|) 
+(-897 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) 
 NIL 
 NIL 
-(-906) 
+(-898) 
 ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) 
 NIL 
 NIL 
-(-907 R) 
+(-899 R) 
 ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) 
 NIL 
 NIL 
-(-908 R S L) 
+(-900 R S L) 
 ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-909 S) 
+(-901 S) 
 ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) 
 NIL 
 NIL 
-(-910 |Base| |Subject| |Pat|) 
+(-902 |Base| |Subject| |Pat|) 
 ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) 
 NIL 
-((-12 (-3036 (|HasCategory| |#2| (QUOTE (-1078)))) (-3036 (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206)))))) (-12 (|HasCategory| |#2| (QUOTE (-1078))) (-3036 (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206))))) 
-(-911 R S) 
+((-12 (-2959 (|HasCategory| |#2| (QUOTE (-1070)))) (-2959 (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198)))))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (-2959 (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198)))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198))))) 
+(-903 R S) 
 ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(vn,{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-912 R A B) 
+(-904 R A B) 
 ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) 
 NIL 
 NIL 
-(-913 R) 
+(-905 R) 
 ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) 
 NIL 
 NIL 
-(-914 R -3147) 
+(-906 R -3070) 
 ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) 
 NIL 
 NIL 
-(-915 R S) 
+(-907 R S) 
 ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) 
 NIL 
 NIL 
-(-916 |VarSet|) 
+(-908 |VarSet|) 
 ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) 
 NIL 
 NIL 
-(-917 UP R) 
+(-909 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-918 A T$ S) 
+(-910 A T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-919 T$ S) 
+(-911 T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-920) 
+(-912) 
 ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-921 UP -3572) 
+(-913 UP -3495) 
 ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) 
 NIL 
 NIL 
-(-922) 
+(-914) 
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline ** At the moment,{} only Second Order Elliptic Partial Differential Equations are solved **"))) 
 NIL 
 NIL 
-(-923) 
+(-915) 
 ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-924 R S) 
+(-916 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
-(-925 S) 
+(-917 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
-(-926 A S) 
+(-918 A S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-927 S) 
+(-919 S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-928 S) 
+(-920 S) 
 ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-929 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-921 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-4499 . T)) 
-((-4034 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-869)))) 
-(-930 |n| R) 
+((-4422 . T)) 
+((-3957 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-861)))) 
+(-922 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) 
 NIL 
 NIL 
-(-931 S) 
+(-923 S) 
 ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
-(-932 S) 
+(-924 S) 
 ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
 NIL 
 NIL 
-(-933 |p|) 
+(-925 |p|) 
 ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 ((|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-381)))) 
-(-934 R E |VarSet| S) 
+(-926 R E |VarSet| S) 
 ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-935 R S) 
+(-927 R S) 
 ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-936 S) 
+(-928 S) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-147)))) 
-(-937) 
+(-929) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-938 R0 -3572 UP UPUP R) 
+(-930 R0 -3495 UP UPUP R) 
 ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) 
 NIL 
 NIL 
-(-939 UP UPUP R) 
+(-931 UP UPUP R) 
 ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) 
 NIL 
 NIL 
-(-940 UP UPUP) 
+(-932 UP UPUP) 
 ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) 
 NIL 
 NIL 
-(-941 R) 
+(-933 R) 
 ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-942 R) 
+(-934 R) 
 ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) 
 NIL 
 NIL 
-(-943 E OV R P) 
+(-935 E OV R P) 
 ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-944) 
+(-936) 
 ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube:   +-----+ +-- B   where: marks Side # :               / U   /|/              /     / |         F(ront)    <->    1      L -->  +-----+ R|         R(ight)    <->    2             |     |  +         U(p)       <->    3             |  F  | /          D(own)     <->    4             |     |/           L(eft)     <->    5             +-----+            B(ack)     <->    6                ^                |                DThe Cube's surface:                               The pieces on each side            +---+              (except the unmoveable center            |567|              piece) are clockwise numbered            |4U8|              from 1 to 8 starting with the            |321|              piece in the upper left        +---+---+---+          corner (see figure on the        |781|123|345|          left).  The moves of the cube        |6L2|8F4|2R6|          are represented as        |543|765|187|          permutations on these pieces.        +---+---+---+          Each of the pieces is            |123|              represented as a two digit            |8D4|              integer ij where i is the            |765|              # of the side ( 1 to 6 for            +---+              F to B (see table above ))            |567|              and j is the # of the piece.            |4B8|            |321|            +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) 
 NIL 
 NIL 
-(-945 -3572) 
+(-937 -3495) 
 ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) 
 NIL 
 NIL 
-(-946) 
+(-938) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4504 "*") . T)) 
+(((-4427 "*") . T)) 
 NIL 
-(-947 R) 
+(-939 R) 
 ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) 
 NIL 
 NIL 
-(-948) 
+(-940) 
 ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-949 |xx| -3572) 
+(-941 |xx| -3495) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) 
 NIL 
 NIL 
-(-950 -3572 P) 
+(-942 -3495 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-951 R |Var| |Expon| GR) 
+(-943 R |Var| |Expon| GR) 
 ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank >= \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} ~= 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) 
 NIL 
 NIL 
-(-952) 
+(-944) 
 ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) 
 NIL 
 NIL 
-(-953 S) 
+(-945 S) 
 ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> SF are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) 
 NIL 
 NIL 
-(-954) 
+(-946) 
 ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) 
 NIL 
 NIL 
-(-955) 
+(-947) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-956) 
+(-948) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) 
 NIL 
 NIL 
-(-957 R -3572) 
+(-949 R -3495) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-958 S A B) 
+(-950 S A B) 
 ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) 
 NIL 
 NIL 
-(-959 S R -3572) 
+(-951 S R -3495) 
 ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-960 I) 
+(-952 I) 
 ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-961 S E) 
+(-953 S E) 
 ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-962 S R L) 
+(-954 S R L) 
 ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-963 S E V R P) 
+(-955 S E V R P) 
 ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -909) (|devaluate| |#1|)))) 
-(-964 -3147) 
+((|HasCategory| |#3| (|%list| (QUOTE -901) (|devaluate| |#1|)))) 
+(-956 -3070) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
-(-965 R -3572 -3147) 
+(-957 R -3495 -3070) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-966 S R Q) 
+(-958 S R Q) 
 ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-967 S) 
+(-959 S) 
 ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) 
 NIL 
 NIL 
-(-968 S R P) 
+(-960 S R P) 
 ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) 
 NIL 
 NIL 
-(-969) 
+(-961) 
 ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = n E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = n B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) 
 NIL 
 NIL 
-(-970 R) 
+(-962 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-971 |lv| R) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-963 |lv| R) 
 ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) 
 NIL 
 NIL 
-(-972 |TheField| |ThePols|) 
+(-964 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@sn,{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}p')}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-868)))) 
-(-973 R) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-965 R) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1206) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1206) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1206) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1206) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1206) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
-(-974 R S) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-929))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-1198) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-1198) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-1198) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-1198) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1198) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-966 R S) 
 ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-975 |x| R) 
+(-967 |x| R) 
 ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) 
 NIL 
 NIL 
-(-976 S R E |VarSet|) 
+(-968 S R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-937))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) 
-(-977 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-929))) (|HasAttribute| |#2| (QUOTE -4423)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#4| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#4| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) 
+(-969 R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
 NIL 
-(-978 E V R P -3572) 
+(-970 E V R P -3495) 
 ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-979 E |Vars| R P S) 
+(-971 E |Vars| R P S) 
 ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) 
 NIL 
 NIL 
-(-980 E V R P -3572) 
+(-972 E V R P -3495) 
 ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-464)))) 
-(-981) 
+(-973) 
 ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) 
 NIL 
 NIL 
-(-982) 
+(-974) 
 ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-983 R E) 
+(-975 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4500))) 
-(-984 R L) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4423))) 
+(-976 R L) 
 ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) 
 NIL 
 NIL 
-(-985 S) 
+(-977 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-986 A B) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-978 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
 NIL 
 NIL 
-(-987) 
+(-979) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) 
 NIL 
 NIL 
-(-988 -3572) 
+(-980 -3495) 
 ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) 
 NIL 
 NIL 
-(-989 I) 
+(-981 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) 
 NIL 
 NIL 
-(-990) 
+(-982) 
 ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) 
 NIL 
 NIL 
-(-991 A B) 
+(-983 A B) 
 ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) 
-((-4499 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-869))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746))))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-869))))) 
-(-992) 
+((-4422 -12 (|has| |#2| (-485)) (|has| |#1| (-485)))) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746))))) (-12 (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-746)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) 
+(-984) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-993 T$) 
+(-985 T$) 
 ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-994 T$) 
+(-986 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-995 S T$) 
+(-987 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-996) 
+(-988) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-997 S) 
+(-989 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) 
-((-4502 . T) (-4503 . T)) 
+((-4425 . T) (-4426 . T)) 
 NIL 
-(-998 R |polR|) 
+(-990 R |polR|) 
 ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.fr}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the gcd of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-464)))) 
-(-999) 
+(-991) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-1000) 
+(-992) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) 
 NIL 
 NIL 
-(-1001 S |Coef| |Expon| |Var|) 
+(-993 S |Coef| |Expon| |Var|) 
 ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) 
 NIL 
 NIL 
-(-1002 |Coef| |Expon| |Var|) 
+(-994 |Coef| |Expon| |Var|) 
 ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1003) 
+(-995) 
 ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-1004 S R E |VarSet| P) 
+(-996 S R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-569)))) 
-(-1005 R E |VarSet| P) 
+(-997 R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((-4502 . T)) 
+((-4425 . T)) 
 NIL 
-(-1006 R E V P) 
+(-998 R E V P) 
 ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-464)))) 
-(-1007 K) 
+(-999 K) 
 ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) 
 NIL 
 NIL 
-(-1008 |VarSet| E RC P) 
+(-1000 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) 
 NIL 
 NIL 
-(-1009 R) 
+(-1001 R) 
 ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
-(-1010 R1 R2) 
+(-1002 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-1011 R) 
+(-1003 R) 
 ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) 
 NIL 
 NIL 
-(-1012 K) 
+(-1004 K) 
 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-1013 R E OV PPR) 
+(-1005 R E OV PPR) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-1014 K R UP -3572) 
+(-1006 K R UP -3495) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) 
 NIL 
 NIL 
-(-1015 R |Var| |Expon| |Dpoly|) 
+(-1007 R |Var| |Expon| |Dpoly|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-319))))) 
-(-1016 |vl| |nv|) 
+(-1008 |vl| |nv|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) 
 NIL 
 NIL 
-(-1017 R E V P TS) 
+(-1009 R E V P TS) 
 ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1018) 
+(-1010) 
 ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) 
 NIL 
 NIL 
-(-1019 A S) 
+(-1011 A S) 
 ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1181)))) 
-(-1020 S) 
+((|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1041))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1173)))) 
+(-1012 S) 
 ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1021 A B R S) 
+(-1013 A B R S) 
 ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) 
 NIL 
 NIL 
-(-1022 |n| K) 
+(-1014 |n| K) 
 ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-1023) 
+(-1015) 
 ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) 
 NIL 
 NIL 
-(-1024 S) 
+(-1016 S) 
 ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) 
-((-4502 . T) (-4503 . T)) 
+((-4425 . T) (-4426 . T)) 
 NIL 
-(-1025 R) 
+(-1017 R) 
 ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) 
-((-4495 |has| |#1| (-302)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1089))) (|HasCategory| |#1| (QUOTE (-557)))) 
-(-1026 S R) 
+((-4418 |has| |#1| (-302)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (|%list| (QUOTE -526) (QUOTE (-1198)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557)))) 
+(-1018 S R) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1089))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-302)))) 
-(-1027 R) 
+((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-302)))) 
+(-1019 R) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-4495 |has| |#1| (-302)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 |has| |#1| (-302)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1028 QR R QS S) 
+(-1020 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-1029 S) 
+(-1021 S) 
 ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-1030 S) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1022 S) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-1031) 
+(-1023) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-1032 -3572 UP UPUP |radicnd| |n|) 
+(-1024 -3495 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-4495 |has| (-419 |#2|) (-376)) (-4500 |has| (-419 |#2|) (-376)) (-4494 |has| (-419 |#2|) (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-4034 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206)))))) (-4034 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -927) (QUOTE (-1206)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-4034 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -927) (QUOTE (-1206))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -925) (QUOTE (-1206)))))) 
-(-1033 |bb|) 
+((-4418 |has| (-419 |#2|) (-376)) (-4423 |has| (-419 |#2|) (-376)) (-4417 |has| (-419 |#2|) (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-419 |#2|) (QUOTE (-147))) (|HasCategory| (-419 |#2|) (QUOTE (-149))) (|HasCategory| (-419 |#2|) (QUOTE (-363))) (-3957 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (QUOTE (-381))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (QUOTE (-363)))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-363))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198)))))) (-3957 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -919) (QUOTE (-1198)))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -658) (QUOTE (-558)))) (-3957 (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-239))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-240))) (|HasCategory| (-419 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-376))) (|HasCategory| (-419 |#2|) (|%list| (QUOTE -917) (QUOTE (-1198)))))) 
+(-1025 |bb|) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-558) (QUOTE (-937))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1049))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869))) (-4034 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-869)))) (|HasCategory| (-558) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1181))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1206)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (-4034 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-937)))) (|HasCategory| (-558) (QUOTE (-147))))) 
-(-1034) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-558) (QUOTE (-929))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-149))) (|HasCategory| (-558) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-1041))) (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861))) (-3957 (|HasCategory| (-558) (QUOTE (-842))) (|HasCategory| (-558) (QUOTE (-861)))) (|HasCategory| (-558) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1173))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-558) (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-558) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-239))) (|HasCategory| (-558) (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| (-558) (QUOTE (-240))) (|HasCategory| (-558) (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| (-558) (|%list| (QUOTE -526) (QUOTE (-1198)) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -321) (QUOTE (-558)))) (|HasCategory| (-558) (|%list| (QUOTE -298) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-319))) (|HasCategory| (-558) (QUOTE (-557))) (|HasCategory| (-558) (|%list| (QUOTE -658) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-558) (QUOTE (-929)))) (|HasCategory| (-558) (QUOTE (-147))))) 
+(-1026) 
 ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) 
 NIL 
 NIL 
-(-1035) 
+(-1027) 
 ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) 
 NIL 
 NIL 
-(-1036 RP) 
+(-1028 RP) 
 ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) 
 NIL 
 NIL 
-(-1037 S) 
+(-1029 S) 
 ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) 
 NIL 
 NIL 
-(-1038 A S) 
+(-1030 A S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-1130)))) 
-(-1039 S) 
+((|HasAttribute| |#1| (QUOTE -4426)) (|HasCategory| |#2| (QUOTE (-1122)))) 
+(-1031 S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
 NIL 
-(-1040 S) 
+(-1032 S) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
 NIL 
 NIL 
-(-1041) 
+(-1033) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
-((-4495 . T) (-4500 . T) (-4494 . T) (-4497 . T) (-4496 . T) ((-4504 "*") . T) (-4499 . T)) 
+((-4418 . T) (-4423 . T) (-4417 . T) (-4420 . T) (-4419 . T) ((-4427 "*") . T) (-4422 . T)) 
 NIL 
-(-1042 R -3572) 
+(-1034 R -3495) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) 
 NIL 
 NIL 
-(-1043 R -3572) 
+(-1035 R -3495) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) 
 NIL 
 NIL 
-(-1044 -3572 UP) 
+(-1036 -3495 UP) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-1045 -3572 UP) 
+(-1037 -3495 UP) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-1046 S) 
+(-1038 S) 
 ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-1047 F1 UP UPUP R F2) 
+(-1039 F1 UP UPUP R F2) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) 
 NIL 
 NIL 
-(-1048) 
+(-1040) 
 ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) 
 NIL 
 NIL 
-(-1049) 
+(-1041) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-1050 |Pol|) 
+(-1042 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-1051 |Pol|) 
+(-1043 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-1052) 
+(-1044) 
 ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) 
 NIL 
 NIL 
-(-1053 |TheField|) 
+(-1045 |TheField|) 
 ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) 
-((-4495 . T) (-4500 . T) (-4494 . T) (-4497 . T) (-4496 . T) ((-4504 "*") . T) (-4499 . T)) 
-((-4034 (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1067) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1067) (QUOTE (-558))))) 
-(-1054 -3572 L) 
+((-4418 . T) (-4423 . T) (-4417 . T) (-4420 . T) (-4419 . T) ((-4427 "*") . T) (-4422 . T)) 
+((-3957 (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-419 (-558)) (|%list| (QUOTE -1059) (QUOTE (-558))))) 
+(-1046 -3495 L) 
 ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) 
 NIL 
 NIL 
-(-1055 S) 
+(-1047 S) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,m)} same as \\spad{setelt(n,m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1130)))) 
-(-1056 R E V P) 
+((|HasCategory| |#1| (QUOTE (-1122)))) 
+(-1048 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1057) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1049) 
 ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 <= \\spad{i} <= \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 <= \\spad{i} <= \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) 
 NIL 
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 ((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker's fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker's fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton's irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) 
 NIL 
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 ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) 
 NIL 
 NIL 
-(-1063 -3572 |Expon| |VarSet| |FPol| |LFPol|) 
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 ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) 
-(((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
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 ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) 
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-(-1065) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1198))) (|%list| (QUOTE |:|) (QUOTE -2286) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-861))) (|HasCategory| (-51) (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102)))) 
+(-1057) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-1066 A S) 
+(-1058 A S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-1067 S) 
+(-1059 S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-1068 Q R) 
+(-1060 Q R) 
 ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) 
 NIL 
 NIL 
-(-1069 R) 
+(-1061 R) 
 ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-1070) 
+(-1062) 
 ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) 
 NIL 
 NIL 
-(-1071 UP) 
+(-1063 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-1072 R) 
+(-1064 R) 
 ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) 
 NIL 
 NIL 
-(-1073 T$) 
+(-1065 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) 
 NIL 
 NIL 
-(-1074 T$) 
+(-1066 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) 
 NIL 
 NIL 
-(-1075 R |ls|) 
+(-1067 R |ls|) 
 ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| (-800 |#1| (-886 |#2|)) (QUOTE (-1130))) (|HasCategory| (-800 |#1| (-886 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -800) (|devaluate| |#1|) (|%list| (QUOTE -886) (|devaluate| |#2|)))))) (|HasCategory| (-800 |#1| (-886 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-800 |#1| (-886 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-886 |#2|) (QUOTE (-381))) (|HasCategory| (-800 |#1| (-886 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-800 |#1| (-886 |#2|)) (QUOTE (-102)))) 
-(-1076) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| (-800 |#1| (-878 |#2|)) (QUOTE (-1122))) (|HasCategory| (-800 |#1| (-878 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -800) (|devaluate| |#1|) (|%list| (QUOTE -878) (|devaluate| |#2|)))))) (|HasCategory| (-800 |#1| (-878 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-800 |#1| (-878 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-878 |#2|) (QUOTE (-381))) (|HasCategory| (-800 |#1| (-878 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-800 |#1| (-878 |#2|)) (QUOTE (-102)))) 
+(-1068) 
 ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-1077 S) 
+(-1069 S) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
 NIL 
 NIL 
-(-1078) 
+(-1070) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
-((-4499 . T)) 
+((-4422 . T)) 
 NIL 
-(-1079 |xx| -3572) 
+(-1071 |xx| -3495) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-1080 S) 
+(-1072 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-1081 S |m| |n| R |Row| |Col|) 
+(-1073 S |m| |n| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) 
 NIL 
 ((|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-376))) (|HasCategory| |#4| (QUOTE (-569))) (|HasCategory| |#4| (QUOTE (-175)))) 
-(-1082 |m| |n| R |Row| |Col|) 
+(-1074 |m| |n| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) 
-((-4502 . T) (-4497 . T) (-4496 . T)) 
+((-4425 . T) (-4420 . T) (-4419 . T)) 
 NIL 
-(-1083 |m| |n| R) 
+(-1075 |m| |n| R) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) 
-((-4502 . T) (-4497 . T) (-4496 . T)) 
-((|HasCategory| |#3| (QUOTE (-175))) (-4034 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-885))))) 
-(-1084 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-4425 . T) (-4420 . T) (-4419 . T)) 
+((|HasCategory| |#3| (QUOTE (-175))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-877))))) 
+(-1076 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-1085 R) 
+(-1077 R) 
 ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-1086) 
+(-1078) 
 ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) 
 NIL 
 NIL 
-(-1087 S T$) 
+(-1079 S T$) 
 ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1130)))) 
-(-1088 S) 
+((|HasCategory| |#1| (QUOTE (-1122)))) 
+(-1080 S) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-1089) 
+(-1081) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1090 |TheField| |ThePolDom|) 
+(-1082 |TheField| |ThePolDom|) 
 ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-1091) 
+(-1083) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-4490 . T) (-4494 . T) (-4489 . T) (-4500 . T) (-4501 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4413 . T) (-4417 . T) (-4412 . T) (-4423 . T) (-4424 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1092) 
+(-1084) 
 ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (QUOTE (-1206))) (|%list| (QUOTE |:|) (QUOTE -2294) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1130))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-1130))) (|HasCategory| (-1206) (QUOTE (-869))) (|HasCategory| (-51) (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1206)) (|:| -2294 (-51))) (QUOTE (-102)))) 
-(-1093 S R E V) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1198))) (|%list| (QUOTE |:|) (QUOTE -2286) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| (-51) (QUOTE (-1122))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-1122))) (|HasCategory| (-1198) (QUOTE (-861))) (|HasCategory| (-51) (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1198)) (|:| -2286 (-51))) (QUOTE (-102)))) 
+(-1085 S R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1020) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-1206))))) 
-(-1094 R E V) 
+((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (|%list| (QUOTE -38) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1012) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-1198))))) 
+(-1086 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
 NIL 
-(-1095) 
+(-1087) 
 ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) 
 NIL 
 NIL 
-(-1096 S |TheField| |ThePols|) 
+(-1088 S |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-1097 |TheField| |ThePols|) 
+(-1089 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-1098 R E V P TS) 
+(-1090 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1099 S R E V P) 
+(-1091 S R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
 NIL 
 NIL 
-(-1100 R E V P) 
+(-1092 R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
-(-1101 R E V P TS) 
+(-1093 R E V P TS) 
 ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1102) 
+(-1094) 
 ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-1103) 
+(-1095) 
 ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) 
 NIL 
 NIL 
-(-1104 |Base| R -3572) 
+(-1096 |Base| R -3495) 
 ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) 
 NIL 
 NIL 
-(-1105 |f|) 
+(-1097 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1106 |Base| R -3572) 
+(-1098 |Base| R -3495) 
 ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) 
 NIL 
 NIL 
-(-1107 R |ls|) 
+(-1099 R |ls|) 
 ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) 
 NIL 
 NIL 
-(-1108 R UP M) 
+(-1100 R UP M) 
 ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) 
-((-4495 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))))) 
-(-1109 UP SAE UPA) 
+((-4418 |has| |#1| (-376)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))))) 
+(-1101 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-1110 UP SAE UPA) 
+(-1102 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-1111) 
+(-1103) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-1112) 
+(-1104) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-1113 S) 
+(-1105 S) 
 ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) 
 NIL 
 NIL 
-(-1114) 
+(-1106) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) 
 NIL 
 NIL 
-(-1115 R) 
+(-1107 R) 
 ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) 
 NIL 
 NIL 
-(-1116 R) 
+(-1108 R) 
 ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1117 (-1206)) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
-(-1117 S) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-929))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1109 (-1198)) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-1109 S) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) 
 NIL 
 NIL 
-(-1118 S) 
+(-1110 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (QUOTE (-1130)))) 
-(-1119 R S) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1122)))) 
+(-1111 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-868)))) 
-(-1120) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-1112) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1121 S) 
+(-1113 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1118 |#1|) (QUOTE (-1130)))) 
-(-1122 R S) 
+((|HasCategory| (-1110 |#1|) (QUOTE (-1122)))) 
+(-1114 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1123 S) 
+(-1115 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) 
 NIL 
 NIL 
-(-1124 S L) 
+(-1116 S L) 
 ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) 
 NIL 
 NIL 
-(-1125) 
+(-1117) 
 ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) 
 NIL 
 NIL 
-(-1126 S) 
+(-1118 S) 
 ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) 
-((-4502 . T) (-4492 . T) (-4503 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-1127 A S) 
+((-4425 . T) (-4415 . T) (-4426 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-1119 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1128 S) 
+(-1120 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
-((-4492 . T)) 
+((-4415 . T)) 
 NIL 
-(-1129 S) 
+(-1121 S) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1130) 
+(-1122) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1131 |m| |n|) 
+(-1123 |m| |n|) 
 ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) 
 NIL 
 NIL 
-(-1132) 
+(-1124) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1133 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1125 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{a1}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of Flt; Error: if \\spad{s} is not an atom that also belongs to Flt.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Flt.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) 
 NIL 
 NIL 
-(-1134 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1126 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1135 R FS) 
+(-1127 R FS) 
 ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,ftype,body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) 
 NIL 
 NIL 
-(-1136 R E V P TS) 
+(-1128 R E V P TS) 
 ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1137 R E V P TS) 
+(-1129 R E V P TS) 
 ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1138 R E V P) 
+(-1130 R E V P) 
 ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
-(-1139) 
+(-1131) 
 ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) 
 NIL 
 NIL 
-(-1140 S) 
+(-1132 S) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1141) 
+(-1133) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1142 |dimtot| |dim1| S) 
+(-1134 |dimtot| |dim1| S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(|HasCategory| |#3| (|%list| (QUOTE -919) (QUOTE (-1198))))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#3| (QUOTE (-1122))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1070)))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-746))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558)))))) (|HasCategory| (-558) (QUOTE (-861))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -919) (QUOTE (-1198))))) (-3957 (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasAttribute| |#3| (QUOTE -4422)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1070)))) (-12 (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1122))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) 
+(-1135 R |x|) 
 ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-464)))) 
-(-1144) 
+(-1136) 
 ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) 
 NIL 
 NIL 
-(-1145) 
+(-1137) 
 ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) 
 NIL 
 NIL 
-(-1146 R -3572) 
+(-1138 R -3495) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1147 R) 
+(-1139 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1148) 
+(-1140) 
 ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) 
 NIL 
 NIL 
-(-1149) 
+(-1141) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) 
-((-4490 . T) (-4494 . T) (-4489 . T) (-4500 . T) (-4501 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4413 . T) (-4417 . T) (-4412 . T) (-4423 . T) (-4424 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1150 S) 
+(-1142 S) 
 ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-4502 . T) (-4503 . T)) 
+((-4425 . T) (-4426 . T)) 
 NIL 
-(-1151 S |ndim| R |Row| |Col|) 
+(-1143 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4504 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) 
-(-1152 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-376))) (|HasAttribute| |#3| (QUOTE (-4427 "*"))) (|HasCategory| |#3| (QUOTE (-175)))) 
+(-1144 |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
-((-4502 . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4425 . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1153 R |Row| |Col| M) 
+(-1145 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-1154 R |VarSet|) 
+(-1146 R |VarSet|) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-937))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-4034 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
-(-1155 |Coef| |Var| SMP) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-929))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-929)))) (-3957 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -901) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#1| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4423)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-1147 |Coef| |Var| SMP) 
 ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-1156 R E V P) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) 
+(-1148 R E V P) 
 ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
-(-1157 UP -3572) 
+(-1149 UP -3495) 
 ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) 
 NIL 
 NIL 
-(-1158 R) 
+(-1150 R) 
 ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) 
 NIL 
 NIL 
-(-1159 R) 
+(-1151 R) 
 ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) 
 NIL 
 NIL 
-(-1160 R) 
+(-1152 R) 
 ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) 
 NIL 
 NIL 
-(-1161 S A) 
+(-1153 S A) 
 ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-869)))) 
-(-1162 R) 
+((|HasCategory| |#1| (QUOTE (-861)))) 
+(-1154 R) 
 ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) 
 NIL 
 NIL 
-(-1163 R) 
+(-1155 R) 
 ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1164) 
+(-1156) 
 ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) 
 NIL 
 NIL 
-(-1165) 
+(-1157) 
 ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) 
 NIL 
 NIL 
-(-1166) 
+(-1158) 
 ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) 
 NIL 
 NIL 
-(-1167) 
+(-1159) 
 ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) 
 NIL 
 NIL 
-(-1168) 
+(-1160) 
 ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) 
 NIL 
 NIL 
-(-1169 V C) 
+(-1161 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) 
 NIL 
 NIL 
-(-1170 V C) 
+(-1162 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| (-1169 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-1130)))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-1130))) (-4034 (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| (-1169 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-1130)))) (|HasCategory| (-1169 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| (-1169 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-1169 |#1| |#2|) (QUOTE (-102)))) 
-(-1171 |ndim| R) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| (-1161 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1122)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1122))) (-3957 (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| (-1161 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1122)))) (|HasCategory| (-1161 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| (-1161 |#1| |#2|) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102)))) 
+(-1163 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) 
-((-4499 . T) (-4491 |has| |#2| (-6 (-4504 "*"))) (-4502 . T) (-4496 . T) (-4497 . T)) 
-((|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4504 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-376))) (-4034 (|HasAttribute| |#2| (QUOTE (-4504 "*"))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) 
-(-1172 S) 
+((-4422 . T) (-4414 |has| |#2| (-6 (-4427 "*"))) (-4425 . T) (-4419 . T) (-4420 . T)) 
+((|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4427 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1059) (QUOTE (-558)))) (-3957 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))))) (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-376))) (-3957 (|HasAttribute| |#2| (QUOTE (-4427 "*"))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198))))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) 
+(-1164 S) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1173) 
+(-1165) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
-(-1174 R E V P TS) 
+(-1166 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1175 R E V P) 
+(-1167 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1176) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1168) 
 ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) 
 NIL 
 NIL 
-(-1177 S) 
+(-1169 S) 
 ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-1178 A S) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1170 A S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
 NIL 
-(-1179 S) 
+(-1171 S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
 NIL 
-(-1180 |Key| |Ent| |dent|) 
+(-1172 |Key| |Ent| |dent|) 
 ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 
-((-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) 
-(-1181) 
+((-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) 
+(-1173) 
 ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}'s are never \\spad{nothing}.}")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
 NIL 
-(-1182) 
+(-1174) 
 ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1183 |Coef|) 
+(-1175 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1184 S) 
+(-1176 S) 
 ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) 
-((-4503 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-1185 S) 
+((-4426 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1177 S) 
 ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) 
 NIL 
 NIL 
-(-1186 A B) 
+(-1178 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) 
 NIL 
 NIL 
-(-1187 A B C) 
+(-1179 A B C) 
 ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) 
 NIL 
 NIL 
-(-1188) 
+(-1180) 
 ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-4034 (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130)))) (|HasCategory| (-146) (QUOTE (-869))) (-4034 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1130))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
-(-1189 |Entry|) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-3957 (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| (-146) (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122)))) (|HasCategory| (-146) (QUOTE (-861))) (-3957 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1122))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) 
+(-1181 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (QUOTE (-1188))) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-1130))) (|HasCategory| (-1188) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 (-1188)) (|:| -2294 |#1|)) (QUOTE (-102)))) 
-(-1190 A) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (QUOTE (-1180))) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-1122))) (|HasCategory| (-1180) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 (-1180)) (|:| -2286 |#1|)) (QUOTE (-102)))) 
+(-1182 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) 
-(-1191 |Coef|) 
+(-1183 |Coef|) 
 ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 
 NIL 
 NIL 
-(-1192 |Coef|) 
+(-1184 |Coef|) 
 ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 
 NIL 
 NIL 
-(-1193 R UP) 
+(-1185 R UP) 
 ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-319)))) 
-(-1194 |n| R) 
+(-1186 |n| R) 
 ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-1195 S1 S2) 
+(-1187 S1 S2) 
 ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form s:t"))) 
 NIL 
 NIL 
-(-1196) 
+(-1188) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1197 |Coef| |var| |cen|) 
+(-1189 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
-(((-4504 "*") -4034 (-3038 (|has| |#1| (-376)) (|has| (-1204 |#1| |#2| |#3|) (-842))) (|has| |#1| (-175)) (-3038 (|has| |#1| (-376)) (|has| (-1204 |#1| |#2| |#3|) (-937)))) (-4495 -4034 (-3038 (|has| |#1| (-376)) (|has| (-1204 |#1| |#2| |#3|) (-842))) (|has| |#1| (-569)) (-3038 (|has| |#1| (-376)) (|has| (-1204 |#1| |#2| |#3|) (-937)))) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1204 |#1| |#2| |#3|) (QUOTE (-842)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1204 |#1| |#2| |#3|) (QUOTE (-937)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1204 |#1| |#2| |#3|) (|%list| (QUOTE -631) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1204 |#1| |#2| |#3|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1204 |#1| |#2| |#3|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1204 |#1| |#2| |#3|) (|%list| (QUOTE -298) (|%list| (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1204 |#1| |#2| |#3|) (|%list| (QUOTE -321) (|%list| (QUOTE -1204) 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-38) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-842)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-175)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1196 |#1| |#2| |#3|) (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-239)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-861)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-929)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-147)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-1196 |#1| |#2| |#3|) (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-1190 R -3495) 
 ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 
 NIL 
 NIL 
-(-1199 R) 
+(-1191 R) 
 ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) 
 NIL 
 NIL 
-(-1200 R) 
+(-1192 R) 
 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
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-(-1201 R S) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4421 |has| |#1| (-376)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
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+(-1193 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1202 E OV R P) 
+(-1194 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) 
 NIL 
 NIL 
-(-1203 |Coef| |var| |cen|) 
+(-1195 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) 
-(-1204 |Coef| |var| |cen|) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
+(-1196 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|)))) (|HasCategory| (-791) (QUOTE (-1141))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) 
-(-1205) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|)))) (|HasCategory| (-791) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
+(-1197) 
 ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-1206) 
+(-1198) 
 ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) 
 NIL 
 NIL 
-(-1207 R) 
+(-1199 R) 
 ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) 
 NIL 
 NIL 
-(-1208 R) 
+(-1200 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-6 -4500)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-4034 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-1000) (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4500))) 
-(-1209) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-6 -4423)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-3957 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-992) (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4423))) 
+(-1201) 
 ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 
 NIL 
 NIL 
-(-1210) 
+(-1202) 
 ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) 
 NIL 
 NIL 
-(-1211) 
+(-1203) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1212 N) 
+(-1204 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1213 N) 
+(-1205 N) 
 ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) 
 NIL 
 NIL 
-(-1214) 
+(-1206) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1215 R) 
+(-1207 R) 
 ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) 
 NIL 
 NIL 
-(-1216) 
+(-1208) 
 ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) 
 NIL 
 NIL 
-(-1217 S) 
+(-1209 S) 
 ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) 
 NIL 
 NIL 
-(-1218 |Key| |Entry|) 
+(-1210 |Key| |Entry|) 
 ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) 
-((-4502 . T) (-4503 . T)) 
-((-12 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4367) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2294) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#2| (QUOTE (-1130))) (-4034 (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885))))) (-4034 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4367 |#1|) (|:| -2294 |#2|)) (QUOTE (-102)))) 
-(-1219 S) 
+((-4425 . T) (-4426 . T)) 
+((-12 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -4290) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2286) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -631) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1122))) (-3957 (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877))))) (-3957 (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (QUOTE (-102)))) 
+(-1211 S) 
 ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) 
 NIL 
 NIL 
-(-1220 S) 
+(-1212 S) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) 
 NIL 
 NIL 
-(-1221 R) 
+(-1213 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) 
 NIL 
 NIL 
-(-1222 S |Key| |Entry|) 
+(-1214 S |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
 NIL 
 NIL 
-(-1223 |Key| |Entry|) 
+(-1215 |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
-((-4503 . T)) 
+((-4426 . T)) 
 NIL 
-(-1224 |Key| |Entry|) 
+(-1216 |Key| |Entry|) 
 ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) 
 NIL 
 NIL 
-(-1225) 
+(-1217) 
 ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) 
 NIL 
 NIL 
-(-1226) 
+(-1218) 
 ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) 
 NIL 
 NIL 
-(-1227 S) 
+(-1219 S) 
 ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) 
 NIL 
 NIL 
-(-1228) 
+(-1220) 
 ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) 
 NIL 
 NIL 
-(-1229 R) 
+(-1221 R) 
 ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-1230) 
+(-1222) 
 ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1231 S) 
+(-1223 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1232) 
+(-1224) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1233 S) 
+(-1225 S) 
 ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) 
-(-1234 S) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1122))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1122)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102)))) 
+(-1226 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1235) 
+(-1227) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1236 R -3572) 
+(-1228 R -3495) 
 ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
-(-1237 R |Row| |Col| M) 
+(-1229 R |Row| |Col| M) 
 ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) 
 NIL 
 NIL 
-(-1238 R -3572) 
+(-1230 R -3495) 
 ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) 
 NIL 
-((-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -909) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -909) (|devaluate| |#1|))))) 
-(-1239 |Coef|) 
+((-12 (|HasCategory| |#1| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -901) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -901) (|devaluate| |#1|))))) 
+(-1231 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-1240 S R E V P) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-376)))) 
+(-1232 S R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
 NIL 
 ((|HasCategory| |#4| (QUOTE (-381)))) 
-(-1241 R E V P) 
+(-1233 R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
-(-1242 |Curve|) 
+(-1234 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) 
 NIL 
 NIL 
-(-1243) 
+(-1235) 
 ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) 
 NIL 
 NIL 
-(-1244 S) 
+(-1236 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) 
-(-1245 -3572) 
+((|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) 
+(-1237 -3495) 
 ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) 
 NIL 
 NIL 
-(-1246) 
+(-1238) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1247) 
+(-1239) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1248 S) 
+(-1240 S) 
 ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-869)))) 
-(-1249) 
+((|HasCategory| |#1| (QUOTE (-861)))) 
+(-1241) 
 ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) 
 NIL 
 NIL 
-(-1250 S) 
+(-1242 S) 
 ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
 NIL 
 NIL 
-(-1251) 
+(-1243) 
 ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1252) 
+(-1244) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1253) 
+(-1245) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1254) 
+(-1246) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1255) 
+(-1247) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1256 |Coef| |var| |cen|) 
+(-1248 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
-(((-4504 "*") -4034 (-3038 (|has| |#1| (-376)) (|has| (-1286 |#1| |#2| |#3|) (-842))) (|has| |#1| (-175)) (-3038 (|has| |#1| (-376)) (|has| (-1286 |#1| |#2| |#3|) (-937)))) (-4495 -4034 (-3038 (|has| |#1| (-376)) (|has| (-1286 |#1| |#2| |#3|) (-842))) (|has| |#1| (-569)) (-3038 (|has| |#1| (-376)) (|has| (-1286 |#1| |#2| |#3|) (-937)))) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1286 |#1| |#2| |#3|) (QUOTE (-937)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1286 |#1| |#2| |#3|) (|%list| (QUOTE -631) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1286 |#1| |#2| |#3|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1286 |#1| |#2| |#3|) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1286 |#1| |#2| |#3|) (|%list| (QUOTE -298) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1286 |#1| |#2| |#3|) (|%list| (QUOTE -321) (|%list| (QUOTE -1286) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) 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(-1278 |#1| |#2| |#3|) (QUOTE (-929)))) (|HasCategory| |#1| (QUOTE (-147))))) 
+(-1249 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1258 |Coef|) 
+(-1250 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree <= \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
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 NIL 
-(-1259 S |Coef| UTS) 
+(-1251 S |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-376)))) 
-(-1260 |Coef| UTS) 
+(-1252 |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
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+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1261 |Coef| UTS) 
+(-1253 |Coef| UTS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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-(-1262 ZP) 
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(|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -905) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -901) (QUOTE (-391))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (QUOTE (-929))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-557)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-147))) (-3957 (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-239))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -919) (QUOTE (-1198))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-929))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-147)))))) 
+(-1254 ZP) 
 ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) 
 NIL 
 NIL 
-(-1263 S) 
+(-1255 S) 
 ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-868))) (|HasCategory| |#1| (QUOTE (-1130)))) 
-(-1264 R S) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1122)))) 
+(-1256 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-868)))) 
-(-1265 |x| R) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-1257 |x| R) 
 ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-4504 "*") |has| |#2| (-175)) (-4495 |has| |#2| (-569)) (-4498 |has| |#2| (-376)) (-4500 |has| |#2| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-391)))) (|HasCategory| (-1111) (|%list| (QUOTE -909) (QUOTE (-391))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -909) (QUOTE (-558)))) (|HasCategory| (-1111) (|%list| (QUOTE -909) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391))))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-391)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558))))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (|%list| (QUOTE -913) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| (-1111) (|%list| (QUOTE -631) (QUOTE (-547))))) (|HasCategory| |#2| (|%list| (QUOTE -658) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (QUOTE (-558)))) (-4034 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| |#2| (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (-4034 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-4034 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1181))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1206)))) (|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (-4034 (-12 (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| $ (QUOTE (-147)))) (|HasCategory| |#2| (QUOTE (-147))))) 
-(-1266 |x| R |y| S) 
+(((-4427 "*") |has| |#2| (-175)) (-4418 |has| |#2| (-569)) (-4421 |has| |#2| (-376)) (-4423 |has| |#2| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
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+(-1258 |x| R |y| S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1267 R Q UP) 
+(-1259 R Q UP) 
 ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) 
 NIL 
 NIL 
-(-1268 R UP) 
+(-1260 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) 
 NIL 
 NIL 
-(-1269 R UP) 
+(-1261 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) 
 NIL 
 NIL 
-(-1270 R U) 
+(-1262 R U) 
 ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) 
 NIL 
 NIL 
-(-1271 S R) 
+(-1263 S R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1181)))) 
-(-1272 R) 
+((|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-1173)))) 
+(-1264 R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4498 |has| |#1| (-376)) (-4500 |has| |#1| (-6 -4500)) (-4497 . T) (-4496 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4421 |has| |#1| (-376)) (-4423 |has| |#1| (-6 -4423)) (-4420 . T) (-4419 . T) (-4422 . T)) 
 NIL 
-(-1273 R PR S PS) 
+(-1265 R PR S PS) 
 ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) 
 NIL 
 NIL 
-(-1274 S |Coef| |Expon|) 
+(-1266 S |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1141))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#2|) (QUOTE (-1206)))))) 
-(-1275 |Coef| |Expon|) 
+((|HasCategory| |#2| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#2|) (QUOTE (-1198)))))) 
+(-1267 |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1276 RC P) 
+(-1268 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1277 |Coef| |var| |cen|) 
+(-1269 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) 
-(-1278 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
+(-1270 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1279 |Coef|) 
+(-1271 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1280 S |Coef| ULS) 
+(-1272 S |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) 
 NIL 
 NIL 
-(-1281 |Coef| ULS) 
+(-1273 |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1282 |Coef| ULS) 
+(-1274 |Coef| ULS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4500 |has| |#1| (-376)) (-4494 |has| |#1| (-376)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1141))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-4034 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) 
-(-1283 R FE |var| |cen|) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4423 |has| |#1| (-376)) (-4417 |has| |#1| (-376)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-175))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-558)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-3957 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -419) (QUOTE (-558)))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558)))))) 
+(-1275 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) 
-(((-4504 "*") |has| (-1277 |#2| |#3| |#4|) (-175)) (-4495 |has| (-1277 |#2| |#3| |#4|) (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-175))) (-4034 (|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -1067) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (|%list| (QUOTE -1067) (QUOTE (-558)))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-569)))) 
-(-1284 A S) 
+(((-4427 "*") |has| (-1269 |#2| |#3| |#4|) (-175)) (-4418 |has| (-1269 |#2| |#3| |#4|) (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-175))) (-3957 (|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558)))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -1059) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (|%list| (QUOTE -1059) (QUOTE (-558)))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-569)))) 
+(-1276 A S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4503))) 
-(-1285 S) 
+((|HasAttribute| |#1| (QUOTE -4426))) 
+(-1277 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1286 |Coef| |var| |cen|) 
+(-1278 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
-((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-4034 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -925) (QUOTE (-1206)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|)))) (|HasCategory| (-791) (QUOTE (-1141))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -4453) (|%list| (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#1|))))))) 
-(-1287 |Coef1| |Coef2| UTS1 UTS2) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
+((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-569))) (-3957 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -917) (QUOTE (-1198)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-791)) (|devaluate| |#1|)))) (|HasCategory| (-791) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasSignature| |#1| (|%list| (QUOTE -4376) (|%list| (|devaluate| |#1|) (QUOTE (-1198)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-791))))) (|HasCategory| |#1| (QUOTE (-376))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-1224))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasSignature| |#1| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1198))))) (|HasSignature| |#1| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#1|))))))) 
+(-1279 |Coef1| |Coef2| UTS1 UTS2) 
 ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) 
 NIL 
 NIL 
-(-1288 S |Coef|) 
+(-1280 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-987))) (|HasCategory| |#2| (QUOTE (-1232))) (|HasSignature| |#2| (|%list| (QUOTE -3561) (|%list| (|%list| (QUOTE -661) (QUOTE (-1206))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -4319) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1206))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376)))) 
-(-1289 |Coef|) 
+((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-1224))) (|HasSignature| |#2| (|%list| (QUOTE -3484) (|%list| (|%list| (QUOTE -661) (QUOTE (-1198))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -4242) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1198))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-376)))) 
+(-1281 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
-(((-4504 "*") |has| |#1| (-175)) (-4495 |has| |#1| (-569)) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") |has| |#1| (-175)) (-4418 |has| |#1| (-569)) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1290 |Coef| UTS) 
+(-1282 |Coef| UTS) 
 ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) 
 NIL 
 NIL 
-(-1291 -3572 UP L UTS) 
+(-1283 -3495 UP L UTS) 
 ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-569)))) 
-(-1292) 
+(-1284) 
 ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) 
 NIL 
 NIL 
-(-1293 |sym|) 
+(-1285 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1294 S R) 
+(-1286 S R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-1078))) (|HasCategory| |#2| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1295 R) 
+((|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-746))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1287 R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-4503 . T) (-4502 . T)) 
+((-4426 . T) (-4425 . T)) 
 NIL 
-(-1296 R) 
+(-1288 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-4503 . T) (-4502 . T)) 
-((-4034 (-12 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-4034 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-4034 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-869))) (-4034 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-558) (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1078))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-1078)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
-(-1297 A B) 
+((-4426 . T) (-4425 . T)) 
+((-3957 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-3957 (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877))))) (|HasCategory| |#1| (|%list| (QUOTE -631) (QUOTE (-547)))) (-3957 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| |#1| (QUOTE (-861))) (-3957 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122)))) (|HasCategory| (-558) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-746))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1122))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) 
+(-1289 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-1298) 
+(-1290) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) 
 NIL 
 NIL 
-(-1299) 
+(-1291) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
 NIL 
-(-1300) 
+(-1292) 
 ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) 
 NIL 
 NIL 
-(-1301) 
+(-1293) 
 ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) 
 NIL 
 NIL 
-(-1302) 
+(-1294) 
 ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1303 A S) 
+(-1295 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1304 S) 
+(-1296 S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
-((-4497 . T) (-4496 . T)) 
+((-4420 . T) (-4419 . T)) 
 NIL 
-(-1305 R) 
+(-1297 R) 
 ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) 
 NIL 
 NIL 
-(-1306 K R UP -3572) 
+(-1298 K R UP -3495) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) 
 NIL 
 NIL 
-(-1307) 
+(-1299) 
 ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) 
 NIL 
 NIL 
-(-1308) 
+(-1300) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1309 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1301 R |VarSet| E P |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) 
-((-4497 |has| |#1| (-175)) (-4496 |has| |#1| (-175)) (-4499 . T)) 
+((-4420 |has| |#1| (-175)) (-4419 |has| |#1| (-175)) (-4422 . T)) 
 ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) 
-(-1310 R E V P) 
+(-1302 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) 
-((-4503 . T) (-4502 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) 
-(-1311 R) 
+((-4426 . T) (-4425 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#4| (|%list| (QUOTE -321) (|devaluate| |#4|)))) (|HasCategory| |#4| (|%list| (QUOTE -631) (QUOTE (-547)))) (|HasCategory| |#4| (QUOTE (-1122))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#4| (|%list| (QUOTE -630) (QUOTE (-877)))) (|HasCategory| |#4| (QUOTE (-102)))) 
+(-1303 R) 
 ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) 
-((-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1312 |vl| R) 
+(-1304 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) 
-((-4499 . T) (-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T)) 
-((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4495))) 
-(-1313 R |VarSet| XPOLY) 
+((-4422 . T) (-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T)) 
+((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4418))) 
+(-1305 R |VarSet| XPOLY) 
 ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) 
 NIL 
 NIL 
-(-1314 S -3572) 
+(-1306 S -3495) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) 
-(-1315 -3572) 
+(-1307 -3495) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
-((-4494 . T) (-4500 . T) (-4495 . T) ((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+((-4417 . T) (-4423 . T) (-4418 . T) ((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
-(-1316 |vl| R) 
+(-1308 |vl| R) 
 ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) 
+((-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) 
 NIL 
-(-1317 |VarSet| R) 
+(-1309 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) 
-((-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -737) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4495))) 
-(-1318 R) 
+((-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -737) (|%list| (QUOTE -419) (QUOTE (-558))))) (|HasAttribute| |#2| (QUOTE -4418))) 
+(-1310 R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) 
-((-4495 |has| |#1| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4495))) 
-(-1319 |vl| R) 
+((-4418 |has| |#1| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasAttribute| |#1| (QUOTE -4418))) 
+(-1311 |vl| R) 
 ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) 
+((-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) 
 NIL 
-(-1320 R E) 
+(-1312 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) 
-((-4499 . T) (-4500 |has| |#1| (-6 -4500)) (-4495 |has| |#1| (-6 -4495)) (-4497 . T) (-4496 . T)) 
-((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4499)) (|HasAttribute| |#1| (QUOTE -4500)) (|HasAttribute| |#1| (QUOTE -4495))) 
-(-1321 |VarSet| R) 
+((-4422 . T) (-4423 |has| |#1| (-6 -4423)) (-4418 |has| |#1| (-6 -4418)) (-4420 . T) (-4419 . T)) 
+((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4422)) (|HasAttribute| |#1| (QUOTE -4423)) (|HasAttribute| |#1| (QUOTE -4418))) 
+(-1313 |VarSet| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) 
-((-4495 |has| |#2| (-6 -4495)) (-4497 . T) (-4496 . T) (-4499 . T)) 
-((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4495))) 
-(-1322) 
+((-4418 |has| |#2| (-6 -4418)) (-4420 . T) (-4419 . T) (-4422 . T)) 
+((|HasCategory| |#2| (QUOTE (-175))) (|HasAttribute| |#2| (QUOTE -4418))) 
+(-1314) 
 ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) 
 NIL 
 NIL 
-(-1323 A) 
+(-1315 A) 
 ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) 
 NIL 
 NIL 
-(-1324 R |ls| |ls2|) 
+(-1316 R |ls| |ls2|) 
 ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.	") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) 
 NIL 
 NIL 
-(-1325 R) 
+(-1317 R) 
 ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-1326 |p|) 
+(-1318 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4504 "*") . T) (-4496 . T) (-4497 . T) (-4499 . T)) 
+(((-4427 "*") . T) (-4419 . T) (-4420 . T) (-4422 . T)) 
 NIL 
 NIL 
 NIL 
@@ -5252,4 +5220,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2287934 2287939 2287944 2287949) (-2 NIL 2287914 2287919 2287924 2287929) (-1 NIL 2287894 2287899 2287904 2287909) (0 NIL 2287874 2287879 2287884 2287889) (-1326 "ZMOD.spad" 2287683 2287696 2287812 2287869) (-1325 "ZLINDEP.spad" 2286781 2286792 2287673 2287678) (-1324 "ZDSOLVE.spad" 2276741 2276763 2286771 2286776) (-1323 "YSTREAM.spad" 2276236 2276247 2276731 2276736) (-1322 "YDIAGRAM.spad" 2275870 2275879 2276226 2276231) (-1321 "XRPOLY.spad" 2275090 2275110 2275726 2275795) (-1320 "XPR.spad" 2272885 2272898 2274808 2274907) (-1319 "XPOLYC.spad" 2272204 2272220 2272811 2272880) (-1318 "XPOLY.spad" 2271759 2271770 2272060 2272129) (-1317 "XPBWPOLY.spad" 2270198 2270218 2271533 2271602) (-1316 "XFALG.spad" 2267246 2267262 2270124 2270193) (-1315 "XF.spad" 2265709 2265724 2267148 2267241) (-1314 "XF.spad" 2264152 2264169 2265593 2265598) (-1313 "XEXPPKG.spad" 2263411 2263437 2264142 2264147) (-1312 "XDPOLY.spad" 2263025 2263041 2263267 2263336) (-1311 "XALG.spad" 2262693 2262704 2262981 2263020) (-1310 "WUTSET.spad" 2258663 2258680 2262294 2262321) (-1309 "WP.spad" 2257870 2257914 2258521 2258588) (-1308 "WHILEAST.spad" 2257668 2257677 2257860 2257865) (-1307 "WHEREAST.spad" 2257339 2257348 2257658 2257663) (-1306 "WFFINTBS.spad" 2255002 2255024 2257329 2257334) (-1305 "WEIER.spad" 2253224 2253235 2254992 2254997) (-1304 "VSPACE.spad" 2252897 2252908 2253192 2253219) (-1303 "VSPACE.spad" 2252590 2252603 2252887 2252892) (-1302 "VOID.spad" 2252267 2252276 2252580 2252585) (-1301 "VIEWDEF.spad" 2247468 2247477 2252257 2252262) (-1300 "VIEW3D.spad" 2231429 2231438 2247458 2247463) (-1299 "VIEW2D.spad" 2219328 2219337 2231419 2231424) (-1298 "VIEW.spad" 2217048 2217057 2219318 2219323) (-1297 "VECTOR2.spad" 2215687 2215700 2217038 2217043) (-1296 "VECTOR.spad" 2214187 2214198 2214438 2214465) (-1295 "VECTCAT.spad" 2212099 2212110 2214155 2214182) (-1294 "VECTCAT.spad" 2209818 2209831 2211876 2211881) (-1293 "VARIABLE.spad" 2209598 2209613 2209808 2209813) (-1292 "UTYPE.spad" 2209242 2209251 2209588 2209593) (-1291 "UTSODETL.spad" 2208537 2208561 2209198 2209203) (-1290 "UTSODE.spad" 2206753 2206773 2208527 2208532) (-1289 "UTSCAT.spad" 2204232 2204248 2206651 2206748) (-1288 "UTSCAT.spad" 2201331 2201349 2203752 2203757) (-1287 "UTS2.spad" 2200926 2200961 2201321 2201326) (-1286 "UTS.spad" 2195804 2195832 2199324 2199421) (-1285 "URAGG.spad" 2190525 2190536 2195794 2195799) (-1284 "URAGG.spad" 2185210 2185223 2190481 2190486) (-1283 "UPXSSING.spad" 2182828 2182854 2184264 2184397) (-1282 "UPXSCONS.spad" 2180506 2180526 2180879 2181028) (-1281 "UPXSCCA.spad" 2179077 2179097 2180352 2180501) (-1280 "UPXSCCA.spad" 2177790 2177812 2179067 2179072) (-1279 "UPXSCAT.spad" 2176379 2176395 2177636 2177785) (-1278 "UPXS2.spad" 2175922 2175975 2176369 2176374) (-1277 "UPXS.spad" 2173137 2173165 2173973 2174122) (-1276 "UPSQFREE.spad" 2171552 2171566 2173127 2173132) (-1275 "UPSCAT.spad" 2169347 2169371 2171450 2171547) (-1274 "UPSCAT.spad" 2166827 2166853 2168932 2168937) (-1273 "UPOLYC2.spad" 2166298 2166317 2166817 2166822) (-1272 "UPOLYC.spad" 2161378 2161389 2166140 2166293) (-1271 "UPOLYC.spad" 2156344 2156357 2161108 2161113) (-1270 "UPMP.spad" 2155276 2155289 2156334 2156339) (-1269 "UPDIVP.spad" 2154841 2154855 2155266 2155271) (-1268 "UPDECOMP.spad" 2153102 2153116 2154831 2154836) (-1267 "UPCDEN.spad" 2152319 2152335 2153092 2153097) (-1266 "UP2.spad" 2151683 2151704 2152309 2152314) (-1265 "UP.spad" 2148711 2148726 2149098 2149251) (-1264 "UNISEG2.spad" 2148208 2148221 2148667 2148672) (-1263 "UNISEG.spad" 2147561 2147572 2148127 2148132) (-1262 "UNIFACT.spad" 2146664 2146676 2147551 2147556) (-1261 "ULSCONS.spad" 2137576 2137596 2137946 2138095) (-1260 "ULSCCAT.spad" 2135313 2135333 2137422 2137571) (-1259 "ULSCCAT.spad" 2133158 2133180 2135269 2135274) (-1258 "ULSCAT.spad" 2131398 2131414 2133004 2133153) (-1257 "ULS2.spad" 2130912 2130965 2131388 2131393) (-1256 "ULS.spad" 2120483 2120511 2121428 2121857) (-1255 "UINT8.spad" 2120360 2120369 2120473 2120478) (-1254 "UINT64.spad" 2120236 2120245 2120350 2120355) (-1253 "UINT32.spad" 2120112 2120121 2120226 2120231) (-1252 "UINT16.spad" 2119988 2119997 2120102 2120107) (-1251 "UFD.spad" 2119053 2119062 2119914 2119983) (-1250 "UFD.spad" 2118180 2118191 2119043 2119048) (-1249 "UDVO.spad" 2117061 2117070 2118170 2118175) (-1248 "UDPO.spad" 2114642 2114653 2117017 2117022) (-1247 "TYPEAST.spad" 2114561 2114570 2114632 2114637) (-1246 "TYPE.spad" 2114493 2114502 2114551 2114556) (-1245 "TWOFACT.spad" 2113145 2113160 2114483 2114488) (-1244 "TUPLE.spad" 2112636 2112647 2113041 2113046) (-1243 "TUBETOOL.spad" 2109503 2109512 2112626 2112631) (-1242 "TUBE.spad" 2108150 2108167 2109493 2109498) (-1241 "TSETCAT.spad" 2096221 2096238 2108118 2108145) (-1240 "TSETCAT.spad" 2084278 2084297 2096177 2096182) (-1239 "TS.spad" 2082871 2082887 2083837 2083934) (-1238 "TRMANIP.spad" 2077235 2077252 2082559 2082564) (-1237 "TRIMAT.spad" 2076198 2076223 2077225 2077230) (-1236 "TRIGMNIP.spad" 2074725 2074742 2076188 2076193) (-1235 "TRIGCAT.spad" 2074237 2074246 2074715 2074720) (-1234 "TRIGCAT.spad" 2073747 2073758 2074227 2074232) (-1233 "TREE.spad" 2072193 2072204 2073225 2073252) (-1232 "TRANFUN.spad" 2072032 2072041 2072183 2072188) (-1231 "TRANFUN.spad" 2071869 2071880 2072022 2072027) (-1230 "TOPSP.spad" 2071543 2071552 2071859 2071864) (-1229 "TOOLSIGN.spad" 2071206 2071217 2071533 2071538) (-1228 "TEXTFILE.spad" 2069767 2069776 2071196 2071201) (-1227 "TEX1.spad" 2069323 2069334 2069757 2069762) (-1226 "TEX.spad" 2066517 2066526 2069313 2069318) (-1225 "TEMUTL.spad" 2066072 2066081 2066507 2066512) (-1224 "TBCMPPK.spad" 2064173 2064196 2066062 2066067) (-1223 "TBAGG.spad" 2063231 2063254 2064153 2064168) (-1222 "TBAGG.spad" 2062297 2062322 2063221 2063226) (-1221 "TANEXP.spad" 2061705 2061716 2062287 2062292) (-1220 "TALGOP.spad" 2061429 2061440 2061695 2061700) (-1219 "TABLEAU.spad" 2060910 2060921 2061419 2061424) (-1218 "TABLE.spad" 2058843 2058866 2059113 2059140) (-1217 "TABLBUMP.spad" 2055622 2055633 2058833 2058838) (-1216 "SYSTEM.spad" 2054850 2054859 2055612 2055617) (-1215 "SYSSOLP.spad" 2052333 2052344 2054840 2054845) (-1214 "SYSPTR.spad" 2052232 2052241 2052323 2052328) (-1213 "SYSNNI.spad" 2051455 2051466 2052222 2052227) (-1212 "SYSINT.spad" 2050859 2050870 2051445 2051450) (-1211 "SYNTAX.spad" 2047193 2047202 2050849 2050854) (-1210 "SYMTAB.spad" 2045261 2045270 2047183 2047188) (-1209 "SYMS.spad" 2041290 2041299 2045251 2045256) (-1208 "SYMPOLY.spad" 2040269 2040280 2040351 2040478) (-1207 "SYMFUNC.spad" 2039770 2039781 2040259 2040264) (-1206 "SYMBOL.spad" 2037265 2037274 2039760 2039765) (-1205 "SWITCH.spad" 2034036 2034045 2037255 2037260) (-1204 "SUTS.spad" 2031015 2031043 2032434 2032531) (-1203 "SUPXS.spad" 2028217 2028245 2029066 2029215) (-1202 "SUPFRACF.spad" 2027322 2027340 2028207 2028212) (-1201 "SUP2.spad" 2026714 2026727 2027312 2027317) (-1200 "SUP.spad" 2023356 2023367 2024129 2024282) (-1199 "SUMRF.spad" 2022330 2022341 2023346 2023351) (-1198 "SUMFS.spad" 2021959 2021976 2022320 2022325) (-1197 "SULS.spad" 2011517 2011545 2012475 2012904) (-1196 "SUCHTAST.spad" 2011286 2011295 2011507 2011512) (-1195 "SUCH.spad" 2010976 2010991 2011276 2011281) (-1194 "SUBSPACE.spad" 2003107 2003122 2010966 2010971) (-1193 "SUBRESP.spad" 2002277 2002291 2003063 2003068) (-1192 "STTFNC.spad" 1998745 1998761 2002267 2002272) (-1191 "STTF.spad" 1994844 1994860 1998735 1998740) (-1190 "STTAYLOR.spad" 1987489 1987500 1994719 1994724) (-1189 "STRTBL.spad" 1985504 1985521 1985653 1985680) (-1188 "STRING.spad" 1984270 1984279 1984491 1984518) (-1187 "STREAM3.spad" 1983843 1983858 1984260 1984265) (-1186 "STREAM2.spad" 1982971 1982984 1983833 1983838) (-1185 "STREAM1.spad" 1982677 1982688 1982961 1982966) (-1184 "STREAM.spad" 1979463 1979474 1982070 1982085) (-1183 "STINPROD.spad" 1978399 1978415 1979453 1979458) (-1182 "STEPAST.spad" 1977633 1977642 1978389 1978394) (-1181 "STEP.spad" 1976842 1976851 1977623 1977628) (-1180 "STBL.spad" 1974890 1974918 1975057 1975072) (-1179 "STAGG.spad" 1973589 1973600 1974880 1974885) (-1178 "STAGG.spad" 1972286 1972299 1973579 1973584) (-1177 "STACK.spad" 1971514 1971525 1971764 1971791) (-1176 "SRING.spad" 1971274 1971283 1971504 1971509) (-1175 "SREGSET.spad" 1968973 1968990 1970875 1970902) (-1174 "SRDCMPK.spad" 1967550 1967570 1968963 1968968) (-1173 "SRAGG.spad" 1962733 1962742 1967518 1967545) (-1172 "SRAGG.spad" 1957936 1957947 1962723 1962728) (-1171 "SQMATRIX.spad" 1955431 1955449 1956347 1956434) (-1170 "SPLTREE.spad" 1949897 1949910 1954693 1954720) (-1169 "SPLNODE.spad" 1946517 1946530 1949887 1949892) (-1168 "SPFCAT.spad" 1945326 1945335 1946507 1946512) (-1167 "SPECOUT.spad" 1943878 1943887 1945316 1945321) (-1166 "SPADXPT.spad" 1935969 1935978 1943868 1943873) (-1165 "spad-parser.spad" 1935434 1935443 1935959 1935964) (-1164 "SPADAST.spad" 1935135 1935144 1935424 1935429) (-1163 "SPACEC.spad" 1919350 1919361 1935125 1935130) (-1162 "SPACE3.spad" 1919126 1919137 1919340 1919345) (-1161 "SORTPAK.spad" 1918675 1918688 1919082 1919087) (-1160 "SOLVETRA.spad" 1916438 1916449 1918665 1918670) (-1159 "SOLVESER.spad" 1914894 1914905 1916428 1916433) (-1158 "SOLVERAD.spad" 1910920 1910931 1914884 1914889) (-1157 "SOLVEFOR.spad" 1909382 1909400 1910910 1910915) (-1156 "SNTSCAT.spad" 1908982 1908999 1909350 1909377) (-1155 "SMTS.spad" 1907264 1907290 1908541 1908638) (-1154 "SMP.spad" 1904667 1904687 1905057 1905184) (-1153 "SMITH.spad" 1903512 1903537 1904657 1904662) (-1152 "SMATCAT.spad" 1901630 1901660 1903456 1903507) (-1151 "SMATCAT.spad" 1899680 1899712 1901508 1901513) (-1150 "SKAGG.spad" 1898649 1898660 1899648 1899675) (-1149 "SINT.spad" 1897589 1897598 1898515 1898644) (-1148 "SIMPAN.spad" 1897317 1897326 1897579 1897584) (-1147 "SIGNRF.spad" 1896442 1896453 1897307 1897312) (-1146 "SIGNEF.spad" 1895728 1895745 1896432 1896437) (-1145 "SIGAST.spad" 1895145 1895154 1895718 1895723) (-1144 "SIG.spad" 1894507 1894516 1895135 1895140) (-1143 "SHP.spad" 1892451 1892466 1894463 1894468) (-1142 "SHDP.spad" 1879806 1879833 1880323 1880422) (-1141 "SGROUP.spad" 1879414 1879423 1879796 1879801) (-1140 "SGROUP.spad" 1879020 1879031 1879404 1879409) (-1139 "SGCF.spad" 1872159 1872168 1879010 1879015) (-1138 "SFRTCAT.spad" 1871105 1871122 1872127 1872154) (-1137 "SFRGCD.spad" 1870168 1870188 1871095 1871100) (-1136 "SFQCMPK.spad" 1864981 1865001 1870158 1870163) (-1135 "SFORT.spad" 1864420 1864434 1864971 1864976) (-1134 "SEXOF.spad" 1864263 1864303 1864410 1864415) (-1133 "SEXCAT.spad" 1862091 1862131 1864253 1864258) (-1132 "SEX.spad" 1861983 1861992 1862081 1862086) (-1131 "SETMN.spad" 1860443 1860460 1861973 1861978) (-1130 "SETCAT.spad" 1859928 1859937 1860433 1860438) (-1129 "SETCAT.spad" 1859411 1859422 1859918 1859923) (-1128 "SETAGG.spad" 1855960 1855971 1859391 1859406) (-1127 "SETAGG.spad" 1852517 1852530 1855950 1855955) (-1126 "SET.spad" 1850790 1850801 1851887 1851926) (-1125 "SEQAST.spad" 1850493 1850502 1850780 1850785) (-1124 "SEGXCAT.spad" 1849649 1849662 1850483 1850488) (-1123 "SEGCAT.spad" 1848574 1848585 1849639 1849644) (-1122 "SEGBIND2.spad" 1848272 1848285 1848564 1848569) (-1121 "SEGBIND.spad" 1848030 1848041 1848219 1848224) (-1120 "SEGAST.spad" 1847760 1847769 1848020 1848025) (-1119 "SEG2.spad" 1847195 1847208 1847716 1847721) (-1118 "SEG.spad" 1847008 1847019 1847114 1847119) (-1117 "SDVAR.spad" 1846284 1846295 1846998 1847003) (-1116 "SDPOL.spad" 1843539 1843550 1843830 1843957) (-1115 "SCPKG.spad" 1841628 1841639 1843529 1843534) (-1114 "SCOPE.spad" 1840805 1840814 1841618 1841623) (-1113 "SCACHE.spad" 1839501 1839512 1840795 1840800) (-1112 "SASTCAT.spad" 1839410 1839419 1839491 1839496) (-1111 "SAOS.spad" 1839282 1839291 1839400 1839405) (-1110 "SAERFFC.spad" 1838995 1839015 1839272 1839277) (-1109 "SAEFACT.spad" 1838696 1838716 1838985 1838990) (-1108 "SAE.spad" 1836130 1836146 1836741 1836876) (-1107 "RURPK.spad" 1833789 1833805 1836120 1836125) (-1106 "RULESET.spad" 1833242 1833266 1833779 1833784) (-1105 "RULECOLD.spad" 1833094 1833107 1833232 1833237) (-1104 "RULE.spad" 1831342 1831366 1833084 1833089) (-1103 "RTVALUE.spad" 1831077 1831086 1831332 1831337) (-1102 "RSTRCAST.spad" 1830794 1830803 1831067 1831072) (-1101 "RSETGCD.spad" 1827236 1827256 1830784 1830789) (-1100 "RSETCAT.spad" 1817204 1817221 1827204 1827231) (-1099 "RSETCAT.spad" 1807192 1807211 1817194 1817199) (-1098 "RSDCMPK.spad" 1805692 1805712 1807182 1807187) (-1097 "RRCC.spad" 1804076 1804106 1805682 1805687) (-1096 "RRCC.spad" 1802458 1802490 1804066 1804071) (-1095 "RPTAST.spad" 1802160 1802169 1802448 1802453) (-1094 "RPOLCAT.spad" 1781664 1781679 1802028 1802155) (-1093 "RPOLCAT.spad" 1760863 1760880 1781229 1781234) (-1092 "ROUTINE.spad" 1756264 1756273 1759012 1759039) (-1091 "ROMAN.spad" 1755592 1755601 1756130 1756259) (-1090 "ROIRC.spad" 1754672 1754704 1755582 1755587) (-1089 "RNS.spad" 1753648 1753657 1754574 1754667) (-1088 "RNS.spad" 1752710 1752721 1753638 1753643) (-1087 "RNGBIND.spad" 1751870 1751884 1752665 1752670) (-1086 "RNG.spad" 1751605 1751614 1751860 1751865) (-1085 "RMODULE.spad" 1751386 1751397 1751595 1751600) (-1084 "RMCAT2.spad" 1750806 1750863 1751376 1751381) (-1083 "RMATRIX.spad" 1749576 1749595 1749919 1749958) (-1082 "RMATCAT.spad" 1745155 1745186 1749532 1749571) (-1081 "RMATCAT.spad" 1740624 1740657 1745003 1745008) (-1080 "RLINSET.spad" 1740328 1740339 1740614 1740619) (-1079 "RINTERP.spad" 1740216 1740236 1740318 1740323) (-1078 "RING.spad" 1739686 1739695 1740196 1740211) (-1077 "RING.spad" 1739164 1739175 1739676 1739681) (-1076 "RIDIST.spad" 1738556 1738565 1739154 1739159) (-1075 "RGCHAIN.spad" 1737077 1737093 1737971 1737998) (-1074 "RGBCSPC.spad" 1736866 1736878 1737067 1737072) (-1073 "RGBCMDL.spad" 1736428 1736440 1736856 1736861) (-1072 "RFFACTOR.spad" 1735890 1735901 1736418 1736423) (-1071 "RFFACT.spad" 1735625 1735637 1735880 1735885) (-1070 "RFDIST.spad" 1734621 1734630 1735615 1735620) (-1069 "RF.spad" 1732295 1732306 1734611 1734616) (-1068 "RETSOL.spad" 1731714 1731727 1732285 1732290) (-1067 "RETRACT.spad" 1731142 1731153 1731704 1731709) (-1066 "RETRACT.spad" 1730568 1730581 1731132 1731137) (-1065 "RETAST.spad" 1730380 1730389 1730558 1730563) (-1064 "RESULT.spad" 1727942 1727951 1728529 1728556) (-1063 "RESRING.spad" 1727289 1727336 1727880 1727937) (-1062 "RESLATC.spad" 1726613 1726624 1727279 1727284) (-1061 "REPSQ.spad" 1726344 1726355 1726603 1726608) (-1060 "REPDB.spad" 1726051 1726062 1726334 1726339) (-1059 "REP2.spad" 1715765 1715776 1725893 1725898) (-1058 "REP1.spad" 1709985 1709996 1715715 1715720) (-1057 "REP.spad" 1707539 1707548 1709975 1709980) (-1056 "REGSET.spad" 1705331 1705348 1707140 1707167) (-1055 "REF.spad" 1704666 1704677 1705286 1705291) (-1054 "REDORDER.spad" 1703872 1703889 1704656 1704661) (-1053 "RECLOS.spad" 1702631 1702651 1703335 1703428) (-1052 "REALSOLV.spad" 1701771 1701780 1702621 1702626) (-1051 "REAL0Q.spad" 1699069 1699084 1701761 1701766) (-1050 "REAL0.spad" 1695913 1695928 1699059 1699064) (-1049 "REAL.spad" 1695785 1695794 1695903 1695908) (-1048 "RDUCEAST.spad" 1695506 1695515 1695775 1695780) (-1047 "RDIV.spad" 1695161 1695186 1695496 1695501) (-1046 "RDIST.spad" 1694728 1694739 1695151 1695156) (-1045 "RDETRS.spad" 1693592 1693610 1694718 1694723) (-1044 "RDETR.spad" 1691731 1691749 1693582 1693587) (-1043 "RDEEFS.spad" 1690830 1690847 1691721 1691726) (-1042 "RDEEF.spad" 1689840 1689857 1690820 1690825) (-1041 "RCFIELD.spad" 1687058 1687067 1689742 1689835) (-1040 "RCFIELD.spad" 1684362 1684373 1687048 1687053) (-1039 "RCAGG.spad" 1682298 1682309 1684352 1684357) (-1038 "RCAGG.spad" 1680161 1680174 1682217 1682222) (-1037 "RATRET.spad" 1679521 1679532 1680151 1680156) (-1036 "RATFACT.spad" 1679213 1679225 1679511 1679516) (-1035 "RANDSRC.spad" 1678532 1678541 1679203 1679208) (-1034 "RADUTIL.spad" 1678288 1678297 1678522 1678527) (-1033 "RADIX.spad" 1675067 1675081 1676613 1676706) (-1032 "RADFF.spad" 1672770 1672807 1672889 1673045) (-1031 "RADCAT.spad" 1672365 1672374 1672760 1672765) (-1030 "RADCAT.spad" 1671958 1671969 1672355 1672360) (-1029 "QUEUE.spad" 1671177 1671188 1671436 1671463) (-1028 "QUATCT2.spad" 1670797 1670816 1671167 1671172) (-1027 "QUATCAT.spad" 1668967 1668978 1670727 1670792) (-1026 "QUATCAT.spad" 1666885 1666898 1668647 1668652) (-1025 "QUAT.spad" 1665337 1665348 1665680 1665745) (-1024 "QUAGG.spad" 1664170 1664181 1665305 1665332) (-1023 "QQUTAST.spad" 1663938 1663947 1664160 1664165) (-1022 "QFORM.spad" 1663556 1663571 1663928 1663933) (-1021 "QFCAT2.spad" 1663248 1663265 1663546 1663551) (-1020 "QFCAT.spad" 1661950 1661961 1663150 1663243) (-1019 "QFCAT.spad" 1660234 1660247 1661436 1661441) (-1018 "QEQUAT.spad" 1659792 1659801 1660224 1660229) (-1017 "QCMPACK.spad" 1654706 1654726 1659782 1659787) (-1016 "QALGSET2.spad" 1652701 1652720 1654696 1654701) (-1015 "QALGSET.spad" 1648805 1648838 1652615 1652620) (-1014 "PWFFINTB.spad" 1646220 1646242 1648795 1648800) (-1013 "PUSHVAR.spad" 1645558 1645578 1646210 1646215) (-1012 "PTRANFN.spad" 1641693 1641704 1645548 1645553) (-1011 "PTPACK.spad" 1638780 1638791 1641683 1641688) (-1010 "PTFUNC2.spad" 1638602 1638617 1638770 1638775) (-1009 "PTCAT.spad" 1637856 1637867 1638570 1638597) (-1008 "PSQFR.spad" 1637170 1637195 1637846 1637851) (-1007 "PSEUDLIN.spad" 1636055 1636066 1637160 1637165) (-1006 "PSETPK.spad" 1622759 1622776 1635933 1635938) (-1005 "PSETCAT.spad" 1617158 1617182 1622739 1622754) (-1004 "PSETCAT.spad" 1611531 1611557 1617114 1617119) (-1003 "PSCURVE.spad" 1610529 1610538 1611521 1611526) (-1002 "PSCAT.spad" 1609311 1609341 1610427 1610524) (-1001 "PSCAT.spad" 1608183 1608215 1609301 1609306) (-1000 "PRTITION.spad" 1606880 1606889 1608173 1608178) (-999 "PRTDAST.spad" 1606599 1606607 1606870 1606875) (-998 "PRS.spad" 1596217 1596234 1606555 1606560) (-997 "PRQAGG.spad" 1595652 1595662 1596185 1596212) (-996 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1576351 1578193 1578198) (-977 "POLYCAT.spad" 1569831 1569852 1576197 1576324) (-976 "POLYCAT.spad" 1562629 1562652 1568997 1569002) (-975 "POLY2UP.spad" 1562081 1562095 1562619 1562624) (-974 "POLY2.spad" 1561678 1561690 1562071 1562076) (-973 "POLY.spad" 1558941 1558951 1559456 1559583) (-972 "POLUTIL.spad" 1557906 1557935 1558897 1558902) (-971 "POLTOPOL.spad" 1556654 1556669 1557896 1557901) (-970 "POINT.spad" 1555318 1555328 1555405 1555432) (-969 "PNTHEORY.spad" 1552020 1552028 1555308 1555313) (-968 "PMTOOLS.spad" 1550795 1550809 1552010 1552015) (-967 "PMSYM.spad" 1550344 1550354 1550785 1550790) (-966 "PMQFCAT.spad" 1549935 1549949 1550334 1550339) (-965 "PMPREDFS.spad" 1549397 1549419 1549925 1549930) (-964 "PMPRED.spad" 1548884 1548898 1549387 1549392) (-963 "PMPLCAT.spad" 1547961 1547979 1548813 1548818) (-962 "PMLSAGG.spad" 1547546 1547560 1547951 1547956) (-961 "PMKERNEL.spad" 1547125 1547137 1547536 1547541) (-960 "PMINS.spad" 1546705 1546715 1547115 1547120) (-959 "PMFS.spad" 1546282 1546300 1546695 1546700) (-958 "PMDOWN.spad" 1545572 1545586 1546272 1546277) (-957 "PMASSFS.spad" 1544547 1544563 1545562 1545567) (-956 "PMASS.spad" 1543565 1543573 1544537 1544542) (-955 "PLOTTOOL.spad" 1543345 1543353 1543555 1543560) (-954 "PLOT3D.spad" 1539809 1539817 1543335 1543340) (-953 "PLOT1.spad" 1538982 1538992 1539799 1539804) (-952 "PLOT.spad" 1533905 1533913 1538972 1538977) (-951 "PLEQN.spad" 1521307 1521334 1533895 1533900) (-950 "PINTERPA.spad" 1521091 1521107 1521297 1521302) (-949 "PINTERP.spad" 1520713 1520732 1521081 1521086) (-948 "PID.spad" 1519687 1519695 1520639 1520708) (-947 "PICOERCE.spad" 1519344 1519354 1519677 1519682) (-946 "PI.spad" 1518961 1518969 1519318 1519339) (-945 "PGROEB.spad" 1517570 1517584 1518951 1518956) (-944 "PGE.spad" 1509243 1509251 1517560 1517565) (-943 "PGCD.spad" 1508197 1508214 1509233 1509238) (-942 "PFRPAC.spad" 1507346 1507356 1508187 1508192) (-941 "PFR.spad" 1504049 1504059 1507248 1507341) (-940 "PFOTOOLS.spad" 1503307 1503323 1504039 1504044) (-939 "PFOQ.spad" 1502677 1502695 1503297 1503302) (-938 "PFO.spad" 1502096 1502123 1502667 1502672) (-937 "PFECAT.spad" 1499806 1499814 1502022 1502091) (-936 "PFECAT.spad" 1497544 1497554 1499762 1499767) (-935 "PFBRU.spad" 1495432 1495444 1497534 1497539) (-934 "PFBR.spad" 1492992 1493015 1495422 1495427) (-933 "PF.spad" 1492566 1492578 1492797 1492890) (-932 "PERMGRP.spad" 1487336 1487346 1492556 1492561) (-931 "PERMCAT.spad" 1485997 1486007 1487316 1487331) (-930 "PERMAN.spad" 1484553 1484567 1485987 1485992) (-929 "PERM.spad" 1480360 1480370 1484383 1484398) (-928 "PENDTREE.spad" 1479580 1479590 1479860 1479865) (-927 "PDSPC.spad" 1478393 1478403 1479570 1479575) (-926 "PDSPC.spad" 1477204 1477216 1478383 1478388) (-925 "PDRING.spad" 1477046 1477056 1477184 1477199) (-924 "PDMOD.spad" 1476862 1476874 1477014 1477041) (-923 "PDEPROB.spad" 1475877 1475885 1476852 1476857) (-922 "PDEPACK.spad" 1470013 1470021 1475867 1475872) (-921 "PDECOMP.spad" 1469483 1469500 1470003 1470008) (-920 "PDECAT.spad" 1467839 1467847 1469473 1469478) (-919 "PDDOM.spad" 1467277 1467290 1467829 1467834) (-918 "PDDOM.spad" 1466713 1466728 1467267 1467272) (-917 "PCOMP.spad" 1466566 1466579 1466703 1466708) (-916 "PBWLB.spad" 1465162 1465179 1466556 1466561) (-915 "PATTERN2.spad" 1464900 1464912 1465152 1465157) (-914 "PATTERN1.spad" 1463244 1463260 1464890 1464895) (-913 "PATTERN.spad" 1457815 1457825 1463234 1463239) (-912 "PATRES2.spad" 1457487 1457501 1457805 1457810) (-911 "PATRES.spad" 1455070 1455082 1457477 1457482) (-910 "PATMATCH.spad" 1453258 1453289 1454769 1454774) (-909 "PATMAB.spad" 1452687 1452697 1453248 1453253) (-908 "PATLRES.spad" 1451773 1451787 1452677 1452682) (-907 "PATAB.spad" 1451537 1451547 1451763 1451768) (-906 "PARTPERM.spad" 1449593 1449601 1451527 1451532) (-905 "PARSURF.spad" 1449027 1449055 1449583 1449588) (-904 "PARSU2.spad" 1448824 1448840 1449017 1449022) (-903 "script-parser.spad" 1448344 1448352 1448814 1448819) (-902 "PARSCURV.spad" 1447778 1447806 1448334 1448339) (-901 "PARSC2.spad" 1447569 1447585 1447768 1447773) (-900 "PARPCURV.spad" 1447031 1447059 1447559 1447564) (-899 "PARPC2.spad" 1446822 1446838 1447021 1447026) (-898 "PARAMAST.spad" 1445950 1445958 1446812 1446817) (-897 "PAN2EXPR.spad" 1445362 1445370 1445940 1445945) (-896 "PALETTE.spad" 1444348 1444356 1445352 1445357) (-895 "PAIR.spad" 1443355 1443368 1443924 1443929) (-894 "PADICRC.spad" 1440559 1440577 1441722 1441815) (-893 "PADICRAT.spad" 1438418 1438430 1438631 1438724) (-892 "PADICCT.spad" 1436967 1436979 1438344 1438413) (-891 "PADIC.spad" 1436670 1436682 1436893 1436962) (-890 "PADEPAC.spad" 1435359 1435378 1436660 1436665) (-889 "PADE.spad" 1434111 1434127 1435349 1435354) (-888 "OWP.spad" 1433359 1433389 1433969 1434036) (-887 "OVERSET.spad" 1432932 1432940 1433349 1433354) (-886 "OVAR.spad" 1432713 1432736 1432922 1432927) (-885 "OUTFORM.spad" 1422121 1422129 1432703 1432708) (-884 "OUTBFILE.spad" 1421555 1421563 1422111 1422116) (-883 "OUTBCON.spad" 1420625 1420633 1421545 1421550) (-882 "OUTBCON.spad" 1419693 1419703 1420615 1420620) (-881 "OUT.spad" 1418811 1418819 1419683 1419688) (-880 "OSI.spad" 1418286 1418294 1418801 1418806) (-879 "OSGROUP.spad" 1418204 1418212 1418276 1418281) (-878 "ORTHPOL.spad" 1416683 1416693 1418115 1418120) (-877 "OREUP.spad" 1416127 1416155 1416354 1416393) (-876 "ORESUP.spad" 1415419 1415443 1415798 1415837) (-875 "OREPCTO.spad" 1413308 1413320 1415339 1415344) (-874 "OREPCAT.spad" 1407495 1407505 1413264 1413303) (-873 "OREPCAT.spad" 1401572 1401584 1407343 1407348) (-872 "ORDTYPE.spad" 1400809 1400817 1401562 1401567) (-871 "ORDTYPE.spad" 1400044 1400054 1400799 1400804) (-870 "ORDSTRCT.spad" 1399814 1399829 1399977 1399982) (-869 "ORDSET.spad" 1399514 1399522 1399804 1399809) (-868 "ORDRING.spad" 1399331 1399339 1399494 1399509) (-867 "ORDMON.spad" 1399186 1399194 1399321 1399326) (-866 "ORDFUNS.spad" 1398318 1398334 1399176 1399181) (-865 "ORDFIN.spad" 1398138 1398146 1398308 1398313) (-864 "ORDCOMP2.spad" 1397431 1397443 1398128 1398133) (-863 "ORDCOMP.spad" 1395884 1395894 1396966 1396995) (-862 "OPTPROB.spad" 1394522 1394530 1395874 1395879) (-861 "OPTPACK.spad" 1386931 1386939 1394512 1394517) (-860 "OPTCAT.spad" 1384610 1384618 1386921 1386926) (-859 "OPSIG.spad" 1384272 1384280 1384600 1384605) (-858 "OPQUERY.spad" 1383853 1383861 1384262 1384267) (-857 "OPERCAT.spad" 1383319 1383329 1383843 1383848) (-856 "OPERCAT.spad" 1382783 1382795 1383309 1383314) (-855 "OP.spad" 1382525 1382535 1382605 1382672) (-854 "ONECOMP2.spad" 1381949 1381961 1382515 1382520) (-853 "ONECOMP.spad" 1380682 1380692 1381484 1381513) (-852 "OMSAGG.spad" 1380470 1380480 1380638 1380677) (-851 "OMPKG.spad" 1379102 1379110 1380460 1380465) (-850 "OMLO.spad" 1378535 1378547 1378988 1379027) (-849 "OMEXPR.spad" 1378369 1378379 1378525 1378530) (-848 "OMERRK.spad" 1377419 1377427 1378359 1378364) (-847 "OMERR.spad" 1376964 1376972 1377409 1377414) (-846 "OMENC.spad" 1376316 1376324 1376954 1376959) (-845 "OMDEV.spad" 1370649 1370657 1376306 1376311) (-844 "OMCONN.spad" 1370058 1370066 1370639 1370644) (-843 "OM.spad" 1369055 1369063 1370048 1370053) (-842 "OINTDOM.spad" 1368818 1368826 1368981 1369050) (-841 "OFMONOID.spad" 1366957 1366967 1368774 1368779) (-840 "ODVAR.spad" 1366218 1366228 1366947 1366952) (-839 "ODR.spad" 1365862 1365888 1366030 1366179) (-838 "ODPOL.spad" 1363073 1363083 1363413 1363540) (-837 "ODP.spad" 1350572 1350592 1350945 1351044) (-836 "ODETOOLS.spad" 1349221 1349240 1350562 1350567) (-835 "ODESYS.spad" 1346915 1346932 1349211 1349216) (-834 "ODERTRIC.spad" 1342948 1342965 1346872 1346877) (-833 "ODERED.spad" 1342347 1342371 1342938 1342943) (-832 "ODERAT.spad" 1339980 1339997 1342337 1342342) (-831 "ODEPRRIC.spad" 1337073 1337095 1339970 1339975) (-830 "ODEPROB.spad" 1336330 1336338 1337063 1337068) (-829 "ODEPRIM.spad" 1333728 1333750 1336320 1336325) (-828 "ODEPAL.spad" 1333114 1333138 1333718 1333723) (-827 "ODEPACK.spad" 1319844 1319852 1333104 1333109) (-826 "ODEINT.spad" 1319279 1319295 1319834 1319839) (-825 "ODEIFTBL.spad" 1316682 1316690 1319269 1319274) (-824 "ODEEF.spad" 1312177 1312193 1316672 1316677) (-823 "ODECONST.spad" 1311722 1311740 1312167 1312172) (-822 "ODECAT.spad" 1310320 1310328 1311712 1311717) (-821 "OCTCT2.spad" 1309958 1309979 1310310 1310315) (-820 "OCT.spad" 1308046 1308056 1308760 1308799) (-819 "OCAMON.spad" 1307894 1307902 1308036 1308041) (-818 "OC.spad" 1305690 1305700 1307850 1307889) (-817 "OC.spad" 1303208 1303220 1305370 1305375) (-816 "OASGP.spad" 1303023 1303031 1303198 1303203) (-815 "OAMONS.spad" 1302545 1302553 1303013 1303018) (-814 "OAMON.spad" 1302303 1302311 1302535 1302540) (-813 "OAMON.spad" 1302059 1302069 1302293 1302298) (-812 "OAGROUP.spad" 1301597 1301605 1302049 1302054) (-811 "OAGROUP.spad" 1301133 1301143 1301587 1301592) (-810 "NUMTUBE.spad" 1300724 1300740 1301123 1301128) (-809 "NUMQUAD.spad" 1288700 1288708 1300714 1300719) (-808 "NUMODE.spad" 1280052 1280060 1288690 1288695) (-807 "NUMINT.spad" 1277618 1277626 1280042 1280047) (-806 "NUMFMT.spad" 1276458 1276466 1277608 1277613) (-805 "NUMERIC.spad" 1268572 1268582 1276263 1276268) (-804 "NTSCAT.spad" 1267080 1267096 1268540 1268567) (-803 "NTPOLFN.spad" 1266625 1266635 1266991 1266996) (-802 "NSUP2.spad" 1266017 1266029 1266615 1266620) (-801 "NSUP.spad" 1259012 1259022 1263432 1263585) (-800 "NSMP.spad" 1255111 1255130 1255403 1255530) (-799 "NREP.spad" 1253513 1253527 1255101 1255106) (-798 "NPCOEF.spad" 1252759 1252779 1253503 1253508) (-797 "NORMRETR.spad" 1252357 1252396 1252749 1252754) (-796 "NORMPK.spad" 1250299 1250318 1252347 1252352) (-795 "NORMMA.spad" 1249987 1250013 1250289 1250294) (-794 "NONE1.spad" 1249663 1249673 1249977 1249982) (-793 "NONE.spad" 1249404 1249412 1249653 1249658) (-792 "NODE1.spad" 1248891 1248907 1249394 1249399) (-791 "NNI.spad" 1247786 1247794 1248865 1248886) (-790 "NLINSOL.spad" 1246412 1246422 1247776 1247781) (-789 "NIPROB.spad" 1244953 1244961 1246402 1246407) (-788 "NFINTBAS.spad" 1242513 1242530 1244943 1244948) (-787 "NETCLT.spad" 1242487 1242498 1242503 1242508) (-786 "NCODIV.spad" 1240711 1240727 1242477 1242482) (-785 "NCNTFRAC.spad" 1240353 1240367 1240701 1240706) (-784 "NCEP.spad" 1238519 1238533 1240343 1240348) (-783 "NASRING.spad" 1238123 1238131 1238509 1238514) (-782 "NASRING.spad" 1237725 1237735 1238113 1238118) (-781 "NARNG.spad" 1237125 1237133 1237715 1237720) (-780 "NARNG.spad" 1236523 1236533 1237115 1237120) (-779 "NAGSP.spad" 1235600 1235608 1236513 1236518) (-778 "NAGS.spad" 1225317 1225325 1235590 1235595) (-777 "NAGF07.spad" 1223748 1223756 1225307 1225312) (-776 "NAGF04.spad" 1218150 1218158 1223738 1223743) (-775 "NAGF02.spad" 1212243 1212251 1218140 1218145) (-774 "NAGF01.spad" 1208012 1208020 1212233 1212238) (-773 "NAGE04.spad" 1201720 1201728 1208002 1208007) (-772 "NAGE02.spad" 1192372 1192380 1201710 1201715) (-771 "NAGE01.spad" 1188366 1188374 1192362 1192367) (-770 "NAGD03.spad" 1186362 1186370 1188356 1188361) (-769 "NAGD02.spad" 1179093 1179101 1186352 1186357) (-768 "NAGD01.spad" 1173378 1173386 1179083 1179088) (-767 "NAGC06.spad" 1169245 1169253 1173368 1173373) (-766 "NAGC05.spad" 1167738 1167746 1169235 1169240) (-765 "NAGC02.spad" 1167013 1167021 1167728 1167733) (-764 "NAALG.spad" 1166578 1166588 1166981 1167008) (-763 "NAALG.spad" 1166163 1166175 1166568 1166573) (-762 "MULTSQFR.spad" 1163121 1163138 1166153 1166158) (-761 "MULTFACT.spad" 1162504 1162521 1163111 1163116) (-760 "MTSCAT.spad" 1160598 1160619 1162402 1162499) (-759 "MTHING.spad" 1160257 1160267 1160588 1160593) (-758 "MSYSCMD.spad" 1159691 1159699 1160247 1160252) (-757 "MSETAGG.spad" 1159536 1159546 1159659 1159686) (-756 "MSET.spad" 1157449 1157459 1159197 1159236) (-755 "MRING.spad" 1154426 1154438 1157157 1157224) (-754 "MRF2.spad" 1153988 1154002 1154416 1154421) (-753 "MRATFAC.spad" 1153534 1153551 1153978 1153983) (-752 "MPRFF.spad" 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995230 995621 995626) (-638 "LALG.spad" 994990 995000 995194 995209) (-637 "LALG.spad" 994774 994786 994980 994985) (-636 "LA.spad" 994214 994228 994696 994735) (-635 "KVTFROM.spad" 993957 993967 994204 994209) (-634 "KTVLOGIC.spad" 993501 993509 993947 993952) (-633 "KRCFROM.spad" 993247 993257 993491 993496) (-632 "KOVACIC.spad" 991978 991995 993237 993242) (-631 "KONVERT.spad" 991700 991710 991968 991973) (-630 "KOERCE.spad" 991437 991447 991690 991695) (-629 "KERNEL2.spad" 991140 991152 991427 991432) (-628 "KERNEL.spad" 989780 989790 990909 990914) (-627 "KDAGG.spad" 988889 988911 989760 989775) (-626 "KDAGG.spad" 988006 988030 988879 988884) (-625 "KAFILE.spad" 986836 986852 987071 987098) (-624 "JVMOP.spad" 986749 986757 986826 986831) (-623 "JVMMDACC.spad" 985803 985811 986739 986744) (-622 "JVMFDACC.spad" 985119 985127 985793 985798) (-621 "JVMCSTTG.spad" 983848 983856 985109 985114) (-620 "JVMCFACC.spad" 983294 983302 983838 983843) (-619 "JVMBCODE.spad" 983205 983213 983284 983289) (-618 "JORDAN.spad" 981013 981025 982474 982619) (-617 "JOINAST.spad" 980715 980723 981003 981008) (-616 "IXAGG.spad" 978848 978872 980705 980710) (-615 "IXAGG.spad" 976836 976862 978695 978700) (-614 "IVECTOR.spad" 975432 975447 975587 975614) (-613 "ITUPLE.spad" 974608 974618 975422 975427) (-612 "ITRIGMNP.spad" 973455 973474 974598 974603) (-611 "ITFUN3.spad" 972961 972975 973445 973450) (-610 "ITFUN2.spad" 972705 972717 972951 972956) (-609 "ITFORM.spad" 972060 972068 972695 972700) (-608 "ITAYLOR.spad" 970054 970069 971924 972021) (-607 "ISUPS.spad" 962452 962467 968989 969086) (-606 "ISUMP.spad" 961953 961969 962442 962447) (-605 "ISTRING.spad" 960859 960872 960940 960967) (-604 "ISAST.spad" 960578 960586 960849 960854) (-603 "IRURPK.spad" 959295 959314 960568 960573) (-602 "IRSN.spad" 957299 957307 959285 959290) (-601 "IRRF2F.spad" 955792 955802 957255 957260) (-600 "IRREDFFX.spad" 955393 955404 955782 955787) (-599 "IROOT.spad" 953732 953742 955383 955388) (-598 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931099 931104) (-577 "INTPACK.spad" 919612 919620 929036 929041) (-576 "INTHERTR.spad" 918886 918903 919602 919607) (-575 "INTHERAL.spad" 918556 918580 918876 918881) (-574 "INTHEORY.spad" 914995 915003 918546 918551) (-573 "INTG0.spad" 908759 908777 914924 914929) (-572 "INTFTBL.spad" 904213 904221 908749 908754) (-571 "INTFACT.spad" 903280 903290 904203 904208) (-570 "INTEF.spad" 901691 901707 903270 903275) (-569 "INTDOM.spad" 900314 900322 901617 901686) (-568 "INTDOM.spad" 898999 899009 900304 900309) (-567 "INTCAT.spad" 897266 897276 898913 898994) (-566 "INTBIT.spad" 896773 896781 897256 897261) (-565 "INTALG.spad" 895961 895988 896763 896768) (-564 "INTAF.spad" 895461 895477 895951 895956) (-563 "INTABL.spad" 893501 893532 893664 893691) (-562 "INT8.spad" 893381 893389 893491 893496) (-561 "INT64.spad" 893260 893268 893371 893376) (-560 "INT32.spad" 893139 893147 893250 893255) (-559 "INT16.spad" 893018 893026 893129 893134) (-558 "INT.spad" 892461 892469 892872 893013) (-557 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"FPC.spad" 656075 656083 656931 657024) (-413 "FPC.spad" 655207 655217 656065 656070) (-412 "FPATMAB.spad" 654969 654979 655197 655202) (-411 "FPARFRAC.spad" 653811 653828 654959 654964) (-410 "FORTRAN.spad" 652317 652360 653801 653806) (-409 "FORTFN.spad" 649487 649495 652307 652312) (-408 "FORTCAT.spad" 649171 649179 649477 649482) (-407 "FORT.spad" 648120 648128 649161 649166) (-406 "FORDER.spad" 647811 647835 648110 648115) (-405 "FOP.spad" 647012 647020 647801 647806) (-404 "FNLA.spad" 646436 646458 646980 647007) (-403 "FNCAT.spad" 645031 645039 646426 646431) (-402 "FNAME.spad" 644923 644931 645021 645026) (-401 "FMTC.spad" 644721 644729 644849 644918) (-400 "FMONOID.spad" 644402 644412 644677 644682) (-399 "FMONCAT.spad" 641571 641581 644392 644397) (-398 "FMFUN.spad" 638601 638609 641561 641566) (-397 "FMCAT.spad" 636277 636295 638569 638596) (-396 "FMC.spad" 635329 635337 636267 636272) (-395 "FM1.spad" 634694 634706 635263 635290) (-394 "FM.spad" 634309 634321 634548 634575) (-393 "FLOATRP.spad" 632052 632066 634299 634304) (-392 "FLOATCP.spad" 629491 629505 632042 632047) (-391 "FLOAT.spad" 622805 622813 629357 629486) (-390 "FLINEXP.spad" 622527 622537 622795 622800) (-389 "FLINEXP.spad" 622190 622202 622460 622465) (-388 "FLASORT.spad" 621516 621528 622180 622185) (-387 "FLALG.spad" 619186 619205 621442 621511) (-386 "FLAGG2.spad" 617903 617919 619176 619181) (-385 "FLAGG.spad" 614969 614979 617883 617898) (-384 "FLAGG.spad" 611936 611948 614852 614857) (-383 "FINRALG.spad" 610021 610034 611892 611931) (-382 "FINRALG.spad" 608032 608047 609905 609910) (-381 "FINITE.spad" 607184 607192 608022 608027) (-380 "FINAALG.spad" 596369 596379 607126 607179) (-379 "FINAALG.spad" 585566 585578 596325 596330) (-378 "FILECAT.spad" 584100 584117 585556 585561) (-377 "FILE.spad" 583683 583693 584090 584095) (-376 "FIELD.spad" 583089 583097 583585 583678) (-375 "FIELD.spad" 582581 582591 583079 583084) (-374 "FGROUP.spad" 581244 581254 582561 582576) (-373 "FGLMICPK.spad" 580039 580054 581234 581239) (-372 "FFX.spad" 579422 579437 579755 579848) (-371 "FFSLPE.spad" 578933 578954 579412 579417) (-370 "FFPOLY2.spad" 577993 578010 578923 578928) (-369 "FFPOLY.spad" 569335 569346 577983 577988) (-368 "FFP.spad" 568740 568760 569051 569144) (-367 "FFNBX.spad" 567260 567280 568456 568549) (-366 "FFNBP.spad" 565781 565798 566976 567069) (-365 "FFNB.spad" 564246 564267 565462 565555) (-364 "FFINTBAS.spad" 561760 561779 564236 564241) (-363 "FFIELDC.spad" 559345 559353 561662 561755) (-362 "FFIELDC.spad" 557016 557026 559335 559340) (-361 "FFHOM.spad" 555788 555805 557006 557011) (-360 "FFF.spad" 553231 553242 555778 555783) (-359 "FFCGX.spad" 552086 552106 552947 553040) (-358 "FFCGP.spad" 550983 551003 551802 551895) (-357 "FFCG.spad" 549775 549796 550664 550757) (-356 "FFCAT2.spad" 549522 549562 549765 549770) (-355 "FFCAT.spad" 542687 542709 549361 549517) (-354 "FFCAT.spad" 535931 535955 542607 542612) (-353 "FF.spad" 535379 535395 535612 535705) (-352 "FEXPR.spad" 527079 527125 535126 535165) (-351 "FEVALAB.spad" 526787 526797 527069 527074) (-350 "FEVALAB.spad" 526271 526283 526555 526560) (-349 "FDIVCAT.spad" 524367 524391 526261 526266) (-348 "FDIVCAT.spad" 522461 522487 524357 524362) (-347 "FDIV2.spad" 522117 522157 522451 522456) (-346 "FDIV.spad" 521575 521599 522107 522112) (-345 "FCTRDATA.spad" 520583 520591 521565 521570) (-344 "FCPAK1.spad" 519118 519126 520573 520578) (-343 "FCOMP.spad" 518497 518507 519108 519113) (-342 "FC.spad" 508504 508512 518487 518492) (-341 "FAXF.spad" 501539 501553 508406 508499) (-340 "FAXF.spad" 494626 494642 501495 501500) (-339 "FARRAY.spad" 492602 492612 493635 493662) (-338 "FAMR.spad" 490746 490758 492500 492597) (-337 "FAMR.spad" 488874 488888 490630 490635) (-336 "FAMONOID.spad" 488558 488568 488828 488833) (-335 "FAMONC.spad" 486878 486890 488548 488553) (-334 "FAGROUP.spad" 486518 486528 486774 486801) (-333 "FACUTIL.spad" 484730 484747 486508 486513) (-332 "FACTFUNC.spad" 483932 483942 484720 484725) (-331 "EXPUPXS.spad" 480684 480707 481983 482132) (-330 "EXPRTUBE.spad" 477972 477980 480674 480679) (-329 "EXPRODE.spad" 475140 475156 477962 477967) (-328 "EXPR2UPS.spad" 471262 471275 475130 475135) (-327 "EXPR2.spad" 470967 470979 471252 471257) (-326 "EXPR.spad" 466052 466062 466766 467061) (-325 "EXPEXPAN.spad" 462796 462821 463428 463521) (-324 "EXITAST.spad" 462532 462540 462786 462791) (-323 "EXIT.spad" 462203 462211 462522 462527) (-322 "EVALCYC.spad" 461663 461677 462193 462198) (-321 "EVALAB.spad" 461243 461253 461653 461658) (-320 "EVALAB.spad" 460821 460833 461233 461238) (-319 "EUCDOM.spad" 458411 458419 460747 460816) (-318 "EUCDOM.spad" 456063 456073 458401 458406) (-317 "ESTOOLS2.spad" 455658 455672 456053 456058) (-316 "ESTOOLS1.spad" 455335 455346 455648 455653) (-315 "ESTOOLS.spad" 447213 447221 455325 455330) (-314 "ESCONT1.spad" 446954 446966 447203 447208) (-313 "ESCONT.spad" 443747 443755 446944 446949) (-312 "ES2.spad" 443260 443276 443737 443742) (-311 "ES1.spad" 442830 442846 443250 443255) (-310 "ES.spad" 435701 435709 442820 442825) (-309 "ES.spad" 428475 428485 435596 435601) (-308 "ERROR.spad" 425802 425810 428465 428470) (-307 "EQTBL.spad" 423796 423818 424005 424032) (-306 "EQ2.spad" 423514 423526 423786 423791) (-305 "EQ.spad" 418290 418300 421085 421197) (-304 "EP.spad" 414616 414626 418280 418285) (-303 "ENV.spad" 413294 413302 414606 414611) (-302 "ENTIRER.spad" 412962 412970 413238 413289) (-301 "EMR.spad" 412250 412291 412888 412957) (-300 "ELTAGG.spad" 410504 410523 412240 412245) (-299 "ELTAGG.spad" 408722 408743 410460 410465) (-298 "ELTAB.spad" 408197 408210 408712 408717) (-297 "ELFUTS.spad" 407632 407651 408187 408192) (-296 "ELEMFUN.spad" 407321 407329 407622 407627) (-295 "ELEMFUN.spad" 407008 407018 407311 407316) (-294 "ELAGG.spad" 404979 404989 406988 407003) (-293 "ELAGG.spad" 402887 402899 404898 404903) (-292 "ELABOR.spad" 402233 402241 402877 402882) (-291 "ELABEXPR.spad" 401165 401173 402223 402228) (-290 "EFUPXS.spad" 397941 397971 401121 401126) (-289 "EFULS.spad" 394777 394800 397897 397902) (-288 "EFSTRUC.spad" 392792 392808 394767 394772) (-287 "EF.spad" 387568 387584 392782 392787) (-286 "EAB.spad" 385868 385876 387558 387563) (-285 "E04UCFA.spad" 385404 385412 385858 385863) (-284 "E04NAFA.spad" 384981 384989 385394 385399) (-283 "E04MBFA.spad" 384561 384569 384971 384976) (-282 "E04JAFA.spad" 384097 384105 384551 384556) (-281 "E04GCFA.spad" 383633 383641 384087 384092) (-280 "E04FDFA.spad" 383169 383177 383623 383628) (-279 "E04DGFA.spad" 382705 382713 383159 383164) (-278 "E04AGNT.spad" 378579 378587 382695 382700) (-277 "DVARCAT.spad" 375469 375479 378569 378574) (-276 "DVARCAT.spad" 372357 372369 375459 375464) (-275 "DSMP.spad" 369653 369667 369958 370085) (-274 "DSEXT.spad" 368955 368965 369643 369648) (-273 "DSEXT.spad" 368161 368173 368851 368856) (-272 "DROPT1.spad" 367826 367836 368151 368156) (-271 "DROPT0.spad" 362691 362699 367816 367821) (-270 "DROPT.spad" 356650 356658 362681 362686) (-269 "DRAWPT.spad" 354823 354831 356640 356645) (-268 "DRAWHACK.spad" 354131 354141 354813 354818) (-267 "DRAWCX.spad" 351609 351617 354121 354126) (-266 "DRAWCURV.spad" 351156 351171 351599 351604) (-265 "DRAWCFUN.spad" 340688 340696 351146 351151) (-264 "DRAW.spad" 333564 333577 340678 340683) (-263 "DQAGG.spad" 331742 331752 333532 333559) (-262 "DPOLCAT.spad" 327099 327115 331610 331737) (-261 "DPOLCAT.spad" 322542 322560 327055 327060) (-260 "DPMO.spad" 314065 314081 314203 314416) (-259 "DPMM.spad" 305601 305619 305726 305939) (-258 "DOMTMPLT.spad" 305372 305380 305591 305596) (-257 "DOMCTOR.spad" 305127 305135 305362 305367) (-256 "DOMAIN.spad" 304238 304246 305117 305122) (-255 "DMP.spad" 301426 301441 301996 302123) (-254 "DMEXT.spad" 301293 301303 301394 301421) (-253 "DLP.spad" 300653 300663 301283 301288) (-252 "DLIST.spad" 299058 299068 299662 299689) (-251 "DLAGG.spad" 297475 297485 299048 299053) (-250 "DIVRING.spad" 297017 297025 297419 297470) (-249 "DIVRING.spad" 296603 296613 297007 297012) (-248 "DISPLAY.spad" 294793 294801 296593 296598) (-247 "DIRPROD2.spad" 293611 293629 294783 294788) (-246 "DIRPROD.spad" 280843 280859 281483 281582) (-245 "DIRPCAT.spad" 280036 280052 280739 280838) (-244 "DIRPCAT.spad" 278856 278874 279561 279566) (-243 "DIOSP.spad" 277681 277689 278846 278851) (-242 "DIOPS.spad" 276677 276687 277661 277676) (-241 "DIOPS.spad" 275647 275659 276633 276638) (-240 "DIFRING.spad" 275485 275493 275627 275642) (-239 "DIFFSPC.spad" 275064 275072 275475 275480) (-238 "DIFFSPC.spad" 274641 274651 275054 275059) (-237 "DIFFMOD.spad" 274130 274140 274609 274636) (-236 "DIFFDOM.spad" 273295 273306 274120 274125) (-235 "DIFFDOM.spad" 272458 272471 273285 273290) (-234 "DIFEXT.spad" 272277 272287 272438 272453) (-233 "DIAGG.spad" 271907 271917 272257 272272) (-232 "DIAGG.spad" 271545 271557 271897 271902) (-231 "DHMATRIX.spad" 269728 269738 270873 270900) (-230 "DFSFUN.spad" 263368 263376 269718 269723) (-229 "DFLOAT.spad" 259975 259983 263258 263363) (-228 "DFINTTLS.spad" 258206 258222 259965 259970) (-227 "DERHAM.spad" 256120 256152 258186 258201) (-226 "DEQUEUE.spad" 255315 255325 255598 255625) (-225 "DEGRED.spad" 254932 254946 255305 255310) (-224 "DEFINTRF.spad" 252514 252524 254922 254927) (-223 "DEFINTEF.spad" 251052 251068 252504 252509) (-222 "DEFAST.spad" 250436 250444 251042 251047) (-221 "DECIMAL.spad" 248400 248408 248761 248854) (-220 "DDFACT.spad" 246221 246238 248390 248395) (-219 "DBLRESP.spad" 245821 245845 246211 246216) (-218 "DBASIS.spad" 245447 245462 245811 245816) (-217 "DBASE.spad" 244111 244121 245437 245442) (-216 "DATAARY.spad" 243597 243610 244101 244106) (-215 "D03FAFA.spad" 243425 243433 243587 243592) (-214 "D03EEFA.spad" 243245 243253 243415 243420) (-213 "D03AGNT.spad" 242331 242339 243235 243240) (-212 "D02EJFA.spad" 241793 241801 242321 242326) (-211 "D02CJFA.spad" 241271 241279 241783 241788) (-210 "D02BHFA.spad" 240761 240769 241261 241266) (-209 "D02BBFA.spad" 240251 240259 240751 240756) (-208 "D02AGNT.spad" 235121 235129 240241 240246) (-207 "D01WGTS.spad" 233440 233448 235111 235116) (-206 "D01TRNS.spad" 233417 233425 233430 233435) (-205 "D01GBFA.spad" 232939 232947 233407 233412) (-204 "D01FCFA.spad" 232461 232469 232929 232934) (-203 "D01ASFA.spad" 231929 231937 232451 232456) (-202 "D01AQFA.spad" 231383 231391 231919 231924) (-201 "D01APFA.spad" 230823 230831 231373 231378) (-200 "D01ANFA.spad" 230317 230325 230813 230818) (-199 "D01AMFA.spad" 229827 229835 230307 230312) (-198 "D01ALFA.spad" 229367 229375 229817 229822) (-197 "D01AKFA.spad" 228893 228901 229357 229362) (-196 "D01AJFA.spad" 228416 228424 228883 228888) (-195 "D01AGNT.spad" 224483 224491 228406 228411) (-194 "CYCLOTOM.spad" 223989 223997 224473 224478) (-193 "CYCLES.spad" 220781 220789 223979 223984) (-192 "CVMP.spad" 220198 220208 220771 220776) (-191 "CTRIGMNP.spad" 218698 218714 220188 220193) (-190 "CTORKIND.spad" 218301 218309 218688 218693) (-189 "CTORCAT.spad" 217542 217550 218291 218296) (-188 "CTORCAT.spad" 216781 216791 217532 217537) (-187 "CTORCALL.spad" 216370 216380 216771 216776) (-186 "CTOR.spad" 216061 216069 216360 216365) (-185 "CSTTOOLS.spad" 215306 215319 216051 216056) (-184 "CRFP.spad" 209078 209091 215296 215301) (-183 "CRCEAST.spad" 208798 208806 209068 209073) (-182 "CRAPACK.spad" 207865 207875 208788 208793) (-181 "CPMATCH.spad" 207366 207381 207787 207792) (-180 "CPIMA.spad" 207071 207090 207356 207361) (-179 "COORDSYS.spad" 202080 202090 207061 207066) (-178 "CONTOUR.spad" 201507 201515 202070 202075) (-177 "CONTFRAC.spad" 197257 197267 201409 201502) (-176 "CONDUIT.spad" 197015 197023 197247 197252) (-175 "COMRING.spad" 196689 196697 196953 197010) (-174 "COMPPROP.spad" 196207 196215 196679 196684) (-173 "COMPLPAT.spad" 195974 195989 196197 196202) (-172 "COMPLEX2.spad" 195689 195701 195964 195969) (-171 "COMPLEX.spad" 191036 191046 191280 191541) (-170 "COMPILER.spad" 190585 190593 191026 191031) (-169 "COMPFACT.spad" 190187 190201 190575 190580) (-168 "COMPCAT.spad" 188259 188269 189921 190182) (-167 "COMPCAT.spad" 186056 186068 187720 187725) (-166 "COMMUPC.spad" 185804 185822 186046 186051) (-165 "COMMONOP.spad" 185337 185345 185794 185799) (-164 "COMMAAST.spad" 185100 185108 185327 185332) (-163 "COMM.spad" 184911 184919 185090 185095) (-162 "COMBOPC.spad" 183834 183842 184901 184906) (-161 "COMBINAT.spad" 182601 182611 183824 183829) (-160 "COMBF.spad" 180023 180039 182591 182596) (-159 "COLOR.spad" 178860 178868 180013 180018) (-158 "COLONAST.spad" 178526 178534 178850 178855) (-157 "CMPLXRT.spad" 178237 178254 178516 178521) (-156 "CLLCTAST.spad" 177899 177907 178227 178232) (-155 "CLIP.spad" 174007 174015 177889 177894) (-154 "CLIF.spad" 172662 172678 173963 174002) (-153 "CLAGG.spad" 169199 169209 172652 172657) (-152 "CLAGG.spad" 165604 165616 169059 169064) (-151 "CINTSLPE.spad" 164959 164972 165594 165599) (-150 "CHVAR.spad" 163097 163119 164949 164954) (-149 "CHARZ.spad" 163012 163020 163077 163092) (-148 "CHARPOL.spad" 162538 162548 163002 163007) (-147 "CHARNZ.spad" 162300 162308 162518 162533) (-146 "CHAR.spad" 159668 159676 162290 162295) (-145 "CFCAT.spad" 158996 159004 159658 159663) (-144 "CDEN.spad" 158216 158230 158986 158991) (-143 "CCLASS.spad" 156312 156320 157574 157613) (-142 "CATEGORY.spad" 155386 155394 156302 156307) (-141 "CATCTOR.spad" 155277 155285 155376 155381) (-140 "CATAST.spad" 154903 154911 155267 155272) (-139 "CASEAST.spad" 154617 154625 154893 154898) (-138 "CARTEN2.spad" 154007 154034 154607 154612) (-137 "CARTEN.spad" 149374 149398 153997 154002) (-136 "CARD.spad" 146669 146677 149348 149369) (-135 "CAPSLAST.spad" 146451 146459 146659 146664) (-134 "CACHSET.spad" 146075 146083 146441 146446) (-133 "CABMON.spad" 145630 145638 146065 146070) (-132 "BYTEORD.spad" 145305 145313 145620 145625) (-131 "BYTEBUF.spad" 143006 143014 144292 144319) (-130 "BYTE.spad" 142481 142489 142996 143001) (-129 "BTREE.spad" 141425 141435 141959 141986) (-128 "BTOURN.spad" 140301 140311 140903 140930) (-127 "BTCAT.spad" 139693 139703 140269 140296) (-126 "BTCAT.spad" 139105 139117 139683 139688) (-125 "BTAGG.spad" 138571 138579 139073 139100) (-124 "BTAGG.spad" 138057 138067 138561 138566) (-123 "BSTREE.spad" 136669 136679 137535 137562) (-122 "BRILL.spad" 134874 134885 136659 136664) (-121 "BRAGG.spad" 133830 133840 134864 134869) (-120 "BRAGG.spad" 132750 132762 133786 133791) (-119 "BPADICRT.spad" 130575 130587 130822 130915) (-118 "BPADIC.spad" 130247 130259 130501 130570) (-117 "BOUNDZRO.spad" 129903 129920 130237 130242) (-116 "BOP1.spad" 127361 127371 129893 129898) (-115 "BOP.spad" 122503 122511 127351 127356) (-114 "BOOLEAN.spad" 122051 122059 122493 122498) (-113 "BOOLE.spad" 121701 121709 122041 122046) (-112 "BOOLE.spad" 121349 121359 121691 121696) (-111 "BMODULE.spad" 121061 121073 121317 121344) (-110 "BITS.spad" 120435 120443 120650 120677) (-109 "BINDING.spad" 119856 119864 120425 120430) (-108 "BINARY.spad" 117825 117833 118181 118274) (-107 "BGAGG.spad" 117030 117040 117805 117820) (-106 "BGAGG.spad" 116243 116255 117020 117025) (-105 "BFUNCT.spad" 115807 115815 116223 116238) (-104 "BEZOUT.spad" 114947 114974 115757 115762) (-103 "BBTREE.spad" 111695 111705 114425 114452) (-102 "BASTYPE.spad" 111194 111202 111685 111690) (-101 "BASTYPE.spad" 110691 110701 111184 111189) (-100 "BALFACT.spad" 110150 110163 110681 110686) (-99 "AUTOMOR.spad" 109601 109610 110130 110145) (-98 "ATTREG.spad" 106324 106331 109353 109596) (-97 "ATTRBUT.spad" 102347 102354 106304 106319) (-96 "ATTRAST.spad" 102064 102071 102337 102342) (-95 "ATRIG.spad" 101534 101541 102054 102059) (-94 "ATRIG.spad" 101002 101011 101524 101529) (-93 "ASTCAT.spad" 100906 100913 100992 100997) (-92 "ASTCAT.spad" 100808 100817 100896 100901) (-91 "ASTACK.spad" 100018 100027 100286 100313) (-90 "ASSOCEQ.spad" 98852 98863 99974 99979) (-89 "ASP9.spad" 97933 97946 98842 98847) (-88 "ASP80.spad" 97255 97268 97923 97928) (-87 "ASP8.spad" 96298 96311 97245 97250) (-86 "ASP78.spad" 95749 95762 96288 96293) (-85 "ASP77.spad" 95118 95131 95739 95744) (-84 "ASP74.spad" 94210 94223 95108 95113) (-83 "ASP73.spad" 93481 93494 94200 94205) (-82 "ASP7.spad" 92641 92654 93471 93476) (-81 "ASP6.spad" 91508 91521 92631 92636) (-80 "ASP55.spad" 90017 90030 91498 91503) (-79 "ASP50.spad" 87834 87847 90007 90012) (-78 "ASP49.spad" 86833 86846 87824 87829) (-77 "ASP42.spad" 85248 85287 86823 86828) (-76 "ASP41.spad" 83835 83874 85238 85243) (-75 "ASP4.spad" 83130 83143 83825 83830) (-74 "ASP35.spad" 82118 82131 83120 83125) (-73 "ASP34.spad" 81419 81432 82108 82113) (-72 "ASP33.spad" 80979 80992 81409 81414) (-71 "ASP31.spad" 80119 80132 80969 80974) (-70 "ASP30.spad" 79011 79024 80109 80114) (-69 "ASP29.spad" 78477 78490 79001 79006) (-68 "ASP28.spad" 69750 69763 78467 78472) (-67 "ASP27.spad" 68647 68660 69740 69745) (-66 "ASP24.spad" 67734 67747 68637 68642) (-65 "ASP20.spad" 67198 67211 67724 67729) (-64 "ASP19.spad" 61884 61897 67188 67193) (-63 "ASP12.spad" 61298 61311 61874 61879) (-62 "ASP10.spad" 60569 60582 61288 61293) (-61 "ASP1.spad" 59950 59963 60559 60564) (-60 "ARRAY2.spad" 59189 59198 59428 59455) (-59 "ARRAY12.spad" 57902 57913 59179 59184) (-58 "ARRAY1.spad" 56565 56574 56911 56938) (-57 "ARR2CAT.spad" 52347 52368 56533 56560) (-56 "ARR2CAT.spad" 48149 48172 52337 52342) (-55 "ARITY.spad" 47521 47528 48139 48144) (-54 "APPRULE.spad" 46805 46827 47511 47516) (-53 "APPLYORE.spad" 46424 46437 46795 46800) (-52 "ANY1.spad" 45495 45504 46414 46419) (-51 "ANY.spad" 44346 44353 45485 45490) (-50 "ANTISYM.spad" 42791 42807 44326 44341) (-49 "ANON.spad" 42500 42507 42781 42786) (-48 "AN.spad" 40806 40813 42313 42406) (-47 "AMR.spad" 38991 39002 40704 40801) (-46 "AMR.spad" 37007 37020 38722 38727) (-45 "ALIST.spad" 33847 33868 34197 34224) (-44 "ALGSC.spad" 32982 33008 33719 33772) (-43 "ALGPKG.spad" 28765 28776 32938 32943) (-42 "ALGMFACT.spad" 27958 27972 28755 28760) (-41 "ALGMANIP.spad" 25442 25457 27785 27790) (-40 "ALGFF.spad" 23047 23074 23264 23420) (-39 "ALGFACT.spad" 22166 22176 23037 23042) (-38 "ALGEBRA.spad" 21999 22008 22122 22161) (-37 "ALGEBRA.spad" 21864 21875 21989 21994) (-36 "ALAGG.spad" 21376 21397 21832 21859) (-35 "AHYP.spad" 20757 20764 21366 21371) (-34 "AGG.spad" 19466 19473 20747 20752) (-33 "AGG.spad" 18139 18148 19422 19427) (-32 "AF.spad" 16567 16582 18071 18076) (-31 "ADDAST.spad" 16253 16260 16557 16562) (-30 "ACPLOT.spad" 14844 14851 16243 16248) (-29 "ACFS.spad" 12701 12710 14746 14839) (-28 "ACFS.spad" 10644 10655 12691 12696) (-27 "ACF.spad" 7398 7405 10546 10639) (-26 "ACF.spad" 4238 4247 7388 7393) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
+((-3 NIL 2277077 2277082 2277087 2277092) (-2 NIL 2277057 2277062 2277067 2277072) (-1 NIL 2277037 2277042 2277047 2277052) (0 NIL 2277017 2277022 2277027 2277032) (-1318 "ZMOD.spad" 2276826 2276839 2276955 2277012) (-1317 "ZLINDEP.spad" 2275924 2275935 2276816 2276821) (-1316 "ZDSOLVE.spad" 2265884 2265906 2275914 2275919) (-1315 "YSTREAM.spad" 2265379 2265390 2265874 2265879) (-1314 "YDIAGRAM.spad" 2265013 2265022 2265369 2265374) (-1313 "XRPOLY.spad" 2264233 2264253 2264869 2264938) (-1312 "XPR.spad" 2262028 2262041 2263951 2264050) (-1311 "XPOLYC.spad" 2261347 2261363 2261954 2262023) (-1310 "XPOLY.spad" 2260902 2260913 2261203 2261272) (-1309 "XPBWPOLY.spad" 2259341 2259361 2260676 2260745) (-1308 "XFALG.spad" 2256389 2256405 2259267 2259336) (-1307 "XF.spad" 2254852 2254867 2256291 2256384) (-1306 "XF.spad" 2253295 2253312 2254736 2254741) (-1305 "XEXPPKG.spad" 2252554 2252580 2253285 2253290) (-1304 "XDPOLY.spad" 2252168 2252184 2252410 2252479) (-1303 "XALG.spad" 2251836 2251847 2252124 2252163) (-1302 "WUTSET.spad" 2247806 2247823 2251437 2251464) (-1301 "WP.spad" 2247013 2247057 2247664 2247731) (-1300 "WHILEAST.spad" 2246811 2246820 2247003 2247008) (-1299 "WHEREAST.spad" 2246482 2246491 2246801 2246806) (-1298 "WFFINTBS.spad" 2244145 2244167 2246472 2246477) (-1297 "WEIER.spad" 2242367 2242378 2244135 2244140) (-1296 "VSPACE.spad" 2242040 2242051 2242335 2242362) (-1295 "VSPACE.spad" 2241733 2241746 2242030 2242035) (-1294 "VOID.spad" 2241410 2241419 2241723 2241728) (-1293 "VIEWDEF.spad" 2236611 2236620 2241400 2241405) (-1292 "VIEW3D.spad" 2220572 2220581 2236601 2236606) (-1291 "VIEW2D.spad" 2208471 2208480 2220562 2220567) (-1290 "VIEW.spad" 2206191 2206200 2208461 2208466) (-1289 "VECTOR2.spad" 2204830 2204843 2206181 2206186) (-1288 "VECTOR.spad" 2203330 2203341 2203581 2203608) (-1287 "VECTCAT.spad" 2201242 2201253 2203298 2203325) (-1286 "VECTCAT.spad" 2198961 2198974 2201019 2201024) (-1285 "VARIABLE.spad" 2198741 2198756 2198951 2198956) (-1284 "UTYPE.spad" 2198385 2198394 2198731 2198736) (-1283 "UTSODETL.spad" 2197680 2197704 2198341 2198346) (-1282 "UTSODE.spad" 2195896 2195916 2197670 2197675) (-1281 "UTSCAT.spad" 2193375 2193391 2195794 2195891) (-1280 "UTSCAT.spad" 2190474 2190492 2192895 2192900) (-1279 "UTS2.spad" 2190069 2190104 2190464 2190469) (-1278 "UTS.spad" 2184947 2184975 2188467 2188564) (-1277 "URAGG.spad" 2179668 2179679 2184937 2184942) (-1276 "URAGG.spad" 2174353 2174366 2179624 2179629) (-1275 "UPXSSING.spad" 2171971 2171997 2173407 2173540) (-1274 "UPXSCONS.spad" 2169649 2169669 2170022 2170171) (-1273 "UPXSCCA.spad" 2168220 2168240 2169495 2169644) (-1272 "UPXSCCA.spad" 2166933 2166955 2168210 2168215) (-1271 "UPXSCAT.spad" 2165522 2165538 2166779 2166928) (-1270 "UPXS2.spad" 2165065 2165118 2165512 2165517) (-1269 "UPXS.spad" 2162280 2162308 2163116 2163265) (-1268 "UPSQFREE.spad" 2160695 2160709 2162270 2162275) (-1267 "UPSCAT.spad" 2158490 2158514 2160593 2160690) (-1266 "UPSCAT.spad" 2155970 2155996 2158075 2158080) (-1265 "UPOLYC2.spad" 2155441 2155460 2155960 2155965) (-1264 "UPOLYC.spad" 2150521 2150532 2155283 2155436) (-1263 "UPOLYC.spad" 2145487 2145500 2150251 2150256) (-1262 "UPMP.spad" 2144419 2144432 2145477 2145482) (-1261 "UPDIVP.spad" 2143984 2143998 2144409 2144414) (-1260 "UPDECOMP.spad" 2142245 2142259 2143974 2143979) (-1259 "UPCDEN.spad" 2141462 2141478 2142235 2142240) (-1258 "UP2.spad" 2140826 2140847 2141452 2141457) (-1257 "UP.spad" 2137854 2137869 2138241 2138394) (-1256 "UNISEG2.spad" 2137351 2137364 2137810 2137815) (-1255 "UNISEG.spad" 2136704 2136715 2137270 2137275) (-1254 "UNIFACT.spad" 2135807 2135819 2136694 2136699) (-1253 "ULSCONS.spad" 2126719 2126739 2127089 2127238) (-1252 "ULSCCAT.spad" 2124456 2124476 2126565 2126714) (-1251 "ULSCCAT.spad" 2122301 2122323 2124412 2124417) (-1250 "ULSCAT.spad" 2120541 2120557 2122147 2122296) (-1249 "ULS2.spad" 2120055 2120108 2120531 2120536) (-1248 "ULS.spad" 2109626 2109654 2110571 2111000) (-1247 "UINT8.spad" 2109503 2109512 2109616 2109621) (-1246 "UINT64.spad" 2109379 2109388 2109493 2109498) (-1245 "UINT32.spad" 2109255 2109264 2109369 2109374) (-1244 "UINT16.spad" 2109131 2109140 2109245 2109250) (-1243 "UFD.spad" 2108196 2108205 2109057 2109126) (-1242 "UFD.spad" 2107323 2107334 2108186 2108191) (-1241 "UDVO.spad" 2106204 2106213 2107313 2107318) (-1240 "UDPO.spad" 2103785 2103796 2106160 2106165) (-1239 "TYPEAST.spad" 2103704 2103713 2103775 2103780) (-1238 "TYPE.spad" 2103636 2103645 2103694 2103699) (-1237 "TWOFACT.spad" 2102288 2102303 2103626 2103631) (-1236 "TUPLE.spad" 2101779 2101790 2102184 2102189) (-1235 "TUBETOOL.spad" 2098646 2098655 2101769 2101774) (-1234 "TUBE.spad" 2097293 2097310 2098636 2098641) (-1233 "TSETCAT.spad" 2085364 2085381 2097261 2097288) (-1232 "TSETCAT.spad" 2073421 2073440 2085320 2085325) (-1231 "TS.spad" 2072014 2072030 2072980 2073077) (-1230 "TRMANIP.spad" 2066378 2066395 2071702 2071707) (-1229 "TRIMAT.spad" 2065341 2065366 2066368 2066373) (-1228 "TRIGMNIP.spad" 2063868 2063885 2065331 2065336) (-1227 "TRIGCAT.spad" 2063380 2063389 2063858 2063863) (-1226 "TRIGCAT.spad" 2062890 2062901 2063370 2063375) (-1225 "TREE.spad" 2061336 2061347 2062368 2062395) (-1224 "TRANFUN.spad" 2061175 2061184 2061326 2061331) (-1223 "TRANFUN.spad" 2061012 2061023 2061165 2061170) (-1222 "TOPSP.spad" 2060686 2060695 2061002 2061007) (-1221 "TOOLSIGN.spad" 2060349 2060360 2060676 2060681) (-1220 "TEXTFILE.spad" 2058910 2058919 2060339 2060344) (-1219 "TEX1.spad" 2058466 2058477 2058900 2058905) (-1218 "TEX.spad" 2055660 2055669 2058456 2058461) (-1217 "TEMUTL.spad" 2055215 2055224 2055650 2055655) (-1216 "TBCMPPK.spad" 2053316 2053339 2055205 2055210) (-1215 "TBAGG.spad" 2052374 2052397 2053296 2053311) (-1214 "TBAGG.spad" 2051440 2051465 2052364 2052369) (-1213 "TANEXP.spad" 2050848 2050859 2051430 2051435) (-1212 "TALGOP.spad" 2050572 2050583 2050838 2050843) (-1211 "TABLEAU.spad" 2050053 2050064 2050562 2050567) (-1210 "TABLE.spad" 2047986 2048009 2048256 2048283) (-1209 "TABLBUMP.spad" 2044765 2044776 2047976 2047981) (-1208 "SYSTEM.spad" 2043993 2044002 2044755 2044760) (-1207 "SYSSOLP.spad" 2041476 2041487 2043983 2043988) (-1206 "SYSPTR.spad" 2041375 2041384 2041466 2041471) (-1205 "SYSNNI.spad" 2040598 2040609 2041365 2041370) (-1204 "SYSINT.spad" 2040002 2040013 2040588 2040593) (-1203 "SYNTAX.spad" 2036336 2036345 2039992 2039997) (-1202 "SYMTAB.spad" 2034404 2034413 2036326 2036331) (-1201 "SYMS.spad" 2030433 2030442 2034394 2034399) (-1200 "SYMPOLY.spad" 2029413 2029424 2029495 2029622) (-1199 "SYMFUNC.spad" 2028914 2028925 2029403 2029408) (-1198 "SYMBOL.spad" 2026409 2026418 2028904 2028909) (-1197 "SWITCH.spad" 2023180 2023189 2026399 2026404) (-1196 "SUTS.spad" 2020159 2020187 2021578 2021675) (-1195 "SUPXS.spad" 2017361 2017389 2018210 2018359) (-1194 "SUPFRACF.spad" 2016466 2016484 2017351 2017356) (-1193 "SUP2.spad" 2015858 2015871 2016456 2016461) (-1192 "SUP.spad" 2012500 2012511 2013273 2013426) (-1191 "SUMRF.spad" 2011474 2011485 2012490 2012495) (-1190 "SUMFS.spad" 2011103 2011120 2011464 2011469) (-1189 "SULS.spad" 2000661 2000689 2001619 2002048) (-1188 "SUCHTAST.spad" 2000430 2000439 2000651 2000656) (-1187 "SUCH.spad" 2000120 2000135 2000420 2000425) (-1186 "SUBSPACE.spad" 1992251 1992266 2000110 2000115) (-1185 "SUBRESP.spad" 1991421 1991435 1992207 1992212) (-1184 "STTFNC.spad" 1987889 1987905 1991411 1991416) (-1183 "STTF.spad" 1983988 1984004 1987879 1987884) (-1182 "STTAYLOR.spad" 1976633 1976644 1983863 1983868) (-1181 "STRTBL.spad" 1974648 1974665 1974797 1974824) (-1180 "STRING.spad" 1973414 1973423 1973635 1973662) (-1179 "STREAM3.spad" 1972987 1973002 1973404 1973409) (-1178 "STREAM2.spad" 1972115 1972128 1972977 1972982) (-1177 "STREAM1.spad" 1971821 1971832 1972105 1972110) (-1176 "STREAM.spad" 1968607 1968618 1971214 1971229) (-1175 "STINPROD.spad" 1967543 1967559 1968597 1968602) (-1174 "STEPAST.spad" 1966777 1966786 1967533 1967538) (-1173 "STEP.spad" 1965986 1965995 1966767 1966772) (-1172 "STBL.spad" 1964034 1964062 1964201 1964216) (-1171 "STAGG.spad" 1962733 1962744 1964024 1964029) (-1170 "STAGG.spad" 1961430 1961443 1962723 1962728) (-1169 "STACK.spad" 1960658 1960669 1960908 1960935) (-1168 "SRING.spad" 1960418 1960427 1960648 1960653) (-1167 "SREGSET.spad" 1958117 1958134 1960019 1960046) (-1166 "SRDCMPK.spad" 1956694 1956714 1958107 1958112) (-1165 "SRAGG.spad" 1951877 1951886 1956662 1956689) (-1164 "SRAGG.spad" 1947080 1947091 1951867 1951872) (-1163 "SQMATRIX.spad" 1944575 1944593 1945491 1945578) (-1162 "SPLTREE.spad" 1939041 1939054 1943837 1943864) (-1161 "SPLNODE.spad" 1935661 1935674 1939031 1939036) (-1160 "SPFCAT.spad" 1934470 1934479 1935651 1935656) (-1159 "SPECOUT.spad" 1933022 1933031 1934460 1934465) (-1158 "SPADXPT.spad" 1925113 1925122 1933012 1933017) (-1157 "spad-parser.spad" 1924578 1924587 1925103 1925108) (-1156 "SPADAST.spad" 1924279 1924288 1924568 1924573) (-1155 "SPACEC.spad" 1908494 1908505 1924269 1924274) (-1154 "SPACE3.spad" 1908270 1908281 1908484 1908489) (-1153 "SORTPAK.spad" 1907819 1907832 1908226 1908231) (-1152 "SOLVETRA.spad" 1905582 1905593 1907809 1907814) (-1151 "SOLVESER.spad" 1904038 1904049 1905572 1905577) (-1150 "SOLVERAD.spad" 1900064 1900075 1904028 1904033) (-1149 "SOLVEFOR.spad" 1898526 1898544 1900054 1900059) (-1148 "SNTSCAT.spad" 1898126 1898143 1898494 1898521) (-1147 "SMTS.spad" 1896408 1896434 1897685 1897782) (-1146 "SMP.spad" 1893811 1893831 1894201 1894328) (-1145 "SMITH.spad" 1892656 1892681 1893801 1893806) (-1144 "SMATCAT.spad" 1890774 1890804 1892600 1892651) (-1143 "SMATCAT.spad" 1888824 1888856 1890652 1890657) (-1142 "SKAGG.spad" 1887793 1887804 1888792 1888819) (-1141 "SINT.spad" 1886733 1886742 1887659 1887788) (-1140 "SIMPAN.spad" 1886461 1886470 1886723 1886728) (-1139 "SIGNRF.spad" 1885586 1885597 1886451 1886456) (-1138 "SIGNEF.spad" 1884872 1884889 1885576 1885581) (-1137 "SIGAST.spad" 1884289 1884298 1884862 1884867) (-1136 "SIG.spad" 1883651 1883660 1884279 1884284) (-1135 "SHP.spad" 1881595 1881610 1883607 1883612) (-1134 "SHDP.spad" 1868950 1868977 1869467 1869566) (-1133 "SGROUP.spad" 1868558 1868567 1868940 1868945) (-1132 "SGROUP.spad" 1868164 1868175 1868548 1868553) (-1131 "SGCF.spad" 1861303 1861312 1868154 1868159) (-1130 "SFRTCAT.spad" 1860249 1860266 1861271 1861298) (-1129 "SFRGCD.spad" 1859312 1859332 1860239 1860244) (-1128 "SFQCMPK.spad" 1854125 1854145 1859302 1859307) (-1127 "SFORT.spad" 1853564 1853578 1854115 1854120) (-1126 "SEXOF.spad" 1853407 1853447 1853554 1853559) (-1125 "SEXCAT.spad" 1851235 1851275 1853397 1853402) (-1124 "SEX.spad" 1851127 1851136 1851225 1851230) (-1123 "SETMN.spad" 1849587 1849604 1851117 1851122) (-1122 "SETCAT.spad" 1849072 1849081 1849577 1849582) (-1121 "SETCAT.spad" 1848555 1848566 1849062 1849067) (-1120 "SETAGG.spad" 1845104 1845115 1848535 1848550) (-1119 "SETAGG.spad" 1841661 1841674 1845094 1845099) (-1118 "SET.spad" 1839934 1839945 1841031 1841070) (-1117 "SEQAST.spad" 1839637 1839646 1839924 1839929) (-1116 "SEGXCAT.spad" 1838793 1838806 1839627 1839632) (-1115 "SEGCAT.spad" 1837718 1837729 1838783 1838788) (-1114 "SEGBIND2.spad" 1837416 1837429 1837708 1837713) (-1113 "SEGBIND.spad" 1837174 1837185 1837363 1837368) (-1112 "SEGAST.spad" 1836904 1836913 1837164 1837169) (-1111 "SEG2.spad" 1836339 1836352 1836860 1836865) (-1110 "SEG.spad" 1836152 1836163 1836258 1836263) (-1109 "SDVAR.spad" 1835428 1835439 1836142 1836147) (-1108 "SDPOL.spad" 1832683 1832694 1832974 1833101) (-1107 "SCPKG.spad" 1830772 1830783 1832673 1832678) (-1106 "SCOPE.spad" 1829949 1829958 1830762 1830767) (-1105 "SCACHE.spad" 1828645 1828656 1829939 1829944) (-1104 "SASTCAT.spad" 1828554 1828563 1828635 1828640) (-1103 "SAOS.spad" 1828426 1828435 1828544 1828549) (-1102 "SAERFFC.spad" 1828139 1828159 1828416 1828421) (-1101 "SAEFACT.spad" 1827840 1827860 1828129 1828134) (-1100 "SAE.spad" 1825274 1825290 1825885 1826020) (-1099 "RURPK.spad" 1822933 1822949 1825264 1825269) (-1098 "RULESET.spad" 1822386 1822410 1822923 1822928) (-1097 "RULECOLD.spad" 1822238 1822251 1822376 1822381) (-1096 "RULE.spad" 1820486 1820510 1822228 1822233) (-1095 "RTVALUE.spad" 1820221 1820230 1820476 1820481) (-1094 "RSTRCAST.spad" 1819938 1819947 1820211 1820216) (-1093 "RSETGCD.spad" 1816380 1816400 1819928 1819933) (-1092 "RSETCAT.spad" 1806348 1806365 1816348 1816375) (-1091 "RSETCAT.spad" 1796336 1796355 1806338 1806343) (-1090 "RSDCMPK.spad" 1794836 1794856 1796326 1796331) (-1089 "RRCC.spad" 1793220 1793250 1794826 1794831) (-1088 "RRCC.spad" 1791602 1791634 1793210 1793215) (-1087 "RPTAST.spad" 1791304 1791313 1791592 1791597) (-1086 "RPOLCAT.spad" 1770808 1770823 1791172 1791299) (-1085 "RPOLCAT.spad" 1750007 1750024 1770373 1770378) (-1084 "ROUTINE.spad" 1745408 1745417 1748156 1748183) (-1083 "ROMAN.spad" 1744736 1744745 1745274 1745403) (-1082 "ROIRC.spad" 1743816 1743848 1744726 1744731) (-1081 "RNS.spad" 1742792 1742801 1743718 1743811) (-1080 "RNS.spad" 1741854 1741865 1742782 1742787) (-1079 "RNGBIND.spad" 1741014 1741028 1741809 1741814) (-1078 "RNG.spad" 1740749 1740758 1741004 1741009) (-1077 "RMODULE.spad" 1740530 1740541 1740739 1740744) (-1076 "RMCAT2.spad" 1739950 1740007 1740520 1740525) (-1075 "RMATRIX.spad" 1738720 1738739 1739063 1739102) (-1074 "RMATCAT.spad" 1734299 1734330 1738676 1738715) (-1073 "RMATCAT.spad" 1729768 1729801 1734147 1734152) (-1072 "RLINSET.spad" 1729472 1729483 1729758 1729763) (-1071 "RINTERP.spad" 1729360 1729380 1729462 1729467) (-1070 "RING.spad" 1728830 1728839 1729340 1729355) (-1069 "RING.spad" 1728308 1728319 1728820 1728825) (-1068 "RIDIST.spad" 1727700 1727709 1728298 1728303) (-1067 "RGCHAIN.spad" 1726221 1726237 1727115 1727142) (-1066 "RGBCSPC.spad" 1726010 1726022 1726211 1726216) (-1065 "RGBCMDL.spad" 1725572 1725584 1726000 1726005) (-1064 "RFFACTOR.spad" 1725034 1725045 1725562 1725567) (-1063 "RFFACT.spad" 1724769 1724781 1725024 1725029) (-1062 "RFDIST.spad" 1723765 1723774 1724759 1724764) (-1061 "RF.spad" 1721439 1721450 1723755 1723760) (-1060 "RETSOL.spad" 1720858 1720871 1721429 1721434) (-1059 "RETRACT.spad" 1720286 1720297 1720848 1720853) (-1058 "RETRACT.spad" 1719712 1719725 1720276 1720281) (-1057 "RETAST.spad" 1719524 1719533 1719702 1719707) (-1056 "RESULT.spad" 1717086 1717095 1717673 1717700) (-1055 "RESRING.spad" 1716433 1716480 1717024 1717081) (-1054 "RESLATC.spad" 1715757 1715768 1716423 1716428) (-1053 "REPSQ.spad" 1715488 1715499 1715747 1715752) (-1052 "REPDB.spad" 1715195 1715206 1715478 1715483) (-1051 "REP2.spad" 1704909 1704920 1715037 1715042) (-1050 "REP1.spad" 1699129 1699140 1704859 1704864) (-1049 "REP.spad" 1696683 1696692 1699119 1699124) (-1048 "REGSET.spad" 1694475 1694492 1696284 1696311) (-1047 "REF.spad" 1693810 1693821 1694430 1694435) (-1046 "REDORDER.spad" 1693016 1693033 1693800 1693805) (-1045 "RECLOS.spad" 1691775 1691795 1692479 1692572) (-1044 "REALSOLV.spad" 1690915 1690924 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\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 65669fa1..3c8d2f7a 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,15 +1,15 @@
 
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@@ -21,18 +21,18 @@
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 ((((-628 $) $) . T) (($ $) . T)) 
@@ -843,7 +843,7 @@
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@@ -916,38 +916,38 @@
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 ((((-558)) . T)) 
 ((((-558)) . T)) 
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+((((-1255 (-558)) $) . T) (((-558) |#1|) . T)) 
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@@ -2192,16 +2192,16 @@
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@@ -2217,19 +2217,19 @@
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@@ -2237,8 +2237,8 @@
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@@ -2252,44 +2252,44 @@
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@@ -3397,10 +3394,10 @@
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 (((|#1| |#2| |#3| |#4|) . T)) 
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-1311) 205171) ((-1321 . -737) 205141) ((-1321 . -660) 205111) ((-1321 . -1085) 205095) ((-1321 . -1080) 205079) ((-1321 . -111) 205058) ((-1321 . -38) 205028) ((-1321 . -1316) 205007) ((-1320 . -1078) T) ((-1320 . -1086) T) ((-1320 . -1141) T) ((-1320 . -746) T) ((-1320 . -21) T) ((-1320 . -666) 204966) ((-1320 . -23) T) ((-1320 . -1130) T) ((-1320 . -630) 204948) ((-1320 . -1246) T) ((-1320 . -102) T) ((-1320 . -25) T) ((-1320 . -133) T) ((-1320 . -668) 204922) ((-1320 . -633) 204878) ((-1320 . -1311) 204862) ((-1320 . -737) 204832) ((-1320 . -660) 204802) ((-1320 . -1085) 204786) ((-1320 . -1080) 204770) ((-1320 . -111) 204749) ((-1320 . -38) 204719) ((-1320 . -397) 204698) ((-1320 . -1067) 204682) ((-1318 . -1319) 204658) ((-1318 . -1067) 204632) ((-1318 . -633) 204578) ((-1318 . -1078) T) ((-1318 . -1086) T) ((-1318 . -1141) T) ((-1318 . -746) T) ((-1318 . -21) T) ((-1318 . -666) 204537) ((-1318 . -23) T) ((-1318 . -1130) T) ((-1318 . -630) 204519) ((-1318 . -1246) T) ((-1318 . -102) T) ((-1318 . -25) T) ((-1318 . -133) T) ((-1318 . -668) 204493) ((-1318 . -1311) 204477) ((-1318 . -737) 204447) ((-1318 . -660) 204417) ((-1318 . -1085) 204401) ((-1318 . -1080) 204385) ((-1318 . -111) 204364) ((-1318 . -38) 204334) ((-1318 . -1316) 204310) ((-1317 . -1319) 204289) ((-1317 . -1067) 204246) ((-1317 . -633) 204175) ((-1317 . -1078) T) ((-1317 . -1086) T) ((-1317 . -1141) T) ((-1317 . -746) T) ((-1317 . -21) T) ((-1317 . -666) 204134) ((-1317 . -23) T) ((-1317 . -1130) T) ((-1317 . -630) 204116) ((-1317 . -1246) T) ((-1317 . -102) T) ((-1317 . -25) T) ((-1317 . -133) T) ((-1317 . -668) 204090) ((-1317 . -1311) 204074) ((-1317 . -737) 204044) ((-1317 . -660) 204014) ((-1317 . -1085) 203998) ((-1317 . -1080) 203982) ((-1317 . -111) 203961) ((-1317 . -38) 203931) ((-1317 . -1316) 203910) ((-1317 . -397) 203882) ((-1312 . -397) 203854) ((-1312 . -633) 203803) ((-1312 . -1067) 203780) ((-1312 . -660) 203750) ((-1312 . -737) 203720) ((-1312 . -668) 203694) ((-1312 . -666) 203653) ((-1312 . -133) T) ((-1312 . -25) T) ((-1312 . -102) T) ((-1312 . -1246) T) ((-1312 . -630) 203635) ((-1312 . -1130) T) ((-1312 . -23) T) ((-1312 . -21) T) ((-1312 . -1085) 203619) ((-1312 . -1080) 203603) ((-1312 . -111) 203582) ((-1312 . -1319) 203561) ((-1312 . -1078) T) ((-1312 . -1086) T) ((-1312 . -1141) T) ((-1312 . -746) T) ((-1312 . -1311) 203545) ((-1312 . -38) 203515) ((-1312 . -1316) 203494) ((-1310 . -1241) 203463) ((-1310 . -630) 203425) ((-1310 . -153) 203409) ((-1310 . -34) T) ((-1310 . -1246) T) ((-1310 . -102) T) ((-1310 . -321) 203347) ((-1310 . -526) 203280) ((-1310 . -1130) T) ((-1310 . -501) 203264) ((-1310 . -631) 203225) ((-1310 . -1005) 203194) ((-1309 . -1078) T) ((-1309 . -1086) T) ((-1309 . -1141) T) ((-1309 . -746) T) ((-1309 . -21) T) ((-1309 . -666) 203139) ((-1309 . -23) T) ((-1309 . -1130) T) ((-1309 . -630) 203108) ((-1309 . -1246) T) ((-1309 . -102) T) ((-1309 . -25) T) ((-1309 . -133) T) ((-1309 . -668) 203068) ((-1309 . -633) 203010) ((-1309 . -502) 202994) ((-1309 . -38) 202964) ((-1309 . -111) 202929) ((-1309 . -1080) 202899) ((-1309 . -1085) 202869) ((-1309 . -660) 202839) ((-1309 . -737) 202809) ((-1308 . -1112) T) ((-1308 . -502) 202790) ((-1308 . -630) 202756) ((-1308 . -633) 202737) ((-1308 . -1130) T) ((-1308 . -1246) T) ((-1308 . -102) T) ((-1308 . -93) T) ((-1307 . -1112) T) ((-1307 . -502) 202718) ((-1307 . -630) 202684) ((-1307 . -633) 202665) ((-1307 . -1130) T) ((-1307 . -1246) T) ((-1307 . -102) T) ((-1307 . -93) T) ((-1302 . -630) 202647) ((-1300 . -1130) T) ((-1300 . -630) 202629) ((-1300 . -1246) T) ((-1300 . -102) T) ((-1299 . -1130) T) ((-1299 . -630) 202611) ((-1299 . -1246) T) ((-1299 . -102) T) ((-1296 . -1295) 202595) ((-1296 . -385) 202579) ((-1296 . -872) 202558) ((-1296 . -869) 202537) ((-1296 . -153) 202521) ((-1296 . -34) T) ((-1296 . -1246) T) ((-1296 . -102) 202451) ((-1296 . -630) 202363) ((-1296 . -321) 202301) ((-1296 . -526) 202234) ((-1296 . -1130) 202184) ((-1296 . -501) 202168) ((-1296 . -631) 202129) ((-1296 . -298) 202081) ((-1296 . -616) 202058) ((-1296 . -300) 202035) ((-1296 . -671) 202019) ((-1296 . -19) 202003) ((-1293 . -1130) T) ((-1293 . -630) 201969) ((-1293 . -1246) T) ((-1293 . -102) T) ((-1286 . -1289) 201953) ((-1286 . -240) 201912) ((-1286 . -633) 201794) ((-1286 . -668) 201719) ((-1286 . -666) 201629) ((-1286 . -133) T) ((-1286 . -25) T) ((-1286 . -102) T) ((-1286 . -630) 201611) ((-1286 . -1130) T) ((-1286 . -23) T) ((-1286 . -21) T) ((-1286 . -746) T) ((-1286 . -1141) T) ((-1286 . -1086) T) ((-1286 . -1078) T) ((-1286 . -236) 201564) ((-1286 . -1246) T) ((-1286 . -239) 201523) ((-1286 . -298) 201488) ((-1286 . -925) 201401) ((-1286 . -919) 201289) ((-1286 . -927) 201202) ((-1286 . -1002) 201171) ((-1286 . -38) 201068) ((-1286 . -111) 200937) ((-1286 . -1080) 200820) ((-1286 . -1085) 200703) ((-1286 . -660) 200600) ((-1286 . -737) 200497) ((-1286 . -147) 200476) ((-1286 . -149) 200455) ((-1286 . -175) 200406) ((-1286 . -569) 200385) ((-1286 . -302) 200364) ((-1286 . -47) 200341) ((-1286 . -1275) 200318) ((-1286 . -35) 200284) ((-1286 . -95) 200250) ((-1286 . -296) 200216) ((-1286 . -505) 200182) ((-1286 . -1235) 200148) ((-1286 . -1232) 200114) ((-1286 . -1031) 200080) ((-1283 . -338) 200024) ((-1283 . -1067) 199990) ((-1283 . -424) 199956) ((-1283 . -38) 199848) ((-1283 . -633) 199722) ((-1283 . -668) 199627) ((-1283 . -666) 199517) ((-1283 . -746) T) ((-1283 . -1141) T) ((-1283 . -1086) T) ((-1283 . -1078) T) ((-1283 . -111) 199409) ((-1283 . -1080) 199314) ((-1283 . -1085) 199219) ((-1283 . -21) T) ((-1283 . -23) T) ((-1283 . -1130) T) ((-1283 . -630) 199201) ((-1283 . -1246) T) ((-1283 . -102) T) ((-1283 . -25) T) ((-1283 . -133) T) ((-1283 . -660) 199093) ((-1283 . -737) 198985) ((-1283 . -147) 198946) ((-1283 . -149) 198907) ((-1283 . -175) T) ((-1283 . -569) T) ((-1283 . -302) T) ((-1283 . -47) 198851) ((-1282 . -1281) 198830) ((-1282 . -376) 198809) ((-1282 . -1251) 198788) ((-1282 . -948) 198767) ((-1282 . -569) 198718) ((-1282 . -175) 198649) ((-1282 . -633) 198462) ((-1282 . -737) 198303) ((-1282 . -660) 198144) ((-1282 . -38) 197985) ((-1282 . -464) 197964) ((-1282 . -319) 197943) ((-1282 . -668) 197840) ((-1282 . -666) 197722) ((-1282 . -746) T) ((-1282 . -1141) T) ((-1282 . -1086) T) ((-1282 . -1078) T) ((-1282 . -111) 197543) ((-1282 . -1080) 197378) ((-1282 . -1085) 197213) ((-1282 . -21) T) ((-1282 . -23) T) ((-1282 . -1130) T) ((-1282 . -630) 197195) ((-1282 . -1246) T) ((-1282 . -102) T) ((-1282 . -25) T) ((-1282 . -133) T) ((-1282 . -302) 197146) ((-1282 . -250) 197125) ((-1282 . -1031) 197091) ((-1282 . -1232) 197057) ((-1282 . -1235) 197023) ((-1282 . -505) 196989) ((-1282 . -296) 196955) ((-1282 . -95) 196921) ((-1282 . -35) 196887) ((-1282 . -1275) 196857) ((-1282 . -47) 196827) ((-1282 . -149) 196806) ((-1282 . -147) 196785) ((-1282 . -1002) 196747) ((-1282 . -927) 196653) ((-1282 . -919) 196557) ((-1282 . -925) 196463) ((-1282 . -298) 196421) ((-1282 . -239) 196373) ((-1282 . -236) 196319) ((-1282 . -240) 196271) ((-1282 . -1279) 196255) ((-1282 . -1067) 196239) ((-1277 . -1281) 196200) ((-1277 . -376) 196179) ((-1277 . -1251) 196158) ((-1277 . -948) 196137) ((-1277 . -569) 196088) ((-1277 . -175) 196019) ((-1277 . -633) 195762) ((-1277 . -737) 195603) ((-1277 . -660) 195444) ((-1277 . -38) 195285) ((-1277 . -464) 195264) ((-1277 . -319) 195243) ((-1277 . -668) 195140) ((-1277 . -666) 195022) ((-1277 . -746) T) ((-1277 . -1141) T) ((-1277 . -1086) T) ((-1277 . -1078) T) ((-1277 . -111) 194843) ((-1277 . -1080) 194678) ((-1277 . -1085) 194513) ((-1277 . -21) T) ((-1277 . -23) T) ((-1277 . -1130) T) ((-1277 . -630) 194495) ((-1277 . -1246) T) ((-1277 . -102) T) ((-1277 . -25) T) ((-1277 . -133) T) ((-1277 . -302) 194446) ((-1277 . -250) 194425) ((-1277 . -1031) 194391) ((-1277 . -1232) 194357) ((-1277 . -1235) 194323) ((-1277 . -505) 194289) ((-1277 . -296) 194255) ((-1277 . -95) 194221) ((-1277 . -35) 194187) ((-1277 . -1275) 194157) ((-1277 . -47) 194127) ((-1277 . -149) 194106) ((-1277 . -147) 194085) ((-1277 . -1002) 194047) ((-1277 . -927) 193953) ((-1277 . -919) 193834) ((-1277 . -925) 193740) ((-1277 . -298) 193698) ((-1277 . -239) 193650) ((-1277 . -236) 193596) ((-1277 . -240) 193548) ((-1277 . -1279) 193532) ((-1277 . -1067) 193467) ((-1265 . -1272) 193451) ((-1265 . -1181) 193429) ((-1265 . -631) NIL) ((-1265 . -321) 193416) ((-1265 . -526) 193363) ((-1265 . -338) 193340) ((-1265 . -1067) 193220) ((-1265 . -424) 193204) ((-1265 . -38) 193033) ((-1265 . -111) 192842) ((-1265 . -1080) 192665) ((-1265 . -1085) 192488) ((-1265 . -666) 192398) ((-1265 . -668) 192287) ((-1265 . -660) 192116) ((-1265 . -737) 191945) ((-1265 . -633) 191693) ((-1265 . -147) 191672) ((-1265 . -149) 191651) ((-1265 . -47) 191628) ((-1265 . -390) 191612) ((-1265 . -658) 191560) ((-1265 . -925) 191503) ((-1265 . -919) 191406) ((-1265 . -927) 191313) ((-1265 . -909) NIL) ((-1265 . -937) 191292) ((-1265 . -1251) 191271) ((-1265 . -977) 191240) ((-1265 . -948) 191219) ((-1265 . -569) 191130) ((-1265 . -302) 191041) ((-1265 . -175) 190932) ((-1265 . -464) 190863) ((-1265 . -319) 190842) ((-1265 . -298) 190769) ((-1265 . -240) T) ((-1265 . -133) T) ((-1265 . -25) T) ((-1265 . -102) T) ((-1265 . -630) 190751) ((-1265 . -1130) T) ((-1265 . -23) T) ((-1265 . -21) T) ((-1265 . -746) T) ((-1265 . -1141) T) ((-1265 . -1086) T) ((-1265 . -1078) T) ((-1265 . -236) 190738) ((-1265 . -1246) T) ((-1265 . -239) T) ((-1265 . -274) 190722) ((-1265 . -234) 190706) ((-1263 . -1123) 190690) ((-1263 . -635) 190674) ((-1263 . -1130) 190652) ((-1263 . -630) 190619) ((-1263 . -1246) 190597) ((-1263 . -102) 190575) ((-1263 . -1124) 190532) ((-1261 . -1260) 190511) ((-1261 . -1031) 190477) ((-1261 . -1232) 190443) ((-1261 . -1235) 190409) ((-1261 . -505) 190375) ((-1261 . -296) 190341) ((-1261 . -95) 190307) ((-1261 . -35) 190273) ((-1261 . -1275) 190250) ((-1261 . -47) 190227) ((-1261 . -633) 189975) ((-1261 . -737) 189789) ((-1261 . -660) 189603) ((-1261 . -668) 189411) ((-1261 . -666) 189266) ((-1261 . -1085) 189074) ((-1261 . -1080) 188882) ((-1261 . -111) 188671) ((-1261 . -38) 188485) ((-1261 . -1002) 188454) ((-1261 . -298) 188354) ((-1261 . -1258) 188338) ((-1261 . -746) T) ((-1261 . -1141) T) ((-1261 . -1086) T) ((-1261 . -1078) T) ((-1261 . -21) T) ((-1261 . -23) T) ((-1261 . -1130) T) ((-1261 . -630) 188320) ((-1261 . -1246) T) ((-1261 . -102) T) ((-1261 . -25) T) ((-1261 . -133) T) ((-1261 . -147) 188245) ((-1261 . -149) 188170) ((-1261 . -631) 187841) ((-1261 . -234) 187811) ((-1261 . -925) 187662) ((-1261 . -927) 187459) ((-1261 . -919) 187254) ((-1261 . -274) 187224) ((-1261 . -239) 187083) ((-1261 . -236) 186936) ((-1261 . -240) 186841) ((-1261 . -376) 186820) ((-1261 . -1251) 186799) ((-1261 . -948) 186778) ((-1261 . -569) 186729) ((-1261 . -175) 186660) ((-1261 . -464) 186639) ((-1261 . -319) 186618) ((-1261 . -302) 186569) ((-1261 . -250) 186548) ((-1261 . -351) 186518) ((-1261 . -526) 186378) ((-1261 . -321) 186317) ((-1261 . -390) 186287) ((-1261 . -658) 186195) ((-1261 . -412) 186165) ((-1261 . -909) 186038) ((-1261 . -842) 185991) ((-1261 . -812) 185944) ((-1261 . -814) 185897) ((-1261 . -869) 185796) ((-1261 . -872) 185695) ((-1261 . -816) 185648) ((-1261 . -819) 185601) ((-1261 . -868) 185554) ((-1261 . -907) 185524) ((-1261 . -937) 185477) ((-1261 . -1049) 185429) ((-1261 . -1067) 185215) ((-1261 . -1181) 185167) ((-1261 . -1020) 185137) ((-1256 . -1260) 185098) ((-1256 . -1031) 185064) ((-1256 . -1232) 185030) ((-1256 . -1235) 184996) ((-1256 . -505) 184962) ((-1256 . -296) 184928) ((-1256 . -95) 184894) ((-1256 . -35) 184860) ((-1256 . -1275) 184837) ((-1256 . -47) 184814) ((-1256 . -633) 184609) ((-1256 . -737) 184405) ((-1256 . -660) 184201) ((-1256 . -668) 184053) ((-1256 . -666) 183890) ((-1256 . -1085) 183680) ((-1256 . -1080) 183470) ((-1256 . -111) 183239) ((-1256 . -38) 183035) ((-1256 . -1002) 183004) ((-1256 . -298) 182832) ((-1256 . -1258) 182816) ((-1256 . -746) T) ((-1256 . -1141) T) ((-1256 . -1086) T) ((-1256 . -1078) T) ((-1256 . -21) T) ((-1256 . -23) T) ((-1256 . -1130) T) ((-1256 . -630) 182798) ((-1256 . -1246) T) ((-1256 . -102) T) ((-1256 . -25) T) ((-1256 . -133) T) ((-1256 . -147) 182705) ((-1256 . -149) 182612) ((-1256 . -631) NIL) ((-1256 . -234) 182564) ((-1256 . -925) 182397) ((-1256 . -927) 182158) ((-1256 . -919) 181894) ((-1256 . -274) 181846) ((-1256 . -239) 181669) ((-1256 . -236) 181486) ((-1256 . -240) 181373) ((-1256 . -376) 181352) ((-1256 . -1251) 181331) ((-1256 . -948) 181310) ((-1256 . -569) 181261) ((-1256 . -175) 181192) ((-1256 . -464) 181171) ((-1256 . -319) 181150) ((-1256 . -302) 181101) ((-1256 . -250) 181080) ((-1256 . -351) 181032) ((-1256 . -526) 180801) ((-1256 . -321) 180686) ((-1256 . -390) 180638) ((-1256 . -658) 180590) ((-1256 . -412) 180542) ((-1256 . -909) NIL) ((-1256 . -842) NIL) ((-1256 . -812) NIL) ((-1256 . -814) NIL) ((-1256 . -869) NIL) ((-1256 . -872) NIL) ((-1256 . -816) NIL) ((-1256 . -819) NIL) ((-1256 . -868) NIL) ((-1256 . -907) 180494) ((-1256 . -937) NIL) ((-1256 . -1049) NIL) ((-1256 . -1067) 180460) ((-1256 . -1181) NIL) ((-1256 . -1020) 180412) ((-1255 . -865) T) ((-1255 . -872) T) ((-1255 . -869) T) ((-1255 . -1130) T) ((-1255 . -630) 180394) ((-1255 . -1246) T) ((-1255 . -102) T) ((-1255 . -381) T) ((-1255 . -682) T) ((-1254 . -865) T) ((-1254 . -872) T) ((-1254 . -869) T) ((-1254 . -1130) T) ((-1254 . -630) 180376) ((-1254 . -1246) T) ((-1254 . -102) T) ((-1254 . -381) T) ((-1254 . -682) T) ((-1253 . -865) T) ((-1253 . -872) T) ((-1253 . -869) T) ((-1253 . -1130) T) ((-1253 . -630) 180358) ((-1253 . -1246) T) ((-1253 . -102) T) ((-1253 . -381) T) ((-1253 . -682) T) ((-1252 . -865) T) ((-1252 . -872) T) ((-1252 . -869) T) ((-1252 . -1130) T) ((-1252 . -630) 180340) ((-1252 . -1246) T) ((-1252 . -102) T) ((-1252 . -381) T) ((-1252 . -682) T) ((-1247 . -1112) T) ((-1247 . -502) 180321) ((-1247 . -630) 180287) ((-1247 . -633) 180268) ((-1247 . -1130) T) ((-1247 . -1246) T) ((-1247 . -102) T) ((-1247 . -93) T) ((-1244 . -502) 180245) ((-1244 . -630) 180157) ((-1244 . -633) 180134) ((-1244 . -1130) 180112) ((-1244 . -1246) 180090) ((-1244 . -102) 180068) ((-1239 . -760) 180044) ((-1239 . -35) 180010) ((-1239 . -95) 179976) ((-1239 . -296) 179942) ((-1239 . -505) 179908) ((-1239 . -1235) 179874) ((-1239 . -1232) 179840) ((-1239 . -1031) 179806) ((-1239 . -47) 179775) ((-1239 . -38) 179672) ((-1239 . -660) 179569) ((-1239 . -737) 179466) ((-1239 . -633) 179348) ((-1239 . -302) 179327) ((-1239 . -569) 179306) ((-1239 . -111) 179175) ((-1239 . -1080) 179058) ((-1239 . -1085) 178941) ((-1239 . -175) 178892) ((-1239 . -149) 178871) ((-1239 . -147) 178850) ((-1239 . -668) 178775) ((-1239 . -666) 178685) ((-1239 . -1002) 178647) ((-1239 . -927) 178628) ((-1239 . -1246) T) ((-1239 . -919) 178607) ((-1239 . -1078) T) ((-1239 . -1086) T) ((-1239 . -1141) T) ((-1239 . -746) T) ((-1239 . -21) T) ((-1239 . -23) T) ((-1239 . -1130) T) ((-1239 . -630) 178589) ((-1239 . -102) T) ((-1239 . -25) T) ((-1239 . -133) T) ((-1239 . -925) 178570) ((-1239 . -526) 178537) ((-1239 . -321) 178524) ((-1233 . -1039) 178508) ((-1233 . -34) T) ((-1233 . -1246) T) ((-1233 . -102) 178458) ((-1233 . -630) 178390) ((-1233 . -321) 178328) ((-1233 . -526) 178261) ((-1233 . -1130) 178239) ((-1233 . -501) 178223) ((-1228 . -378) 178197) ((-1228 . -102) T) ((-1228 . -1246) T) ((-1228 . -630) 178179) ((-1228 . -1130) T) ((-1226 . -1130) T) ((-1226 . -630) 178161) ((-1226 . -1246) T) ((-1226 . -102) T) ((-1226 . -633) 178143) ((-1220 . -857) 178127) ((-1220 . -102) T) ((-1220 . -1246) T) ((-1220 . -630) 178109) ((-1220 . -1130) T) ((-1218 . -1223) 178088) ((-1218 . -233) 178038) ((-1218 . -107) 177988) ((-1218 . -321) 177792) ((-1218 . -526) 177584) ((-1218 . -501) 177521) ((-1218 . -153) 177471) ((-1218 . -631) NIL) ((-1218 . -242) 177421) ((-1218 . -627) 177400) ((-1218 . -300) 177379) ((-1218 . -1246) T) ((-1218 . -298) 177358) ((-1218 . -1130) T) ((-1218 . -630) 177340) ((-1218 . -102) T) ((-1218 . -34) T) ((-1218 . -616) 177319) ((-1216 . -1246) T) ((-1214 . -1130) T) ((-1214 . -630) 177301) ((-1214 . -1246) T) ((-1214 . -102) T) ((-1213 . -865) T) ((-1213 . -872) T) ((-1213 . -869) T) ((-1213 . -1130) T) ((-1213 . -630) 177283) ((-1213 . -1246) T) ((-1213 . -102) T) ((-1213 . -381) T) ((-1213 . -682) T) ((-1212 . -865) T) ((-1212 . -872) T) ((-1212 . -869) T) ((-1212 . -1130) T) ((-1212 . -630) 177265) ((-1212 . -1246) T) ((-1212 . -102) T) ((-1212 . -381) T) ((-1211 . -1292) T) ((-1211 . -1130) T) ((-1211 . -630) 177232) ((-1211 . -1246) T) ((-1211 . -102) T) ((-1211 . -1067) 177168) ((-1211 . -633) 177104) ((-1210 . -630) 177086) ((-1209 . -630) 177068) ((-1208 . -338) 177044) ((-1208 . -1067) 176940) ((-1208 . -424) 176924) ((-1208 . -38) 176821) ((-1208 . -633) 176674) ((-1208 . -668) 176599) ((-1208 . -666) 176509) ((-1208 . -746) T) ((-1208 . -1141) T) ((-1208 . -1086) T) ((-1208 . -1078) T) ((-1208 . -111) 176378) ((-1208 . -1080) 176261) ((-1208 . -1085) 176144) ((-1208 . -21) T) ((-1208 . -23) T) ((-1208 . -1130) T) ((-1208 . -630) 176126) ((-1208 . -1246) T) ((-1208 . -102) T) ((-1208 . -25) T) ((-1208 . -133) T) ((-1208 . -660) 176023) ((-1208 . -737) 175920) ((-1208 . -147) 175899) ((-1208 . -149) 175878) ((-1208 . -175) 175829) ((-1208 . -569) 175808) ((-1208 . -302) 175787) ((-1208 . -47) 175763) ((-1206 . -869) T) ((-1206 . -630) 175745) ((-1206 . -1130) T) ((-1206 . -102) T) ((-1206 . -1246) T) ((-1206 . -872) T) ((-1206 . -631) 175667) ((-1206 . -633) 175648) ((-1206 . -909) 175615) ((-1205 . -630) 175597) ((-1204 . -1289) 175581) ((-1204 . -240) 175540) ((-1204 . -633) 175422) ((-1204 . -668) 175347) ((-1204 . -666) 175257) ((-1204 . -133) T) ((-1204 . -25) T) ((-1204 . -102) T) ((-1204 . -630) 175239) ((-1204 . -1130) T) ((-1204 . -23) T) ((-1204 . -21) T) ((-1204 . -746) T) ((-1204 . -1141) T) ((-1204 . -1086) T) ((-1204 . -1078) T) ((-1204 . -236) 175192) ((-1204 . -1246) T) ((-1204 . -239) 175151) ((-1204 . -298) 175116) ((-1204 . -925) 175029) ((-1204 . -919) 174917) ((-1204 . -927) 174830) ((-1204 . -1002) 174799) ((-1204 . -38) 174696) ((-1204 . -111) 174565) ((-1204 . -1080) 174448) ((-1204 . -1085) 174331) ((-1204 . -660) 174228) ((-1204 . -737) 174125) ((-1204 . -147) 174104) ((-1204 . -149) 174083) ((-1204 . -175) 174034) ((-1204 . -569) 174013) ((-1204 . -302) 173992) ((-1204 . -47) 173969) ((-1204 . -1275) 173946) ((-1204 . -35) 173912) ((-1204 . -95) 173878) ((-1204 . -296) 173844) ((-1204 . -505) 173810) ((-1204 . -1235) 173776) ((-1204 . -1232) 173742) ((-1204 . -1031) 173708) ((-1203 . -1281) 173669) ((-1203 . -376) 173648) ((-1203 . -1251) 173627) ((-1203 . -948) 173606) ((-1203 . -569) 173557) ((-1203 . -175) 173488) ((-1203 . -633) 173231) ((-1203 . -737) 173072) ((-1203 . -660) 172913) ((-1203 . -38) 172754) ((-1203 . -464) 172733) ((-1203 . -319) 172712) ((-1203 . -668) 172609) ((-1203 . -666) 172491) ((-1203 . -746) T) ((-1203 . -1141) T) ((-1203 . -1086) T) ((-1203 . -1078) T) ((-1203 . -111) 172312) ((-1203 . -1080) 172147) ((-1203 . -1085) 171982) ((-1203 . -21) T) ((-1203 . -23) T) ((-1203 . -1130) T) ((-1203 . -630) 171964) ((-1203 . -1246) T) ((-1203 . -102) T) ((-1203 . -25) T) ((-1203 . -133) T) ((-1203 . -302) 171915) ((-1203 . -250) 171894) ((-1203 . -1031) 171860) ((-1203 . -1232) 171826) ((-1203 . -1235) 171792) ((-1203 . -505) 171758) ((-1203 . -296) 171724) ((-1203 . -95) 171690) ((-1203 . -35) 171656) ((-1203 . -1275) 171626) ((-1203 . -47) 171596) ((-1203 . -149) 171575) ((-1203 . -147) 171554) ((-1203 . -1002) 171516) ((-1203 . -927) 171422) ((-1203 . -919) 171303) ((-1203 . -925) 171209) ((-1203 . -298) 171167) ((-1203 . -239) 171119) ((-1203 . -236) 171065) ((-1203 . -240) 171017) ((-1203 . -1279) 171001) ((-1203 . -1067) 170936) ((-1200 . -1272) 170920) ((-1200 . -1181) 170898) ((-1200 . -631) NIL) ((-1200 . -321) 170885) ((-1200 . -526) 170832) ((-1200 . -338) 170809) ((-1200 . -1067) 170689) ((-1200 . -424) 170673) ((-1200 . -38) 170502) ((-1200 . -111) 170311) ((-1200 . -1080) 170134) ((-1200 . -1085) 169957) ((-1200 . -666) 169867) ((-1200 . -668) 169756) ((-1200 . -660) 169585) ((-1200 . -737) 169414) ((-1200 . -633) 169183) ((-1200 . -147) 169162) ((-1200 . -149) 169141) ((-1200 . -47) 169118) ((-1200 . -390) 169102) ((-1200 . -658) 169050) ((-1200 . -925) 168993) ((-1200 . -919) 168896) ((-1200 . -927) 168803) ((-1200 . -909) NIL) ((-1200 . -937) 168782) ((-1200 . -1251) 168761) ((-1200 . -977) 168730) ((-1200 . -948) 168709) ((-1200 . -569) 168620) ((-1200 . -302) 168531) ((-1200 . -175) 168422) ((-1200 . -464) 168353) ((-1200 . -319) 168332) ((-1200 . -298) 168259) ((-1200 . -240) T) ((-1200 . -133) T) ((-1200 . -25) T) ((-1200 . -102) T) ((-1200 . -630) 168241) ((-1200 . -1130) T) ((-1200 . -23) T) ((-1200 . -21) T) ((-1200 . -746) T) ((-1200 . -1141) T) ((-1200 . -1086) T) ((-1200 . -1078) T) ((-1200 . -236) 168228) ((-1200 . -1246) T) ((-1200 . -239) T) ((-1200 . -274) 168212) ((-1200 . -234) 168196) ((-1197 . -1260) 168157) ((-1197 . -1031) 168123) ((-1197 . -1232) 168089) ((-1197 . -1235) 168055) ((-1197 . -505) 168021) ((-1197 . -296) 167987) ((-1197 . -95) 167953) ((-1197 . -35) 167919) ((-1197 . -1275) 167896) ((-1197 . -47) 167873) ((-1197 . -633) 167668) ((-1197 . -737) 167464) ((-1197 . -660) 167260) ((-1197 . -668) 167112) ((-1197 . -666) 166949) ((-1197 . -1085) 166739) ((-1197 . -1080) 166529) ((-1197 . -111) 166298) ((-1197 . -38) 166094) ((-1197 . -1002) 166063) ((-1197 . -298) 165891) ((-1197 . -1258) 165875) ((-1197 . -746) T) ((-1197 . -1141) T) ((-1197 . -1086) T) ((-1197 . -1078) T) ((-1197 . -21) T) ((-1197 . -23) T) ((-1197 . -1130) T) ((-1197 . -630) 165857) ((-1197 . -1246) T) ((-1197 . -102) T) ((-1197 . -25) T) ((-1197 . -133) T) ((-1197 . -147) 165764) ((-1197 . -149) 165671) ((-1197 . -631) NIL) ((-1197 . -234) 165623) ((-1197 . -925) 165456) ((-1197 . -927) 165217) ((-1197 . -919) 164953) ((-1197 . -274) 164905) ((-1197 . -239) 164728) ((-1197 . -236) 164545) ((-1197 . -240) 164432) ((-1197 . -376) 164411) ((-1197 . -1251) 164390) ((-1197 . -948) 164369) ((-1197 . -569) 164320) ((-1197 . -175) 164251) ((-1197 . -464) 164230) ((-1197 . -319) 164209) ((-1197 . -302) 164160) ((-1197 . -250) 164139) ((-1197 . -351) 164091) ((-1197 . -526) 163860) ((-1197 . -321) 163745) ((-1197 . -390) 163697) ((-1197 . -658) 163649) ((-1197 . -412) 163601) ((-1197 . -909) NIL) ((-1197 . -842) NIL) ((-1197 . -812) NIL) ((-1197 . -814) NIL) ((-1197 . -869) NIL) ((-1197 . -872) NIL) ((-1197 . -816) NIL) ((-1197 . -819) NIL) ((-1197 . -868) NIL) ((-1197 . -907) 163553) ((-1197 . -937) NIL) ((-1197 . -1049) NIL) ((-1197 . -1067) 163519) ((-1197 . -1181) NIL) ((-1197 . -1020) 163471) ((-1196 . -1112) T) ((-1196 . -502) 163452) ((-1196 . -630) 163418) ((-1196 . -633) 163399) ((-1196 . -1130) T) ((-1196 . -1246) T) ((-1196 . -102) T) ((-1196 . -93) T) ((-1195 . -1130) T) ((-1195 . -630) 163381) ((-1195 . -1246) T) ((-1195 . -102) T) ((-1194 . -1130) T) ((-1194 . -630) 163363) ((-1194 . -1246) T) ((-1194 . -102) T) ((-1189 . -1223) 163339) ((-1189 . -233) 163286) ((-1189 . -107) 163233) ((-1189 . -321) 163028) ((-1189 . -526) 162811) ((-1189 . -501) 162745) ((-1189 . -153) 162692) ((-1189 . -631) NIL) ((-1189 . -242) 162639) ((-1189 . -627) 162615) ((-1189 . -300) 162591) ((-1189 . -1246) T) ((-1189 . -298) 162567) ((-1189 . -1130) T) ((-1189 . -630) 162549) ((-1189 . -102) T) ((-1189 . -34) T) ((-1189 . -616) 162525) ((-1188 . -1173) T) ((-1188 . -385) 162507) ((-1188 . -872) T) ((-1188 . -869) T) ((-1188 . -153) 162489) ((-1188 . -34) T) ((-1188 . -1246) T) ((-1188 . -102) T) ((-1188 . -630) 162471) ((-1188 . -321) NIL) ((-1188 . -526) NIL) ((-1188 . -1130) T) ((-1188 . -501) 162453) ((-1188 . -631) NIL) ((-1188 . -298) 162403) ((-1188 . -616) 162378) ((-1188 . -300) 162353) ((-1188 . -671) 162335) ((-1188 . -19) 162317) ((-1184 . -694) 162301) ((-1184 . -671) 162285) ((-1184 . -300) 162262) ((-1184 . -298) 162214) ((-1184 . -616) 162191) ((-1184 . -631) 162152) ((-1184 . -501) 162136) ((-1184 . -1130) 162114) ((-1184 . -526) 162047) ((-1184 . -321) 161985) ((-1184 . -630) 161917) ((-1184 . -102) 161867) ((-1184 . -1246) T) ((-1184 . -34) T) ((-1184 . -153) 161851) ((-1184 . -1285) 161835) ((-1184 . -1039) 161819) ((-1184 . -1179) 161803) ((-1184 . -633) 161780) ((-1182 . -1112) T) ((-1182 . -502) 161761) ((-1182 . -630) 161727) ((-1182 . -633) 161708) ((-1182 . -1130) T) ((-1182 . -1246) T) ((-1182 . -102) T) ((-1182 . -93) T) ((-1180 . -1223) 161687) ((-1180 . -233) 161637) ((-1180 . -107) 161587) ((-1180 . -321) 161391) ((-1180 . -526) 161183) ((-1180 . -501) 161120) ((-1180 . -153) 161070) ((-1180 . -631) NIL) ((-1180 . -242) 161020) ((-1180 . -627) 160999) ((-1180 . -300) 160978) ((-1180 . -1246) T) ((-1180 . -298) 160957) ((-1180 . -1130) T) ((-1180 . -630) 160939) ((-1180 . -102) T) ((-1180 . -34) T) ((-1180 . -616) 160918) ((-1177 . -1150) 160902) ((-1177 . -501) 160886) ((-1177 . -1130) 160864) ((-1177 . -526) 160797) ((-1177 . -321) 160735) ((-1177 . -630) 160667) ((-1177 . -102) 160617) ((-1177 . -1246) T) ((-1177 . -34) T) ((-1177 . -107) 160601) ((-1175 . -1138) 160570) ((-1175 . -1241) 160539) ((-1175 . -630) 160501) ((-1175 . -153) 160485) ((-1175 . -34) T) ((-1175 . -1246) T) ((-1175 . -102) T) ((-1175 . -321) 160423) ((-1175 . -526) 160356) ((-1175 . -1130) T) ((-1175 . -501) 160340) ((-1175 . -631) 160301) ((-1175 . -1005) 160270) ((-1175 . -1100) 160239) ((-1171 . -1152) 160184) ((-1171 . -501) 160168) ((-1171 . -526) 160101) ((-1171 . -321) 160039) ((-1171 . -34) T) ((-1171 . -1082) 159979) ((-1171 . -1067) 159875) ((-1171 . -633) 159793) ((-1171 . -424) 159777) ((-1171 . -658) 159725) ((-1171 . -668) 159663) ((-1171 . -390) 159647) ((-1171 . -240) 159626) ((-1171 . -236) 159571) ((-1171 . -239) 159522) ((-1171 . -274) 159506) ((-1171 . -919) 159427) ((-1171 . -927) 159350) ((-1171 . -925) 159309) ((-1171 . -234) 159293) ((-1171 . -737) 159225) ((-1171 . -660) 159157) ((-1171 . -666) 159116) ((-1171 . -133) T) ((-1171 . -25) T) ((-1171 . -102) T) ((-1171 . -1246) T) ((-1171 . -630) 159078) ((-1171 . -1130) T) ((-1171 . -23) T) ((-1171 . -21) T) ((-1171 . -1085) 159062) ((-1171 . -1080) 159046) ((-1171 . -111) 159025) ((-1171 . -1078) T) ((-1171 . -1086) T) ((-1171 . -1141) T) ((-1171 . -746) T) ((-1171 . -38) 158985) ((-1171 . -631) 158946) ((-1170 . -1039) 158917) ((-1170 . -34) T) ((-1170 . -1246) T) ((-1170 . -102) T) ((-1170 . -630) 158899) ((-1170 . -321) 158825) ((-1170 . -526) 158744) ((-1170 . -1130) T) ((-1170 . -501) 158715) ((-1169 . -1130) T) ((-1169 . -630) 158697) ((-1169 . -1246) T) ((-1169 . -102) T) ((-1164 . -1166) T) ((-1164 . -1292) T) ((-1164 . -93) T) ((-1164 . -102) T) ((-1164 . -1246) T) ((-1164 . -630) 158663) ((-1164 . -1130) T) ((-1164 . -633) 158644) ((-1164 . -502) 158625) ((-1164 . -1112) T) ((-1162 . -1163) 158609) ((-1162 . -102) T) ((-1162 . -1246) T) ((-1162 . -630) 158591) ((-1162 . -1130) T) ((-1155 . -760) 158570) ((-1155 . -35) 158536) ((-1155 . -95) 158502) ((-1155 . -296) 158468) ((-1155 . -505) 158434) ((-1155 . -1235) 158400) ((-1155 . -1232) 158366) ((-1155 . -1031) 158332) ((-1155 . -47) 158304) ((-1155 . -38) 158201) ((-1155 . -660) 158098) ((-1155 . -737) 157995) ((-1155 . -633) 157877) ((-1155 . -302) 157856) ((-1155 . -569) 157835) ((-1155 . -111) 157704) ((-1155 . -1080) 157587) ((-1155 . -1085) 157470) ((-1155 . -175) 157421) ((-1155 . -149) 157400) ((-1155 . -147) 157379) ((-1155 . -668) 157304) ((-1155 . -666) 157214) ((-1155 . -1002) 157181) ((-1155 . -927) 157165) ((-1155 . -1246) T) ((-1155 . -919) 157147) ((-1155 . -1078) T) ((-1155 . -1086) T) ((-1155 . -1141) T) ((-1155 . -746) T) ((-1155 . -21) T) ((-1155 . -23) T) ((-1155 . -1130) T) ((-1155 . -630) 157129) ((-1155 . -102) T) ((-1155 . -25) T) ((-1155 . -133) T) ((-1155 . -925) 157113) ((-1155 . -526) 157083) ((-1155 . -321) 157070) ((-1154 . -977) 157037) ((-1154 . -633) 156829) ((-1154 . -1067) 156712) ((-1154 . -1251) 156691) ((-1154 . -937) 156670) ((-1154 . -909) 156529) ((-1154 . -927) 156513) ((-1154 . -919) 156495) ((-1154 . -925) 156479) ((-1154 . -526) 156431) ((-1154 . -464) 156382) ((-1154 . -658) 156330) ((-1154 . -668) 156219) ((-1154 . -390) 156203) ((-1154 . -47) 156175) ((-1154 . -38) 156024) ((-1154 . -660) 155873) ((-1154 . -737) 155722) ((-1154 . -302) 155653) ((-1154 . -569) 155584) ((-1154 . -111) 155413) ((-1154 . -1080) 155256) ((-1154 . -1085) 155099) ((-1154 . -175) 155010) ((-1154 . -149) 154989) ((-1154 . -147) 154968) ((-1154 . -666) 154878) ((-1154 . -133) T) ((-1154 . -25) T) ((-1154 . -102) T) ((-1154 . -1246) T) ((-1154 . -630) 154860) ((-1154 . -1130) T) ((-1154 . -23) T) ((-1154 . -21) T) ((-1154 . -1078) T) ((-1154 . -1086) T) ((-1154 . -1141) T) ((-1154 . -746) T) ((-1154 . -424) 154844) ((-1154 . -338) 154816) ((-1154 . -321) 154803) ((-1154 . -631) 154551) ((-1149 . -557) T) ((-1149 . -1251) T) ((-1149 . -1181) T) ((-1149 . -1067) 154533) ((-1149 . -631) 154448) ((-1149 . -1049) T) ((-1149 . -909) 154430) ((-1149 . -868) T) ((-1149 . -819) T) ((-1149 . -816) T) ((-1149 . -872) T) ((-1149 . -869) T) ((-1149 . -814) T) ((-1149 . -812) T) ((-1149 . -842) T) ((-1149 . -668) 154402) ((-1149 . -658) 154384) ((-1149 . -948) T) ((-1149 . -569) T) ((-1149 . -302) T) ((-1149 . -175) T) ((-1149 . -633) 154356) ((-1149 . -737) 154343) ((-1149 . -660) 154330) ((-1149 . -1085) 154317) ((-1149 . -1080) 154304) ((-1149 . -111) 154289) ((-1149 . -38) 154276) ((-1149 . -464) T) ((-1149 . -319) T) ((-1149 . -239) T) ((-1149 . -236) 154263) ((-1149 . -240) T) ((-1149 . -145) T) ((-1149 . -1078) T) ((-1149 . -1086) T) ((-1149 . -1141) T) ((-1149 . -746) T) ((-1149 . -21) T) ((-1149 . -666) 154235) ((-1149 . -23) T) ((-1149 . -1130) T) ((-1149 . -630) 154217) ((-1149 . -1246) T) ((-1149 . -102) T) ((-1149 . -25) T) ((-1149 . -133) T) ((-1149 . -149) T) ((-1149 . -865) T) ((-1149 . -381) T) ((-1149 . -113) T) ((-1149 . -682) T) ((-1145 . -1112) T) ((-1145 . -502) 154198) ((-1145 . -630) 154164) ((-1145 . -633) 154145) ((-1145 . -1130) T) ((-1145 . -1246) T) ((-1145 . -102) T) ((-1145 . -93) T) ((-1144 . -1130) T) ((-1144 . -630) 154127) ((-1144 . -1246) T) ((-1144 . -102) T) ((-1142 . -245) 154106) ((-1142 . -1304) 154076) ((-1142 . -819) 154055) ((-1142 . -816) 154034) ((-1142 . -872) 153985) ((-1142 . -869) 153936) ((-1142 . -814) 153915) ((-1142 . -815) 153894) ((-1142 . -737) 153836) ((-1142 . -660) 153758) ((-1142 . -300) 153735) ((-1142 . -298) 153712) ((-1142 . -501) 153696) ((-1142 . -526) 153629) ((-1142 . -321) 153567) ((-1142 . -34) T) ((-1142 . -616) 153544) ((-1142 . -1067) 153371) ((-1142 . -633) 153169) ((-1142 . -424) 153138) ((-1142 . -658) 153044) ((-1142 . -668) 152877) ((-1142 . -390) 152846) ((-1142 . -381) 152825) ((-1142 . -240) 152777) ((-1142 . -666) 152556) ((-1142 . -746) 152534) ((-1142 . -1141) 152512) ((-1142 . -1086) 152490) ((-1142 . -1078) 152468) ((-1142 . -236) 152359) ((-1142 . -239) 152256) ((-1142 . -274) 152225) ((-1142 . -919) 152092) ((-1142 . -927) 151961) ((-1142 . -925) 151893) ((-1142 . -234) 151862) ((-1142 . -630) 151555) ((-1142 . -1085) 151476) ((-1142 . -1080) 151377) ((-1142 . -111) 151293) ((-1142 . -133) 151164) ((-1142 . -25) 150997) ((-1142 . -102) 150729) ((-1142 . -1246) T) ((-1142 . -1130) 150481) ((-1142 . -23) 150333) ((-1142 . -21) 150244) ((-1135 . -408) T) ((-1135 . -1246) T) ((-1135 . -630) 150226) ((-1134 . -1133) 150190) ((-1134 . -102) T) ((-1134 . -630) 150172) ((-1134 . -1130) T) ((-1134 . -298) 150128) ((-1134 . -1246) T) ((-1134 . -635) 150043) ((-1132 . -1133) 149995) ((-1132 . -102) T) ((-1132 . -630) 149977) ((-1132 . -1130) T) ((-1132 . -298) 149933) ((-1132 . -1246) T) ((-1132 . -635) 149836) ((-1131 . -381) T) ((-1131 . -102) T) ((-1131 . -1246) T) ((-1131 . -630) 149818) ((-1131 . -1130) T) ((-1126 . -438) 149802) ((-1126 . -1128) 149786) ((-1126 . -381) 149765) ((-1126 . -242) 149749) ((-1126 . -631) 149710) ((-1126 . -153) 149694) ((-1126 . -501) 149678) ((-1126 . -1130) T) ((-1126 . -526) 149611) ((-1126 . -321) 149549) ((-1126 . -630) 149531) ((-1126 . -102) T) ((-1126 . -1246) T) ((-1126 . -34) T) ((-1126 . -107) 149515) ((-1126 . -233) 149499) ((-1125 . -1112) T) ((-1125 . -502) 149480) ((-1125 . -630) 149446) ((-1125 . -633) 149427) ((-1125 . -1130) T) ((-1125 . -1246) T) ((-1125 . -102) T) ((-1125 . -93) T) ((-1121 . -1246) T) ((-1121 . -1130) 149397) ((-1121 . -630) 149356) ((-1121 . -102) 149326) ((-1120 . -1112) T) ((-1120 . -502) 149307) ((-1120 . -630) 149273) ((-1120 . -633) 149254) ((-1120 . -1130) T) ((-1120 . -1246) T) ((-1120 . -102) T) ((-1120 . -93) T) ((-1118 . -1123) 149238) ((-1118 . -635) 149222) ((-1118 . -1130) 149200) ((-1118 . -630) 149167) ((-1118 . -1246) 149145) ((-1118 . -102) 149123) ((-1118 . -1124) 149081) ((-1117 . -277) 149065) ((-1117 . -633) 149049) ((-1117 . -1067) 149033) ((-1117 . -872) T) ((-1117 . -102) T) ((-1117 . -1130) T) ((-1117 . -630) 149015) ((-1117 . -869) T) ((-1117 . -236) 149002) ((-1117 . -1246) T) ((-1117 . -239) T) ((-1116 . -262) 148939) ((-1116 . -633) 148675) ((-1116 . -1067) 148502) ((-1116 . -631) NIL) ((-1116 . -338) 148463) ((-1116 . -424) 148447) ((-1116 . -38) 148296) ((-1116 . -111) 148125) ((-1116 . -1080) 147968) ((-1116 . -1085) 147811) ((-1116 . -666) 147721) ((-1116 . -668) 147610) ((-1116 . -660) 147459) ((-1116 . -737) 147308) ((-1116 . -147) 147287) ((-1116 . -149) 147266) ((-1116 . -175) 147177) ((-1116 . -569) 147108) ((-1116 . -302) 147039) ((-1116 . -47) 147000) ((-1116 . -390) 146984) ((-1116 . -658) 146932) ((-1116 . -464) 146883) ((-1116 . -526) 146750) ((-1116 . -925) 146685) ((-1116 . -919) 146580) ((-1116 . -927) 146479) ((-1116 . -909) NIL) ((-1116 . -937) 146458) ((-1116 . -1251) 146437) ((-1116 . -977) 146382) ((-1116 . -321) 146369) ((-1116 . -240) 146348) ((-1116 . -133) T) ((-1116 . -25) T) ((-1116 . -102) T) ((-1116 . -630) 146330) ((-1116 . -1130) T) ((-1116 . -23) T) ((-1116 . -21) T) ((-1116 . -746) T) ((-1116 . -1141) T) ((-1116 . -1086) T) ((-1116 . -1078) T) ((-1116 . -236) 146275) ((-1116 . -1246) T) ((-1116 . -239) 146226) ((-1116 . -274) 146210) ((-1116 . -234) 146194) ((-1114 . -630) 146176) ((-1111 . -869) T) ((-1111 . -630) 146158) ((-1111 . -1130) T) ((-1111 . -102) T) ((-1111 . -1246) T) ((-1111 . -872) T) ((-1111 . -631) 146139) ((-1108 . -744) 146118) ((-1108 . -1067) 146014) ((-1108 . -424) 145998) ((-1108 . -658) 145946) ((-1108 . -668) 145820) ((-1108 . -390) 145804) ((-1108 . -383) 145783) ((-1108 . -149) 145762) ((-1108 . -633) 145580) ((-1108 . -737) 145448) ((-1108 . -660) 145316) ((-1108 . -666) 145211) ((-1108 . -1085) 145121) ((-1108 . -1080) 145031) ((-1108 . -111) 144927) ((-1108 . -38) 144795) ((-1108 . -422) 144774) ((-1108 . -414) 144753) ((-1108 . -147) 144704) ((-1108 . -1181) 144683) ((-1108 . -363) 144662) ((-1108 . -381) 144613) ((-1108 . -250) 144564) ((-1108 . -302) 144515) ((-1108 . -319) 144466) ((-1108 . -464) 144417) ((-1108 . -569) 144368) ((-1108 . -948) 144319) ((-1108 . -1251) 144270) ((-1108 . -376) 144221) ((-1108 . -240) 144146) ((-1108 . -236) 144019) ((-1108 . -239) 143898) ((-1108 . -274) 143868) ((-1108 . -919) 143737) ((-1108 . -927) 143608) ((-1108 . -925) 143541) ((-1108 . -234) 143511) ((-1108 . -631) 143495) ((-1108 . -21) T) ((-1108 . -23) T) ((-1108 . -1130) T) ((-1108 . -630) 143477) ((-1108 . -1246) T) ((-1108 . -102) T) ((-1108 . -25) T) ((-1108 . -133) T) ((-1108 . -1078) T) ((-1108 . -1086) T) ((-1108 . -1141) T) ((-1108 . -746) T) ((-1108 . -175) T) ((-1106 . -1130) T) ((-1106 . -630) 143459) ((-1106 . -1246) T) ((-1106 . -102) T) ((-1106 . -298) 143438) ((-1105 . -1130) T) ((-1105 . -630) 143420) ((-1105 . -1246) T) ((-1105 . -102) T) ((-1104 . -1130) T) ((-1104 . -630) 143402) ((-1104 . -1246) T) ((-1104 . -102) T) ((-1104 . -298) 143381) ((-1104 . -1067) 143358) ((-1104 . -633) 143335) ((-1103 . -1246) T) ((-1102 . -1112) T) ((-1102 . -502) 143316) ((-1102 . -630) 143282) ((-1102 . -633) 143263) ((-1102 . -1130) T) ((-1102 . -1246) T) ((-1102 . -102) T) ((-1102 . -93) T) ((-1095 . -1112) T) ((-1095 . -502) 143244) ((-1095 . -630) 143210) ((-1095 . -633) 143191) ((-1095 . -1130) T) ((-1095 . -1246) T) ((-1095 . -102) T) ((-1095 . -93) T) ((-1092 . -1223) 143166) ((-1092 . -233) 143112) ((-1092 . -107) 143058) ((-1092 . -321) 142909) ((-1092 . -526) 142753) ((-1092 . -501) 142684) ((-1092 . -153) 142630) ((-1092 . -631) NIL) ((-1092 . -242) 142576) ((-1092 . -627) 142551) ((-1092 . -300) 142526) ((-1092 . -1246) T) ((-1092 . -298) 142501) ((-1092 . -1130) T) ((-1092 . -630) 142483) ((-1092 . -102) T) ((-1092 . -34) T) ((-1092 . -616) 142458) ((-1091 . -557) T) ((-1091 . -1251) T) ((-1091 . -1181) T) ((-1091 . -1067) 142440) ((-1091 . -631) 142355) ((-1091 . -1049) T) ((-1091 . -909) 142337) ((-1091 . -868) T) ((-1091 . -819) T) ((-1091 . -816) T) ((-1091 . -872) T) ((-1091 . -869) T) ((-1091 . -814) T) ((-1091 . -812) T) ((-1091 . -842) T) ((-1091 . -668) 142309) ((-1091 . -658) 142291) ((-1091 . -948) T) ((-1091 . -569) T) ((-1091 . -302) T) ((-1091 . -175) T) ((-1091 . -633) 142263) ((-1091 . -737) 142250) ((-1091 . -660) 142237) ((-1091 . -1085) 142224) ((-1091 . -1080) 142211) ((-1091 . -111) 142196) ((-1091 . -38) 142183) ((-1091 . -464) T) ((-1091 . -319) T) ((-1091 . -239) T) ((-1091 . -236) 142170) ((-1091 . -240) T) ((-1091 . -145) T) ((-1091 . -1078) T) ((-1091 . -1086) T) ((-1091 . -1141) T) ((-1091 . -746) T) ((-1091 . -21) T) ((-1091 . -666) 142142) ((-1091 . -23) T) ((-1091 . -1130) T) ((-1091 . -630) 142124) ((-1091 . -1246) T) ((-1091 . -102) T) ((-1091 . -25) T) ((-1091 . -133) T) ((-1091 . -149) T) ((-1091 . -635) 142105) ((-1090 . -1097) 142084) ((-1090 . -102) T) ((-1090 . -1246) T) ((-1090 . -630) 142066) ((-1090 . -1130) T) ((-1087 . -1246) T) ((-1087 . -1130) 142044) ((-1087 . -630) 142011) ((-1087 . -102) 141989) ((-1083 . -1082) 141929) ((-1083 . -660) 141871) ((-1083 . -737) 141813) ((-1083 . -34) T) ((-1083 . -321) 141751) ((-1083 . -526) 141684) ((-1083 . -501) 141668) ((-1083 . -668) 141652) ((-1083 . -666) 141621) ((-1083 . -133) T) ((-1083 . -25) T) ((-1083 . -102) T) ((-1083 . -1246) T) ((-1083 . -630) 141583) ((-1083 . -1130) T) ((-1083 . -23) T) ((-1083 . -21) T) ((-1083 . -1085) 141567) ((-1083 . -1080) 141551) ((-1083 . -111) 141530) ((-1083 . -1304) 141500) ((-1083 . -631) 141461) ((-1075 . -1100) 141390) ((-1075 . -1005) 141319) ((-1075 . -631) 141261) ((-1075 . -501) 141226) ((-1075 . -1130) T) ((-1075 . -526) 141127) ((-1075 . -321) 141035) ((-1075 . -630) 140978) ((-1075 . -102) T) ((-1075 . -1246) T) ((-1075 . -34) T) ((-1075 . -153) 140943) ((-1075 . -1241) 140872) ((-1065 . -1112) T) ((-1065 . -502) 140853) ((-1065 . -630) 140819) ((-1065 . -633) 140800) ((-1065 . -1130) T) ((-1065 . -1246) T) ((-1065 . -102) T) ((-1065 . -93) T) ((-1064 . -1223) 140775) ((-1064 . -233) 140721) ((-1064 . -107) 140667) ((-1064 . -321) 140518) ((-1064 . -526) 140362) ((-1064 . -501) 140293) ((-1064 . -153) 140239) ((-1064 . -631) NIL) ((-1064 . -242) 140185) ((-1064 . -627) 140160) ((-1064 . -300) 140135) ((-1064 . -1246) T) ((-1064 . -298) 140110) ((-1064 . -1130) T) ((-1064 . -630) 140092) ((-1064 . -102) T) ((-1064 . -34) T) ((-1064 . -616) 140067) ((-1063 . -175) T) ((-1063 . -633) 140036) ((-1063 . -746) T) ((-1063 . -1141) T) ((-1063 . -1086) T) ((-1063 . -1078) T) ((-1063 . -668) 140010) ((-1063 . -666) 139969) ((-1063 . -133) T) ((-1063 . -25) T) ((-1063 . -102) T) ((-1063 . -1246) T) ((-1063 . -630) 139951) ((-1063 . -1130) T) ((-1063 . -23) T) ((-1063 . -21) T) ((-1063 . -1085) 139925) ((-1063 . -1080) 139899) ((-1063 . -111) 139866) ((-1063 . -38) 139850) ((-1063 . -660) 139834) ((-1063 . -737) 139818) ((-1056 . -1100) 139787) ((-1056 . -1005) 139756) ((-1056 . -631) 139717) ((-1056 . -501) 139701) ((-1056 . -1130) T) ((-1056 . -526) 139634) ((-1056 . -321) 139572) ((-1056 . -630) 139534) ((-1056 . -102) T) ((-1056 . -1246) T) ((-1056 . -34) T) ((-1056 . -153) 139518) ((-1056 . -1241) 139487) ((-1055 . -1246) T) ((-1055 . -1130) 139465) ((-1055 . -630) 139432) ((-1055 . -102) 139410) ((-1053 . -1041) T) ((-1053 . -1031) T) ((-1053 . -812) T) ((-1053 . -814) T) ((-1053 . -869) T) ((-1053 . -872) T) ((-1053 . -816) T) ((-1053 . -819) T) ((-1053 . -868) T) ((-1053 . -1067) 139290) ((-1053 . -424) 139252) ((-1053 . -250) T) ((-1053 . -302) T) ((-1053 . -319) T) ((-1053 . -464) T) ((-1053 . -38) 139189) ((-1053 . -660) 139126) ((-1053 . -737) 139063) ((-1053 . -633) 139000) ((-1053 . -569) T) ((-1053 . -948) T) ((-1053 . -1251) T) ((-1053 . -376) T) ((-1053 . -111) 138916) ((-1053 . -1080) 138853) ((-1053 . -1085) 138790) ((-1053 . -175) T) ((-1053 . -149) T) ((-1053 . -668) 138727) ((-1053 . -666) 138664) ((-1053 . -133) T) ((-1053 . -25) T) ((-1053 . -102) T) ((-1053 . -1246) T) ((-1053 . -630) 138646) ((-1053 . -1130) T) ((-1053 . -23) T) ((-1053 . -21) T) ((-1053 . -1078) T) ((-1053 . -1086) T) ((-1053 . -1141) T) ((-1053 . -746) T) ((-1048 . -1112) T) ((-1048 . -502) 138627) ((-1048 . -630) 138593) ((-1048 . -633) 138574) ((-1048 . -1130) T) ((-1048 . -1246) T) ((-1048 . -102) T) ((-1048 . -93) T) ((-1033 . -1020) 138556) ((-1033 . -1181) T) ((-1033 . -633) 138506) ((-1033 . -1067) 138466) ((-1033 . -631) 138396) ((-1033 . -1049) T) ((-1033 . -937) NIL) ((-1033 . -907) 138378) ((-1033 . -868) T) ((-1033 . -819) T) ((-1033 . -816) T) ((-1033 . -872) T) ((-1033 . -869) T) ((-1033 . -814) T) ((-1033 . -812) T) ((-1033 . -842) T) ((-1033 . -909) 138360) ((-1033 . -412) 138342) ((-1033 . -658) 138324) ((-1033 . -390) 138306) ((-1033 . -298) NIL) ((-1033 . -321) NIL) ((-1033 . -526) NIL) ((-1033 . -351) 138288) ((-1033 . -250) T) ((-1033 . -111) 138222) ((-1033 . -1080) 138172) ((-1033 . -1085) 138122) ((-1033 . -302) T) ((-1033 . -737) 138072) ((-1033 . -660) 138022) ((-1033 . -668) 137972) ((-1033 . -666) 137922) ((-1033 . -38) 137872) ((-1033 . -319) T) ((-1033 . -464) T) ((-1033 . -175) T) ((-1033 . -569) T) ((-1033 . -948) T) ((-1033 . -1251) T) ((-1033 . -376) T) ((-1033 . -240) T) ((-1033 . -236) 137859) ((-1033 . -239) T) ((-1033 . -274) 137841) ((-1033 . -919) NIL) ((-1033 . -927) NIL) ((-1033 . -925) NIL) ((-1033 . -234) 137823) ((-1033 . -149) T) ((-1033 . -147) NIL) ((-1033 . -133) T) ((-1033 . -25) T) ((-1033 . -102) T) ((-1033 . -1246) T) ((-1033 . -630) 137783) ((-1033 . -1130) T) ((-1033 . -23) T) ((-1033 . -21) T) ((-1033 . -1078) T) ((-1033 . -1086) T) ((-1033 . -1141) T) ((-1033 . -746) T) ((-1032 . -355) 137757) ((-1032 . -175) T) ((-1032 . -633) 137687) ((-1032 . -746) T) ((-1032 . -1141) T) ((-1032 . -1086) T) ((-1032 . -1078) T) ((-1032 . -668) 137594) ((-1032 . -666) 137524) ((-1032 . -133) T) ((-1032 . -25) T) ((-1032 . -102) T) ((-1032 . -1246) T) ((-1032 . -630) 137506) ((-1032 . -1130) T) ((-1032 . -23) T) ((-1032 . -21) T) ((-1032 . -1085) 137451) ((-1032 . -1080) 137396) ((-1032 . -111) 137325) ((-1032 . -631) 137309) ((-1032 . -234) 137286) ((-1032 . -925) 137238) ((-1032 . -927) 137147) ((-1032 . -919) 137054) ((-1032 . -274) 137031) ((-1032 . -239) 136968) ((-1032 . -236) 136899) ((-1032 . -240) 136871) ((-1032 . -376) T) ((-1032 . -1251) T) ((-1032 . -948) T) ((-1032 . -569) T) ((-1032 . -737) 136816) ((-1032 . -660) 136761) ((-1032 . -38) 136706) ((-1032 . -464) T) ((-1032 . -319) T) ((-1032 . -302) T) ((-1032 . -250) T) ((-1032 . -381) NIL) ((-1032 . -363) NIL) ((-1032 . -1181) NIL) ((-1032 . -147) 136678) ((-1032 . -414) NIL) ((-1032 . -422) 136650) ((-1032 . -149) 136622) ((-1032 . -383) 136594) ((-1032 . -390) 136571) ((-1032 . -658) 136510) ((-1032 . -424) 136487) ((-1032 . -1067) 136375) ((-1032 . -744) 136347) ((-1029 . -1024) 136331) ((-1029 . -501) 136315) ((-1029 . -1130) 136293) ((-1029 . -526) 136226) ((-1029 . -321) 136164) ((-1029 . -630) 136096) ((-1029 . -102) 136046) ((-1029 . -1246) T) ((-1029 . -34) T) ((-1029 . -107) 136030) ((-1025 . -1027) 136014) ((-1025 . -872) 135993) ((-1025 . -869) 135972) ((-1025 . -1067) 135868) ((-1025 . -424) 135852) ((-1025 . -658) 135800) ((-1025 . -668) 135702) ((-1025 . -390) 135686) ((-1025 . -298) 135644) ((-1025 . -321) 135609) ((-1025 . -526) 135521) ((-1025 . -351) 135505) ((-1025 . -38) 135453) ((-1025 . -111) 135335) ((-1025 . -1080) 135231) ((-1025 . -1085) 135127) ((-1025 . -666) 135050) ((-1025 . -660) 134998) ((-1025 . -737) 134946) ((-1025 . -633) 134836) ((-1025 . -302) 134787) ((-1025 . -250) 134766) ((-1025 . -240) 134745) ((-1025 . -236) 134690) ((-1025 . -239) 134641) ((-1025 . -274) 134625) ((-1025 . -919) 134546) ((-1025 . -927) 134469) ((-1025 . -925) 134428) ((-1025 . -234) 134412) ((-1025 . -631) 134373) ((-1025 . -149) 134352) ((-1025 . -147) 134331) ((-1025 . -133) T) ((-1025 . -25) T) ((-1025 . -102) T) ((-1025 . -1246) T) ((-1025 . -630) 134313) ((-1025 . -1130) T) ((-1025 . -23) T) ((-1025 . -21) T) ((-1025 . -1078) T) ((-1025 . -1086) T) ((-1025 . -1141) T) ((-1025 . -746) T) ((-1023 . -1112) T) ((-1023 . -502) 134294) ((-1023 . -630) 134260) ((-1023 . -633) 134241) ((-1023 . -1130) T) ((-1023 . -1246) T) ((-1023 . -102) T) ((-1023 . -93) T) ((-1022 . -21) T) ((-1022 . -666) 134223) ((-1022 . -23) T) ((-1022 . -1130) T) ((-1022 . -630) 134205) ((-1022 . -1246) T) ((-1022 . -102) T) ((-1022 . -25) T) ((-1022 . -133) T) ((-1022 . -298) 134172) ((-1018 . -630) 134154) ((-1015 . -1130) T) ((-1015 . -630) 134136) ((-1015 . -1246) T) ((-1015 . -102) T) ((-1000 . -819) T) ((-1000 . -816) T) ((-1000 . -872) T) ((-1000 . -869) T) ((-1000 . -814) T) ((-1000 . -23) T) ((-1000 . -1130) T) ((-1000 . -630) 134096) ((-1000 . -1246) T) ((-1000 . -102) T) ((-1000 . -25) T) ((-1000 . -133) T) ((-999 . -1112) T) ((-999 . -502) 134077) ((-999 . -630) 134043) ((-999 . -633) 134024) ((-999 . -1130) T) ((-999 . -1246) T) ((-999 . -102) T) ((-999 . -93) T) ((-995 . -1246) T) ((-994 . -1246) T) ((-993 . -996) T) ((-993 . -102) T) ((-993 . -630) 134006) ((-993 . -1130) T) ((-993 . -682) T) ((-993 . -1246) T) ((-993 . -113) T) ((-993 . -633) 133990) ((-992 . -630) 133972) ((-991 . 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. -240) T) ((-801 . -133) T) ((-801 . -25) T) ((-801 . -102) T) ((-801 . -630) 107171) ((-801 . -1130) T) ((-801 . -23) T) ((-801 . -21) T) ((-801 . -746) T) ((-801 . -1141) T) ((-801 . -1086) T) ((-801 . -1078) T) ((-801 . -236) 107158) ((-801 . -1246) T) ((-801 . -239) T) ((-801 . -274) 107142) ((-801 . -234) 107126) ((-800 . -1094) 107093) ((-800 . -631) 106727) ((-800 . -321) 106714) ((-800 . -526) 106666) ((-800 . -338) 106638) ((-800 . -1067) 106495) ((-800 . -424) 106479) ((-800 . -38) 106328) ((-800 . -633) 106094) ((-800 . -668) 105983) ((-800 . -666) 105893) ((-800 . -746) T) ((-800 . -1141) T) ((-800 . -1086) T) ((-800 . -1078) T) ((-800 . -111) 105722) ((-800 . -1080) 105565) ((-800 . -1085) 105408) ((-800 . -21) T) ((-800 . -23) T) ((-800 . -1130) T) ((-800 . -630) 105322) ((-800 . -1246) T) ((-800 . -102) T) ((-800 . -25) T) ((-800 . -133) T) ((-800 . -660) 105171) ((-800 . -737) 105020) ((-800 . -147) 104999) ((-800 . -149) 104978) ((-800 . -175) 104889) ((-800 . -569) 104820) ((-800 . -302) 104751) ((-800 . -47) 104723) ((-800 . -390) 104707) ((-800 . -658) 104655) ((-800 . -464) 104606) ((-800 . -925) 104590) ((-800 . -919) 104572) ((-800 . -927) 104556) ((-800 . -909) 104415) ((-800 . -937) 104394) ((-800 . -1251) 104373) ((-800 . -977) 104340) ((-793 . -1130) T) ((-793 . -630) 104322) ((-793 . -1246) T) ((-793 . -102) T) ((-791 . -815) T) ((-791 . -133) T) ((-791 . -25) T) ((-791 . -102) T) ((-791 . -1246) T) ((-791 . -630) 104304) ((-791 . -1130) T) ((-791 . -23) T) ((-791 . -814) T) ((-791 . -869) T) ((-791 . -872) T) ((-791 . -816) T) ((-791 . -819) T) ((-791 . -746) T) ((-791 . -1141) T) ((-789 . -1130) T) ((-789 . -630) 104286) ((-789 . -1246) T) ((-789 . -102) T) ((-756 . -757) 104270) ((-756 . -1128) 104254) ((-756 . -242) 104238) ((-756 . -631) 104199) ((-756 . -153) 104183) ((-756 . -501) 104167) ((-756 . -1130) T) ((-756 . -526) 104100) ((-756 . -321) 104038) ((-756 . -630) 104020) ((-756 . -102) T) ((-756 . -1246) T) ((-756 . -34) T) 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97529) ((-731 . -666) 97479) ((-731 . -746) T) ((-731 . -1141) T) ((-731 . -1086) T) ((-731 . -1078) T) ((-731 . -111) 97435) ((-731 . -1080) 97400) ((-731 . -1085) 97365) ((-731 . -21) T) ((-731 . -23) T) ((-731 . -1130) T) ((-731 . -630) 97347) ((-731 . -1246) T) ((-731 . -102) T) ((-731 . -25) T) ((-731 . -133) T) ((-731 . -302) T) ((-731 . -250) T) ((-730 . -1130) T) ((-730 . -630) 97329) ((-730 . -1246) T) ((-730 . -102) T) ((-721 . -401) T) ((-721 . -1067) 97311) ((-721 . -872) T) ((-721 . -869) T) ((-721 . -38) 97298) ((-721 . -633) 97270) ((-721 . -746) T) ((-721 . -1141) T) ((-721 . -1086) T) ((-721 . -1078) T) ((-721 . -111) 97255) ((-721 . -1080) 97242) ((-721 . -1085) 97229) ((-721 . -21) T) ((-721 . -666) 97201) ((-721 . -23) T) ((-721 . -1130) T) ((-721 . -630) 97183) ((-721 . -1246) T) ((-721 . -102) T) ((-721 . -25) T) ((-721 . -133) T) ((-721 . -668) 97155) ((-721 . -660) 97142) ((-721 . -737) 97129) ((-721 . -175) T) ((-721 . -302) T) ((-721 . -569) T) ((-721 . -557) T) ((-721 . -1251) T) ((-721 . -1181) T) ((-721 . -631) 97044) ((-721 . -1049) T) ((-721 . -909) 97026) ((-721 . -868) T) ((-721 . -819) T) ((-721 . -816) T) ((-721 . -814) T) ((-721 . -812) T) ((-721 . -842) T) ((-721 . -658) 97008) ((-721 . -948) T) ((-721 . -464) T) ((-721 . -319) T) ((-721 . -239) T) ((-721 . -236) 96995) ((-721 . -240) T) ((-721 . -145) T) ((-721 . -149) T) ((-719 . -416) T) ((-719 . -149) T) ((-719 . -633) 96930) ((-719 . -668) 96895) ((-719 . -666) 96845) ((-719 . -133) T) ((-719 . -25) T) ((-719 . -102) T) ((-719 . -1246) T) ((-719 . -630) 96827) ((-719 . -1130) T) ((-719 . -23) T) ((-719 . -21) T) ((-719 . -746) T) ((-719 . -1141) T) ((-719 . -1086) T) ((-719 . -1078) T) ((-719 . -631) 96772) ((-719 . -376) T) ((-719 . -1251) T) ((-719 . -948) T) ((-719 . -569) T) ((-719 . -175) T) ((-719 . -737) 96737) ((-719 . -660) 96702) ((-719 . -38) 96667) ((-719 . -464) T) ((-719 . -319) T) ((-719 . -111) 96623) ((-719 . -1080) 96588) ((-719 . -1085) 96553) ((-719 . 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. -630) 70750) ((-494 . -1085) 70671) ((-494 . -1080) 70572) ((-494 . -111) 70488) ((-494 . -133) 70359) ((-494 . -25) 70192) ((-494 . -102) 69924) ((-494 . -1246) T) ((-494 . -1130) 69676) ((-494 . -23) 69528) ((-494 . -21) 69439) ((-493 . -977) 69384) ((-493 . -633) 69169) ((-493 . -1067) 69045) ((-493 . -1251) 69024) ((-493 . -937) 69003) ((-493 . -909) NIL) ((-493 . -927) 68980) ((-493 . -919) 68955) ((-493 . -925) 68932) ((-493 . -526) 68875) ((-493 . -464) 68826) ((-493 . -658) 68774) ((-493 . -668) 68663) ((-493 . -390) 68647) ((-493 . -47) 68604) ((-493 . -38) 68453) ((-493 . -660) 68302) ((-493 . -737) 68151) ((-493 . -302) 68082) ((-493 . -569) 68013) ((-493 . -111) 67842) ((-493 . -1080) 67685) ((-493 . -1085) 67528) ((-493 . -175) 67439) ((-493 . -149) 67418) ((-493 . -147) 67397) ((-493 . -666) 67307) ((-493 . -133) T) ((-493 . -25) T) ((-493 . -102) T) ((-493 . -1246) T) ((-493 . -630) 67289) ((-493 . -1130) T) ((-493 . -23) T) ((-493 . -21) T) ((-493 . -1078) T) ((-493 . 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. -274) 7817) ((-119 . -919) NIL) ((-119 . -927) NIL) ((-119 . -925) NIL) ((-119 . -234) 7794) ((-119 . -149) T) ((-119 . -147) NIL) ((-119 . -133) T) ((-119 . -25) T) ((-119 . -102) T) ((-119 . -1246) T) ((-119 . -630) 7776) ((-119 . -1130) T) ((-119 . -23) T) ((-119 . -21) T) ((-119 . -1078) T) ((-119 . -1086) T) ((-119 . -1141) T) ((-119 . -746) T) ((-118 . -892) 7760) ((-118 . -948) T) ((-118 . -569) T) ((-118 . -302) T) ((-118 . -175) T) ((-118 . -633) 7732) ((-118 . -737) 7719) ((-118 . -660) 7706) ((-118 . -1085) 7693) ((-118 . -1080) 7680) ((-118 . -111) 7665) ((-118 . -38) 7652) ((-118 . -464) T) ((-118 . -319) T) ((-118 . -1078) T) ((-118 . -1086) T) ((-118 . -1141) T) ((-118 . -746) T) ((-118 . -21) T) ((-118 . -666) 7624) ((-118 . -23) T) ((-118 . -1130) T) ((-118 . -630) 7606) ((-118 . -1246) T) ((-118 . -102) T) ((-118 . -25) T) ((-118 . -133) T) ((-118 . -668) 7593) ((-118 . -149) T) ((-115 . -869) T) ((-115 . -630) 7575) ((-115 . -1130) T) ((-115 . -102) T) ((-115 . 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. -102) T) ((-48 . -1246) T) ((-48 . -630) 3847) ((-48 . -1130) T) ((-48 . -633) 3780) ((-48 . -1067) 3723) ((-48 . -526) 3689) ((-48 . -321) 3676) ((-48 . -27) T) ((-48 . -1031) T) ((-48 . -250) T) ((-48 . -111) 3632) ((-48 . -1080) 3597) ((-48 . -1085) 3562) ((-48 . -302) T) ((-48 . -737) 3527) ((-48 . -660) 3492) ((-48 . -668) 3442) ((-48 . -666) 3392) ((-48 . -133) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -1078) T) ((-48 . -1086) T) ((-48 . -1141) T) ((-48 . -746) T) ((-48 . -38) 3357) ((-48 . -319) T) ((-48 . -464) T) ((-48 . -175) T) ((-48 . -569) T) ((-48 . -948) T) ((-48 . -1251) T) ((-48 . -376) T) ((-48 . -658) 3317) ((-48 . -1049) T) ((-48 . -631) 3262) ((-48 . -149) T) ((-48 . -240) T) ((-48 . -236) 3249) ((-48 . -239) T) ((-45 . -36) 3228) ((-45 . -616) 3153) ((-45 . -321) 2957) ((-45 . -526) 2749) ((-45 . -501) 2686) ((-45 . -298) 2586) ((-45 . -300) 2511) ((-45 . -627) 2490) ((-45 . -242) 2440) ((-45 . -107) 2390) ((-45 . -233) 2340) ((-45 . -1223) 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\ No newline at end of file
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191163) ((-1257 . -569) 191074) ((-1257 . -302) 190985) ((-1257 . -175) 190876) ((-1257 . -464) 190807) ((-1257 . -319) 190786) ((-1257 . -298) 190713) ((-1257 . -240) T) ((-1257 . -133) T) ((-1257 . -25) T) ((-1257 . -102) T) ((-1257 . -630) 190695) ((-1257 . -1122) T) ((-1257 . -23) T) ((-1257 . -21) T) ((-1257 . -746) T) ((-1257 . -1133) T) ((-1257 . -1078) T) ((-1257 . -1070) T) ((-1257 . -236) 190682) ((-1257 . -1238) T) ((-1257 . -239) T) ((-1257 . -274) 190666) ((-1257 . -234) 190650) ((-1255 . -1115) 190634) ((-1255 . -635) 190618) ((-1255 . -1122) 190596) ((-1255 . -630) 190563) ((-1255 . -1238) 190541) ((-1255 . -102) 190519) ((-1255 . -1116) 190476) ((-1253 . -1252) 190455) ((-1253 . -1023) 190421) ((-1253 . -1224) 190387) ((-1253 . -1227) 190353) ((-1253 . -505) 190319) ((-1253 . -296) 190285) ((-1253 . -95) 190251) ((-1253 . -35) 190217) ((-1253 . -1267) 190194) ((-1253 . -47) 190171) ((-1253 . -633) 189919) ((-1253 . -737) 189733) ((-1253 . -660) 189547) ((-1253 . -668) 189355) ((-1253 . -666) 189210) ((-1253 . -1077) 189018) ((-1253 . -1072) 188826) ((-1253 . -111) 188615) ((-1253 . -38) 188429) ((-1253 . -994) 188398) ((-1253 . -298) 188298) ((-1253 . -1250) 188282) ((-1253 . -746) T) ((-1253 . -1133) T) ((-1253 . -1078) T) ((-1253 . -1070) T) ((-1253 . -21) T) ((-1253 . -23) T) ((-1253 . -1122) T) ((-1253 . -630) 188264) ((-1253 . -1238) T) ((-1253 . -102) T) ((-1253 . -25) T) ((-1253 . -133) T) ((-1253 . -147) 188189) ((-1253 . -149) 188114) ((-1253 . -631) 187785) ((-1253 . -234) 187755) ((-1253 . -917) 187606) ((-1253 . -919) 187403) ((-1253 . -911) 187198) ((-1253 . -274) 187168) ((-1253 . -239) 187027) ((-1253 . -236) 186880) ((-1253 . -240) 186785) ((-1253 . -376) 186764) ((-1253 . -1243) 186743) ((-1253 . -940) 186722) ((-1253 . -569) 186673) ((-1253 . -175) 186604) ((-1253 . -464) 186583) ((-1253 . -319) 186562) ((-1253 . -302) 186513) ((-1253 . -250) 186492) ((-1253 . -351) 186462) ((-1253 . -526) 186322) ((-1253 . -321) 186261) ((-1253 . -390) 186231) ((-1253 . -658) 186139) ((-1253 . -412) 186109) ((-1253 . -901) 185982) ((-1253 . -842) 185935) ((-1253 . -812) 185888) ((-1253 . -814) 185841) ((-1253 . -861) 185740) ((-1253 . -864) 185639) ((-1253 . -816) 185592) ((-1253 . -819) 185545) ((-1253 . -860) 185498) ((-1253 . -899) 185468) ((-1253 . -929) 185421) ((-1253 . -1041) 185373) ((-1253 . -1059) 185159) ((-1253 . -1173) 185111) ((-1253 . -1012) 185081) ((-1248 . -1252) 185042) ((-1248 . -1023) 185008) ((-1248 . -1224) 184974) ((-1248 . -1227) 184940) ((-1248 . -505) 184906) ((-1248 . -296) 184872) ((-1248 . -95) 184838) ((-1248 . -35) 184804) ((-1248 . -1267) 184781) ((-1248 . -47) 184758) ((-1248 . -633) 184553) ((-1248 . -737) 184349) ((-1248 . -660) 184145) ((-1248 . -668) 183997) ((-1248 . -666) 183834) ((-1248 . -1077) 183624) ((-1248 . -1072) 183414) ((-1248 . -111) 183183) ((-1248 . -38) 182979) ((-1248 . -994) 182948) ((-1248 . -298) 182776) ((-1248 . -1250) 182760) ((-1248 . -746) T) ((-1248 . -1133) T) ((-1248 . -1078) T) ((-1248 . -1070) T) ((-1248 . -21) T) ((-1248 . -23) T) ((-1248 . -1122) T) ((-1248 . -630) 182742) ((-1248 . -1238) T) ((-1248 . -102) T) ((-1248 . -25) T) ((-1248 . -133) T) ((-1248 . -147) 182649) ((-1248 . -149) 182556) ((-1248 . -631) NIL) ((-1248 . -234) 182508) ((-1248 . -917) 182341) ((-1248 . -919) 182102) ((-1248 . -911) 181838) ((-1248 . -274) 181790) ((-1248 . -239) 181613) ((-1248 . -236) 181430) ((-1248 . -240) 181317) ((-1248 . -376) 181296) ((-1248 . -1243) 181275) ((-1248 . -940) 181254) ((-1248 . -569) 181205) ((-1248 . -175) 181136) ((-1248 . -464) 181115) ((-1248 . -319) 181094) ((-1248 . -302) 181045) ((-1248 . -250) 181024) ((-1248 . -351) 180976) ((-1248 . -526) 180745) ((-1248 . -321) 180630) ((-1248 . -390) 180582) ((-1248 . -658) 180534) ((-1248 . -412) 180486) ((-1248 . -901) NIL) ((-1248 . -842) NIL) ((-1248 . -812) NIL) ((-1248 . -814) NIL) ((-1248 . -861) NIL) ((-1248 . -864) NIL) ((-1248 . -816) NIL) ((-1248 . -819) NIL) ((-1248 . -860) NIL) ((-1248 . -899) 180438) ((-1248 . -929) NIL) ((-1248 . -1041) NIL) ((-1248 . -1059) 180404) ((-1248 . -1173) NIL) ((-1248 . -1012) 180356) ((-1247 . -857) T) ((-1247 . -864) T) ((-1247 . -861) T) ((-1247 . -1122) T) ((-1247 . -630) 180338) ((-1247 . -1238) T) ((-1247 . -102) T) ((-1247 . -381) T) ((-1247 . -682) T) ((-1246 . -857) T) ((-1246 . -864) T) ((-1246 . -861) T) ((-1246 . -1122) T) ((-1246 . -630) 180320) ((-1246 . -1238) T) ((-1246 . -102) T) ((-1246 . -381) T) ((-1246 . -682) T) ((-1245 . -857) T) ((-1245 . -864) T) ((-1245 . -861) T) ((-1245 . -1122) T) ((-1245 . -630) 180302) ((-1245 . -1238) T) ((-1245 . -102) T) ((-1245 . -381) T) ((-1245 . -682) T) ((-1244 . -857) T) ((-1244 . -864) T) ((-1244 . -861) T) ((-1244 . -1122) T) ((-1244 . -630) 180284) ((-1244 . -1238) T) ((-1244 . -102) T) ((-1244 . -381) T) ((-1244 . -682) T) ((-1239 . -1104) T) ((-1239 . -502) 180265) ((-1239 . -630) 180231) ((-1239 . -633) 180212) ((-1239 . -1122) T) ((-1239 . -1238) T) ((-1239 . -102) T) ((-1239 . -93) T) ((-1236 . -502) 180189) ((-1236 . -630) 180101) ((-1236 . -633) 180078) ((-1236 . -1122) 180056) ((-1236 . -1238) 180034) ((-1236 . -102) 180012) ((-1231 . -760) 179988) ((-1231 . -35) 179954) ((-1231 . -95) 179920) ((-1231 . -296) 179886) ((-1231 . -505) 179852) ((-1231 . -1227) 179818) ((-1231 . -1224) 179784) ((-1231 . -1023) 179750) ((-1231 . -47) 179719) ((-1231 . -38) 179616) ((-1231 . -660) 179513) ((-1231 . -737) 179410) ((-1231 . -633) 179292) ((-1231 . -302) 179271) ((-1231 . -569) 179250) ((-1231 . -111) 179119) ((-1231 . -1072) 179002) ((-1231 . -1077) 178885) ((-1231 . -175) 178836) ((-1231 . -149) 178815) ((-1231 . -147) 178794) ((-1231 . -668) 178719) ((-1231 . -666) 178629) ((-1231 . -994) 178591) ((-1231 . -919) 178572) ((-1231 . -1238) T) ((-1231 . -911) 178551) ((-1231 . -1070) T) ((-1231 . -1078) T) ((-1231 . -1133) T) ((-1231 . -746) T) ((-1231 . -21) T) ((-1231 . -23) T) ((-1231 . -1122) T) ((-1231 . -630) 178533) ((-1231 . -102) T) ((-1231 . -25) T) ((-1231 . -133) T) ((-1231 . -917) 178514) ((-1231 . -526) 178481) ((-1231 . -321) 178468) ((-1225 . -1031) 178452) ((-1225 . -34) T) ((-1225 . -1238) T) ((-1225 . -102) 178402) ((-1225 . -630) 178334) ((-1225 . -321) 178272) ((-1225 . -526) 178205) ((-1225 . -1122) 178183) ((-1225 . -501) 178167) ((-1220 . -378) 178141) ((-1220 . -102) T) ((-1220 . -1238) T) ((-1220 . -630) 178123) ((-1220 . -1122) T) ((-1218 . -1122) T) ((-1218 . -630) 178105) ((-1218 . -1238) T) ((-1218 . -102) T) ((-1218 . -633) 178087) ((-1212 . -849) 178071) ((-1212 . -102) T) ((-1212 . -1238) T) ((-1212 . -630) 178053) ((-1212 . -1122) T) ((-1210 . -1215) 178032) ((-1210 . -233) 177982) ((-1210 . -107) 177932) ((-1210 . -321) 177736) ((-1210 . -526) 177528) ((-1210 . -501) 177465) ((-1210 . -153) 177415) ((-1210 . -631) NIL) ((-1210 . -242) 177365) ((-1210 . -627) 177344) ((-1210 . -300) 177323) ((-1210 . -1238) T) ((-1210 . -298) 177302) ((-1210 . -1122) T) ((-1210 . -630) 177284) ((-1210 . -102) T) ((-1210 . -34) T) ((-1210 . -616) 177263) ((-1208 . -1238) T) ((-1206 . -1122) T) ((-1206 . -630) 177245) ((-1206 . -1238) T) ((-1206 . -102) T) ((-1205 . -857) T) ((-1205 . -864) T) ((-1205 . -861) T) ((-1205 . -1122) T) ((-1205 . -630) 177227) ((-1205 . -1238) T) ((-1205 . -102) T) ((-1205 . -381) T) ((-1205 . -682) T) ((-1204 . -857) T) ((-1204 . -864) T) ((-1204 . -861) T) ((-1204 . -1122) T) ((-1204 . -630) 177209) ((-1204 . -1238) T) ((-1204 . -102) T) ((-1204 . -381) T) ((-1203 . -1284) T) ((-1203 . -1122) T) ((-1203 . -630) 177176) ((-1203 . -1238) T) ((-1203 . -102) T) ((-1203 . -1059) 177112) ((-1203 . -633) 177048) ((-1202 . -630) 177030) ((-1201 . -630) 177012) ((-1200 . -338) 176989) ((-1200 . -1059) 176885) ((-1200 . -424) 176869) ((-1200 . -38) 176766) ((-1200 . -633) 176619) ((-1200 . -668) 176544) ((-1200 . -666) 176454) ((-1200 . -746) T) ((-1200 . -1133) T) ((-1200 . -1078) T) ((-1200 . -1070) T) ((-1200 . -111) 176323) ((-1200 . -1072) 176206) ((-1200 . -1077) 176089) ((-1200 . -21) T) ((-1200 . -23) T) ((-1200 . -1122) T) ((-1200 . -630) 176071) ((-1200 . -1238) T) ((-1200 . -102) T) ((-1200 . -25) T) ((-1200 . -133) T) ((-1200 . -660) 175968) ((-1200 . -737) 175865) ((-1200 . -147) 175844) ((-1200 . -149) 175823) ((-1200 . -175) 175774) ((-1200 . -569) 175753) ((-1200 . -302) 175732) ((-1200 . -47) 175709) ((-1198 . -861) T) ((-1198 . -630) 175691) ((-1198 . -1122) T) ((-1198 . -102) T) ((-1198 . -1238) T) ((-1198 . -864) T) ((-1198 . -631) 175613) ((-1198 . -633) 175594) ((-1198 . -901) 175561) ((-1197 . -630) 175543) ((-1196 . -1281) 175527) ((-1196 . -240) 175486) ((-1196 . -633) 175368) ((-1196 . -668) 175293) ((-1196 . -666) 175203) ((-1196 . -133) T) ((-1196 . -25) T) ((-1196 . -102) T) ((-1196 . -630) 175185) ((-1196 . -1122) T) ((-1196 . -23) T) ((-1196 . -21) T) ((-1196 . -746) T) ((-1196 . -1133) T) ((-1196 . -1078) T) ((-1196 . -1070) T) ((-1196 . -236) 175138) ((-1196 . -1238) T) ((-1196 . -239) 175097) ((-1196 . -298) 175062) ((-1196 . -917) 174975) ((-1196 . -911) 174863) ((-1196 . -919) 174776) ((-1196 . -994) 174745) ((-1196 . -38) 174642) ((-1196 . -111) 174511) ((-1196 . -1072) 174394) ((-1196 . -1077) 174277) ((-1196 . -660) 174174) ((-1196 . -737) 174071) ((-1196 . -147) 174050) ((-1196 . -149) 174029) ((-1196 . -175) 173980) ((-1196 . -569) 173959) ((-1196 . -302) 173938) ((-1196 . -47) 173915) ((-1196 . -1267) 173892) ((-1196 . -35) 173858) ((-1196 . -95) 173824) ((-1196 . -296) 173790) ((-1196 . -505) 173756) ((-1196 . -1227) 173722) ((-1196 . -1224) 173688) ((-1196 . -1023) 173654) ((-1195 . -1273) 173615) ((-1195 . -376) 173594) ((-1195 . -1243) 173573) ((-1195 . -940) 173552) ((-1195 . -569) 173503) ((-1195 . -175) 173434) ((-1195 . -633) 173177) ((-1195 . -737) 173018) ((-1195 . -660) 172859) ((-1195 . -38) 172700) ((-1195 . -464) 172679) ((-1195 . -319) 172658) ((-1195 . -668) 172555) ((-1195 . -666) 172437) ((-1195 . -746) T) ((-1195 . -1133) T) ((-1195 . -1078) T) ((-1195 . -1070) T) ((-1195 . -111) 172258) ((-1195 . -1072) 172093) ((-1195 . -1077) 171928) ((-1195 . -21) T) ((-1195 . -23) T) ((-1195 . -1122) T) ((-1195 . -630) 171910) ((-1195 . -1238) T) ((-1195 . -102) T) ((-1195 . -25) T) ((-1195 . -133) T) ((-1195 . -302) 171861) ((-1195 . -250) 171840) ((-1195 . -1023) 171806) ((-1195 . -1224) 171772) ((-1195 . -1227) 171738) ((-1195 . -505) 171704) ((-1195 . -296) 171670) ((-1195 . -95) 171636) ((-1195 . -35) 171602) ((-1195 . -1267) 171572) ((-1195 . -47) 171542) ((-1195 . -149) 171521) ((-1195 . -147) 171500) ((-1195 . -994) 171462) ((-1195 . -919) 171368) ((-1195 . -911) 171249) ((-1195 . -917) 171155) ((-1195 . -298) 171113) ((-1195 . -239) 171065) ((-1195 . -236) 171011) ((-1195 . -240) 170963) ((-1195 . -1271) 170947) ((-1195 . -1059) 170882) ((-1192 . -1264) 170866) ((-1192 . -1173) 170844) ((-1192 . -631) NIL) ((-1192 . -321) 170831) ((-1192 . -526) 170778) ((-1192 . -338) 170755) ((-1192 . -1059) 170635) ((-1192 . -424) 170619) ((-1192 . -38) 170448) ((-1192 . -111) 170257) ((-1192 . -1072) 170080) ((-1192 . -1077) 169903) ((-1192 . -666) 169813) ((-1192 . -668) 169702) ((-1192 . -660) 169531) ((-1192 . -737) 169360) ((-1192 . -633) 169129) ((-1192 . -147) 169108) ((-1192 . -149) 169087) ((-1192 . -47) 169064) ((-1192 . -390) 169048) ((-1192 . -658) 168996) ((-1192 . -917) 168939) ((-1192 . -911) 168842) ((-1192 . -919) 168749) ((-1192 . -901) NIL) ((-1192 . -929) 168728) ((-1192 . -1243) 168707) ((-1192 . -969) 168676) ((-1192 . -940) 168655) ((-1192 . -569) 168566) ((-1192 . -302) 168477) ((-1192 . -175) 168368) ((-1192 . -464) 168299) ((-1192 . -319) 168278) ((-1192 . -298) 168205) ((-1192 . -240) T) ((-1192 . -133) T) ((-1192 . -25) T) ((-1192 . -102) T) ((-1192 . -630) 168187) ((-1192 . -1122) T) ((-1192 . -23) T) ((-1192 . -21) T) ((-1192 . -746) T) ((-1192 . -1133) T) ((-1192 . -1078) T) ((-1192 . -1070) T) ((-1192 . -236) 168174) ((-1192 . -1238) T) ((-1192 . -239) T) ((-1192 . -274) 168158) ((-1192 . -234) 168142) ((-1189 . -1252) 168103) ((-1189 . -1023) 168069) ((-1189 . -1224) 168035) ((-1189 . -1227) 168001) ((-1189 . -505) 167967) ((-1189 . -296) 167933) ((-1189 . -95) 167899) ((-1189 . -35) 167865) ((-1189 . -1267) 167842) ((-1189 . -47) 167819) ((-1189 . -633) 167614) ((-1189 . -737) 167410) ((-1189 . -660) 167206) ((-1189 . -668) 167058) ((-1189 . -666) 166895) ((-1189 . -1077) 166685) ((-1189 . -1072) 166475) ((-1189 . -111) 166244) ((-1189 . -38) 166040) ((-1189 . -994) 166009) ((-1189 . -298) 165837) ((-1189 . -1250) 165821) ((-1189 . -746) T) ((-1189 . -1133) T) ((-1189 . -1078) T) ((-1189 . -1070) T) ((-1189 . -21) T) ((-1189 . -23) T) ((-1189 . -1122) T) ((-1189 . -630) 165803) ((-1189 . -1238) T) ((-1189 . -102) T) ((-1189 . -25) T) ((-1189 . -133) T) ((-1189 . -147) 165710) ((-1189 . -149) 165617) ((-1189 . -631) NIL) ((-1189 . -234) 165569) ((-1189 . -917) 165402) ((-1189 . -919) 165163) ((-1189 . -911) 164899) ((-1189 . -274) 164851) ((-1189 . -239) 164674) ((-1189 . -236) 164491) ((-1189 . -240) 164378) ((-1189 . -376) 164357) ((-1189 . -1243) 164336) ((-1189 . -940) 164315) ((-1189 . -569) 164266) ((-1189 . -175) 164197) ((-1189 . -464) 164176) ((-1189 . -319) 164155) ((-1189 . -302) 164106) ((-1189 . -250) 164085) ((-1189 . -351) 164037) ((-1189 . -526) 163806) ((-1189 . -321) 163691) ((-1189 . -390) 163643) ((-1189 . -658) 163595) ((-1189 . -412) 163547) ((-1189 . -901) NIL) ((-1189 . -842) NIL) ((-1189 . -812) NIL) ((-1189 . -814) NIL) ((-1189 . -861) NIL) ((-1189 . -864) NIL) ((-1189 . -816) NIL) ((-1189 . -819) NIL) ((-1189 . -860) NIL) ((-1189 . -899) 163499) ((-1189 . -929) NIL) ((-1189 . -1041) NIL) ((-1189 . -1059) 163465) ((-1189 . -1173) NIL) ((-1189 . -1012) 163417) ((-1188 . -1104) T) ((-1188 . -502) 163398) ((-1188 . -630) 163364) ((-1188 . -633) 163345) ((-1188 . -1122) T) ((-1188 . -1238) T) ((-1188 . -102) T) ((-1188 . -93) T) ((-1187 . -1122) T) ((-1187 . -630) 163327) ((-1187 . -1238) T) ((-1187 . -102) T) ((-1186 . -1122) T) ((-1186 . -630) 163309) ((-1186 . -1238) T) ((-1186 . -102) T) ((-1181 . -1215) 163285) ((-1181 . -233) 163232) ((-1181 . -107) 163179) ((-1181 . -321) 162974) ((-1181 . -526) 162757) ((-1181 . -501) 162691) ((-1181 . -153) 162638) ((-1181 . -631) NIL) ((-1181 . -242) 162585) ((-1181 . -627) 162561) ((-1181 . -300) 162537) ((-1181 . -1238) T) ((-1181 . -298) 162513) ((-1181 . -1122) T) ((-1181 . -630) 162495) ((-1181 . -102) T) ((-1181 . -34) T) ((-1181 . -616) 162471) ((-1180 . -1165) T) ((-1180 . -385) 162453) ((-1180 . -864) T) ((-1180 . -861) T) ((-1180 . -153) 162435) ((-1180 . -34) T) ((-1180 . -1238) T) ((-1180 . -102) T) ((-1180 . -630) 162417) ((-1180 . -321) NIL) ((-1180 . -526) NIL) ((-1180 . -1122) T) ((-1180 . -501) 162399) ((-1180 . -631) NIL) ((-1180 . -298) 162349) ((-1180 . -616) 162324) ((-1180 . -300) 162299) ((-1180 . -671) 162281) ((-1180 . -19) 162263) ((-1176 . -694) 162247) ((-1176 . -671) 162231) ((-1176 . -300) 162208) ((-1176 . -298) 162160) ((-1176 . -616) 162137) ((-1176 . -631) 162098) ((-1176 . -501) 162082) ((-1176 . -1122) 162060) ((-1176 . -526) 161993) ((-1176 . -321) 161931) ((-1176 . -630) 161863) ((-1176 . -102) 161813) ((-1176 . -1238) T) ((-1176 . -34) T) ((-1176 . -153) 161797) ((-1176 . -1277) 161781) ((-1176 . -1031) 161765) ((-1176 . -1171) 161749) ((-1176 . -633) 161726) ((-1174 . -1104) T) ((-1174 . -502) 161707) ((-1174 . -630) 161673) ((-1174 . -633) 161654) ((-1174 . -1122) T) ((-1174 . -1238) T) ((-1174 . -102) T) ((-1174 . -93) T) ((-1172 . -1215) 161633) ((-1172 . -233) 161583) ((-1172 . -107) 161533) ((-1172 . -321) 161337) ((-1172 . -526) 161129) ((-1172 . -501) 161066) ((-1172 . -153) 161016) ((-1172 . -631) NIL) ((-1172 . -242) 160966) ((-1172 . -627) 160945) ((-1172 . -300) 160924) ((-1172 . -1238) T) ((-1172 . -298) 160903) ((-1172 . -1122) T) ((-1172 . -630) 160885) ((-1172 . -102) T) ((-1172 . -34) T) ((-1172 . -616) 160864) ((-1169 . -1142) 160848) ((-1169 . -501) 160832) ((-1169 . -1122) 160810) ((-1169 . -526) 160743) ((-1169 . -321) 160681) ((-1169 . -630) 160613) ((-1169 . -102) 160563) ((-1169 . -1238) T) ((-1169 . -34) T) ((-1169 . -107) 160547) ((-1167 . -1130) 160516) ((-1167 . -1233) 160485) ((-1167 . -630) 160447) ((-1167 . -153) 160431) ((-1167 . -34) T) ((-1167 . -1238) T) ((-1167 . -102) T) ((-1167 . -321) 160369) ((-1167 . -526) 160302) ((-1167 . -1122) T) ((-1167 . -501) 160286) ((-1167 . -631) 160247) ((-1167 . -997) 160216) ((-1167 . -1092) 160185) ((-1163 . -1144) 160130) ((-1163 . -501) 160114) ((-1163 . -526) 160047) ((-1163 . -321) 159985) ((-1163 . -34) T) ((-1163 . -1074) 159925) ((-1163 . -1059) 159821) ((-1163 . -633) 159739) ((-1163 . -424) 159723) ((-1163 . -658) 159671) ((-1163 . -668) 159609) ((-1163 . -390) 159593) ((-1163 . -240) 159572) ((-1163 . -236) 159517) ((-1163 . -239) 159468) ((-1163 . -274) 159452) ((-1163 . -911) 159373) ((-1163 . -919) 159296) ((-1163 . -917) 159255) ((-1163 . -234) 159239) ((-1163 . -737) 159171) ((-1163 . -660) 159103) ((-1163 . -666) 159062) ((-1163 . -133) T) ((-1163 . -25) T) ((-1163 . -102) T) ((-1163 . -1238) T) ((-1163 . -630) 159024) ((-1163 . -1122) T) ((-1163 . -23) T) ((-1163 . -21) T) ((-1163 . -1077) 159008) ((-1163 . -1072) 158992) ((-1163 . -111) 158971) ((-1163 . -1070) T) ((-1163 . -1078) T) ((-1163 . -1133) T) ((-1163 . -746) T) ((-1163 . -38) 158931) ((-1163 . -631) 158892) ((-1162 . -1031) 158863) ((-1162 . -34) T) ((-1162 . -1238) T) ((-1162 . -102) T) ((-1162 . -630) 158845) ((-1162 . -321) 158771) ((-1162 . -526) 158690) ((-1162 . -1122) T) ((-1162 . -501) 158661) ((-1161 . -1122) T) ((-1161 . -630) 158643) ((-1161 . -1238) T) ((-1161 . -102) T) ((-1156 . -1158) T) ((-1156 . -1284) T) ((-1156 . -93) T) ((-1156 . -102) T) ((-1156 . -1238) T) ((-1156 . -630) 158609) ((-1156 . -1122) T) ((-1156 . -633) 158590) ((-1156 . -502) 158571) ((-1156 . -1104) T) ((-1154 . -1155) 158555) ((-1154 . -102) T) ((-1154 . -1238) T) ((-1154 . -630) 158537) ((-1154 . -1122) T) ((-1147 . -760) 158516) ((-1147 . -35) 158482) ((-1147 . -95) 158448) ((-1147 . -296) 158414) ((-1147 . -505) 158380) ((-1147 . -1227) 158346) ((-1147 . -1224) 158312) ((-1147 . -1023) 158278) ((-1147 . -47) 158250) ((-1147 . -38) 158147) ((-1147 . -660) 158044) ((-1147 . -737) 157941) ((-1147 . -633) 157823) ((-1147 . -302) 157802) ((-1147 . -569) 157781) ((-1147 . -111) 157650) ((-1147 . -1072) 157533) ((-1147 . -1077) 157416) ((-1147 . -175) 157367) ((-1147 . -149) 157346) ((-1147 . -147) 157325) ((-1147 . -668) 157250) ((-1147 . -666) 157160) ((-1147 . -994) 157127) ((-1147 . -919) 157111) ((-1147 . -1238) T) ((-1147 . -911) 157093) ((-1147 . -1070) T) ((-1147 . -1078) T) ((-1147 . -1133) T) ((-1147 . -746) T) ((-1147 . -21) T) ((-1147 . -23) T) ((-1147 . -1122) T) ((-1147 . -630) 157075) ((-1147 . -102) T) ((-1147 . -25) T) ((-1147 . -133) T) ((-1147 . -917) 157059) ((-1147 . -526) 157029) ((-1147 . -321) 157016) ((-1146 . -969) 156983) ((-1146 . -633) 156775) ((-1146 . -1059) 156658) ((-1146 . -1243) 156637) ((-1146 . -929) 156616) ((-1146 . -901) 156475) ((-1146 . -919) 156459) ((-1146 . -911) 156441) ((-1146 . -917) 156425) ((-1146 . -526) 156377) ((-1146 . -464) 156328) ((-1146 . -658) 156276) ((-1146 . -668) 156165) ((-1146 . -390) 156149) ((-1146 . -47) 156121) ((-1146 . -38) 155970) ((-1146 . -660) 155819) ((-1146 . -737) 155668) ((-1146 . -302) 155599) ((-1146 . -569) 155530) ((-1146 . -111) 155359) ((-1146 . -1072) 155202) ((-1146 . -1077) 155045) ((-1146 . -175) 154956) ((-1146 . -149) 154935) ((-1146 . -147) 154914) ((-1146 . -666) 154824) ((-1146 . -133) T) ((-1146 . -25) T) ((-1146 . -102) T) ((-1146 . -1238) T) ((-1146 . -630) 154806) ((-1146 . -1122) T) ((-1146 . -23) T) ((-1146 . -21) T) ((-1146 . -1070) T) ((-1146 . -1078) T) ((-1146 . -1133) T) ((-1146 . -746) T) ((-1146 . -424) 154790) ((-1146 . -338) 154762) ((-1146 . -321) 154749) ((-1146 . -631) 154497) ((-1141 . -557) T) ((-1141 . -1243) T) ((-1141 . -1173) T) ((-1141 . -1059) 154479) ((-1141 . -631) 154394) ((-1141 . -1041) T) ((-1141 . -901) 154376) ((-1141 . -860) T) ((-1141 . -819) T) ((-1141 . -816) T) ((-1141 . -864) T) ((-1141 . -861) T) ((-1141 . -814) T) ((-1141 . -812) T) ((-1141 . -842) T) ((-1141 . -668) 154348) ((-1141 . -658) 154330) ((-1141 . -940) T) ((-1141 . -569) T) ((-1141 . -302) T) ((-1141 . -175) T) ((-1141 . -633) 154302) ((-1141 . -737) 154289) ((-1141 . -660) 154276) ((-1141 . -1077) 154263) ((-1141 . -1072) 154250) ((-1141 . -111) 154235) ((-1141 . -38) 154222) ((-1141 . -464) T) ((-1141 . -319) T) ((-1141 . -239) T) ((-1141 . -236) 154209) ((-1141 . -240) T) ((-1141 . -145) T) ((-1141 . -1070) T) ((-1141 . -1078) T) ((-1141 . -1133) T) ((-1141 . -746) T) ((-1141 . -21) T) ((-1141 . -666) 154181) ((-1141 . -23) T) ((-1141 . -1122) T) ((-1141 . -630) 154163) ((-1141 . -1238) T) ((-1141 . -102) T) ((-1141 . -25) T) ((-1141 . -133) T) ((-1141 . -149) T) ((-1141 . -857) T) ((-1141 . -381) T) ((-1141 . -113) T) ((-1141 . -682) T) ((-1137 . -1104) T) ((-1137 . -502) 154144) ((-1137 . -630) 154110) ((-1137 . -633) 154091) ((-1137 . -1122) T) ((-1137 . -1238) T) ((-1137 . -102) T) ((-1137 . -93) T) ((-1136 . -1122) T) ((-1136 . -630) 154073) ((-1136 . -1238) T) ((-1136 . -102) T) ((-1134 . -245) 154052) ((-1134 . -1296) 154022) ((-1134 . -819) 154001) ((-1134 . -816) 153980) ((-1134 . -864) 153931) ((-1134 . -861) 153882) ((-1134 . -814) 153861) ((-1134 . -815) 153840) ((-1134 . -737) 153782) ((-1134 . -660) 153704) ((-1134 . -300) 153681) ((-1134 . -298) 153658) ((-1134 . -501) 153642) ((-1134 . -526) 153575) ((-1134 . -321) 153513) ((-1134 . -34) T) ((-1134 . -616) 153490) ((-1134 . -1059) 153317) ((-1134 . -633) 153115) ((-1134 . -424) 153084) ((-1134 . -658) 152990) ((-1134 . -668) 152823) ((-1134 . -390) 152792) ((-1134 . -381) 152771) ((-1134 . -240) 152723) ((-1134 . -666) 152502) ((-1134 . -746) 152480) ((-1134 . -1133) 152458) ((-1134 . -1078) 152436) ((-1134 . -1070) 152414) ((-1134 . -236) 152305) ((-1134 . -239) 152202) ((-1134 . -274) 152171) ((-1134 . -911) 152038) ((-1134 . -919) 151907) ((-1134 . -917) 151839) ((-1134 . -234) 151808) ((-1134 . -630) 151501) ((-1134 . -1077) 151422) ((-1134 . -1072) 151323) ((-1134 . -111) 151239) ((-1134 . -133) 151110) ((-1134 . -25) 150943) ((-1134 . -102) 150675) ((-1134 . -1238) T) ((-1134 . -1122) 150427) ((-1134 . -23) 150279) ((-1134 . -21) 150190) ((-1127 . -408) T) ((-1127 . -1238) T) ((-1127 . -630) 150172) ((-1126 . -1125) 150136) ((-1126 . -102) T) ((-1126 . -630) 150118) ((-1126 . -1122) T) ((-1126 . -298) 150074) ((-1126 . -1238) T) ((-1126 . -635) 149989) ((-1124 . -1125) 149941) ((-1124 . -102) T) ((-1124 . -630) 149923) ((-1124 . -1122) T) ((-1124 . -298) 149879) ((-1124 . -1238) T) ((-1124 . -635) 149782) ((-1123 . -381) T) ((-1123 . -102) T) ((-1123 . -1238) T) ((-1123 . -630) 149764) ((-1123 . -1122) T) ((-1118 . -438) 149748) ((-1118 . -1120) 149732) ((-1118 . -381) 149711) ((-1118 . -242) 149695) ((-1118 . -631) 149656) ((-1118 . -153) 149640) ((-1118 . -501) 149624) ((-1118 . -1122) T) ((-1118 . -526) 149557) ((-1118 . -321) 149495) ((-1118 . -630) 149477) ((-1118 . -102) T) ((-1118 . -1238) T) ((-1118 . -34) T) ((-1118 . -107) 149461) ((-1118 . -233) 149445) ((-1117 . -1104) T) ((-1117 . -502) 149426) ((-1117 . -630) 149392) ((-1117 . -633) 149373) ((-1117 . -1122) T) ((-1117 . -1238) T) ((-1117 . -102) T) ((-1117 . -93) T) ((-1113 . -1238) T) ((-1113 . -1122) 149343) ((-1113 . -630) 149302) ((-1113 . -102) 149272) ((-1112 . -1104) T) ((-1112 . -502) 149253) ((-1112 . -630) 149219) ((-1112 . -633) 149200) ((-1112 . -1122) T) ((-1112 . -1238) T) ((-1112 . -102) T) ((-1112 . -93) T) ((-1110 . -1115) 149184) ((-1110 . -635) 149168) ((-1110 . -1122) 149146) ((-1110 . -630) 149113) ((-1110 . -1238) 149091) ((-1110 . -102) 149069) ((-1110 . -1116) 149027) ((-1109 . -277) 149011) ((-1109 . -633) 148995) ((-1109 . -1059) 148979) ((-1109 . -864) T) ((-1109 . -102) T) ((-1109 . -1122) T) ((-1109 . -630) 148961) ((-1109 . -861) T) ((-1109 . -236) 148948) ((-1109 . -1238) T) ((-1109 . -239) T) ((-1108 . -262) 148885) ((-1108 . -633) 148621) ((-1108 . -1059) 148448) ((-1108 . -631) NIL) ((-1108 . -338) 148409) ((-1108 . -424) 148393) ((-1108 . -38) 148242) ((-1108 . -111) 148071) ((-1108 . -1072) 147914) ((-1108 . -1077) 147757) ((-1108 . -666) 147667) ((-1108 . -668) 147556) ((-1108 . -660) 147405) ((-1108 . -737) 147254) ((-1108 . -147) 147233) ((-1108 . -149) 147212) ((-1108 . -175) 147123) ((-1108 . -569) 147054) ((-1108 . -302) 146985) ((-1108 . -47) 146946) ((-1108 . -390) 146930) ((-1108 . -658) 146878) ((-1108 . -464) 146829) ((-1108 . -526) 146696) ((-1108 . -917) 146631) ((-1108 . -911) 146526) ((-1108 . -919) 146425) ((-1108 . -901) NIL) ((-1108 . -929) 146404) ((-1108 . -1243) 146383) ((-1108 . -969) 146328) ((-1108 . -321) 146315) ((-1108 . -240) 146294) ((-1108 . -133) T) ((-1108 . -25) T) ((-1108 . -102) T) ((-1108 . -630) 146276) ((-1108 . -1122) T) ((-1108 . -23) T) ((-1108 . -21) T) ((-1108 . -746) T) ((-1108 . -1133) T) ((-1108 . -1078) T) ((-1108 . -1070) T) ((-1108 . -236) 146221) ((-1108 . -1238) T) ((-1108 . -239) 146172) ((-1108 . -274) 146156) ((-1108 . -234) 146140) ((-1106 . -630) 146122) ((-1103 . -861) T) ((-1103 . -630) 146104) ((-1103 . -1122) T) ((-1103 . -102) T) ((-1103 . -1238) T) ((-1103 . -864) T) ((-1103 . -631) 146085) ((-1100 . -744) 146064) ((-1100 . -1059) 145960) ((-1100 . -424) 145944) ((-1100 . -658) 145892) ((-1100 . -668) 145766) ((-1100 . -390) 145750) ((-1100 . -383) 145729) ((-1100 . -149) 145708) ((-1100 . -633) 145526) ((-1100 . -737) 145394) ((-1100 . -660) 145262) ((-1100 . -666) 145157) ((-1100 . -1077) 145067) ((-1100 . -1072) 144977) ((-1100 . -111) 144873) ((-1100 . -38) 144741) ((-1100 . -422) 144720) ((-1100 . -414) 144699) ((-1100 . -147) 144650) ((-1100 . -1173) 144629) ((-1100 . -363) 144608) ((-1100 . -381) 144559) ((-1100 . -250) 144510) ((-1100 . -302) 144461) ((-1100 . -319) 144412) ((-1100 . -464) 144363) ((-1100 . -569) 144314) ((-1100 . -940) 144265) ((-1100 . -1243) 144216) ((-1100 . -376) 144167) ((-1100 . -240) 144092) ((-1100 . -236) 143965) ((-1100 . -239) 143844) ((-1100 . -274) 143814) ((-1100 . -911) 143683) ((-1100 . -919) 143554) ((-1100 . -917) 143487) ((-1100 . -234) 143457) ((-1100 . -631) 143441) ((-1100 . -21) T) ((-1100 . -23) T) ((-1100 . -1122) T) ((-1100 . -630) 143423) ((-1100 . -1238) T) ((-1100 . -102) T) ((-1100 . -25) T) ((-1100 . -133) T) ((-1100 . -1070) T) ((-1100 . -1078) T) ((-1100 . -1133) T) ((-1100 . -746) T) ((-1100 . -175) T) ((-1098 . -1122) T) ((-1098 . -630) 143405) ((-1098 . -1238) T) ((-1098 . -102) T) ((-1098 . -298) 143384) ((-1097 . -1122) T) ((-1097 . -630) 143366) ((-1097 . -1238) T) ((-1097 . -102) T) ((-1096 . -1122) T) ((-1096 . -630) 143348) ((-1096 . -1238) T) ((-1096 . -102) T) ((-1096 . -298) 143327) ((-1096 . -1059) 143304) ((-1096 . -633) 143281) ((-1095 . -1238) T) ((-1094 . -1104) T) ((-1094 . -502) 143262) ((-1094 . -630) 143228) ((-1094 . -633) 143209) ((-1094 . -1122) T) ((-1094 . -1238) T) ((-1094 . -102) T) ((-1094 . -93) T) ((-1087 . -1104) T) ((-1087 . -502) 143190) ((-1087 . -630) 143156) ((-1087 . -633) 143137) ((-1087 . -1122) T) ((-1087 . -1238) T) ((-1087 . -102) T) ((-1087 . -93) T) ((-1084 . -1215) 143112) ((-1084 . -233) 143058) ((-1084 . -107) 143004) ((-1084 . -321) 142855) ((-1084 . -526) 142699) ((-1084 . -501) 142630) ((-1084 . -153) 142576) ((-1084 . -631) NIL) ((-1084 . -242) 142522) ((-1084 . -627) 142497) ((-1084 . -300) 142472) ((-1084 . -1238) T) ((-1084 . -298) 142447) ((-1084 . -1122) T) ((-1084 . -630) 142429) ((-1084 . -102) T) ((-1084 . -34) T) ((-1084 . -616) 142404) ((-1083 . -557) T) ((-1083 . -1243) T) ((-1083 . -1173) T) ((-1083 . -1059) 142386) ((-1083 . -631) 142301) ((-1083 . -1041) T) ((-1083 . -901) 142283) ((-1083 . -860) T) ((-1083 . -819) T) ((-1083 . -816) T) ((-1083 . -864) T) ((-1083 . -861) T) ((-1083 . -814) T) ((-1083 . -812) T) ((-1083 . -842) T) ((-1083 . -668) 142255) ((-1083 . -658) 142237) ((-1083 . -940) T) ((-1083 . -569) T) ((-1083 . -302) T) ((-1083 . -175) T) ((-1083 . -633) 142209) ((-1083 . -737) 142196) ((-1083 . -660) 142183) ((-1083 . -1077) 142170) ((-1083 . -1072) 142157) ((-1083 . -111) 142142) ((-1083 . -38) 142129) ((-1083 . -464) T) ((-1083 . -319) T) ((-1083 . -239) T) ((-1083 . -236) 142116) ((-1083 . -240) T) ((-1083 . -145) T) ((-1083 . -1070) T) ((-1083 . -1078) T) ((-1083 . -1133) T) ((-1083 . -746) T) ((-1083 . -21) T) ((-1083 . -666) 142088) ((-1083 . -23) T) ((-1083 . -1122) T) ((-1083 . -630) 142070) ((-1083 . -1238) T) ((-1083 . -102) T) ((-1083 . -25) T) ((-1083 . -133) T) ((-1083 . -149) T) ((-1083 . -635) 142051) ((-1082 . -1089) 142030) ((-1082 . -102) T) ((-1082 . -1238) T) ((-1082 . -630) 142012) ((-1082 . -1122) T) ((-1079 . -1238) T) ((-1079 . -1122) 141990) ((-1079 . -630) 141957) ((-1079 . -102) 141935) ((-1075 . -1074) 141875) ((-1075 . -660) 141817) ((-1075 . -737) 141759) ((-1075 . -34) T) ((-1075 . -321) 141697) ((-1075 . -526) 141630) ((-1075 . -501) 141614) ((-1075 . -668) 141598) ((-1075 . -666) 141567) ((-1075 . -133) T) ((-1075 . -25) T) ((-1075 . -102) T) ((-1075 . -1238) T) ((-1075 . -630) 141529) ((-1075 . -1122) T) ((-1075 . -23) T) ((-1075 . -21) T) ((-1075 . -1077) 141513) ((-1075 . -1072) 141497) ((-1075 . -111) 141476) ((-1075 . -1296) 141446) ((-1075 . -631) 141407) ((-1067 . -1092) 141336) ((-1067 . -997) 141265) ((-1067 . -631) 141207) ((-1067 . -501) 141172) ((-1067 . -1122) T) ((-1067 . -526) 141073) ((-1067 . -321) 140981) ((-1067 . -630) 140924) ((-1067 . -102) T) ((-1067 . -1238) T) ((-1067 . -34) T) ((-1067 . -153) 140889) ((-1067 . -1233) 140818) ((-1057 . -1104) T) ((-1057 . -502) 140799) ((-1057 . -630) 140765) ((-1057 . -633) 140746) ((-1057 . -1122) T) ((-1057 . -1238) T) ((-1057 . -102) T) ((-1057 . -93) T) ((-1056 . -1215) 140721) ((-1056 . -233) 140667) ((-1056 . -107) 140613) ((-1056 . -321) 140464) ((-1056 . -526) 140308) ((-1056 . -501) 140239) ((-1056 . -153) 140185) 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139433) ((-1047 . -1238) T) ((-1047 . -1122) 139411) ((-1047 . -630) 139378) ((-1047 . -102) 139356) ((-1045 . -1033) T) ((-1045 . -1023) T) ((-1045 . -812) T) ((-1045 . -814) T) ((-1045 . -861) T) ((-1045 . -864) T) ((-1045 . -816) T) ((-1045 . -819) T) ((-1045 . -860) T) ((-1045 . -1059) 139236) ((-1045 . -424) 139198) ((-1045 . -250) T) ((-1045 . -302) T) ((-1045 . -319) T) ((-1045 . -464) T) ((-1045 . -38) 139135) ((-1045 . -660) 139072) ((-1045 . -737) 139009) ((-1045 . -633) 138946) ((-1045 . -569) T) ((-1045 . -940) T) ((-1045 . -1243) T) ((-1045 . -376) T) ((-1045 . -111) 138862) ((-1045 . -1072) 138799) ((-1045 . -1077) 138736) ((-1045 . -175) T) ((-1045 . -149) T) ((-1045 . -668) 138673) ((-1045 . -666) 138610) ((-1045 . -133) T) ((-1045 . -25) T) ((-1045 . -102) T) ((-1045 . -1238) T) ((-1045 . -630) 138592) ((-1045 . -1122) T) ((-1045 . -23) T) ((-1045 . -21) T) ((-1045 . -1070) T) ((-1045 . -1078) T) ((-1045 . -1133) T) ((-1045 . -746) T) ((-1040 . -1104) T) ((-1040 . 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. -737) 127013) ((-925 . -660) 126978) ((-925 . -38) 126943) ((-925 . -464) T) ((-925 . -319) T) ((-925 . -111) 126899) ((-925 . -1072) 126864) ((-925 . -1077) 126829) ((-925 . -666) 126779) ((-925 . -668) 126744) ((-925 . -302) T) ((-925 . -250) T) ((-925 . -414) T) ((-925 . -239) T) ((-925 . -1238) T) ((-925 . -236) 126731) ((-925 . -1070) T) ((-925 . -1078) T) ((-925 . -1133) T) ((-925 . -746) T) ((-925 . -21) T) ((-925 . -23) T) ((-925 . -1122) T) ((-925 . -630) 126713) ((-925 . -102) T) ((-925 . -25) T) ((-925 . -133) T) ((-925 . -240) T) ((-925 . -341) 126700) ((-925 . -149) 126682) ((-925 . -1059) 126669) ((-925 . -1296) 126656) ((-925 . -1307) 126643) ((-925 . -631) 126625) ((-924 . -1122) T) ((-924 . -630) 126607) ((-924 . -1238) T) ((-924 . -102) T) ((-921 . -923) 126591) ((-921 . -864) 126542) ((-921 . -861) 126493) ((-921 . -746) T) ((-921 . -1122) T) ((-921 . -630) 126475) ((-921 . -102) T) ((-921 . -1133) T) ((-921 . -485) T) ((-921 . -1238) T) ((-921 . -298) 126454) 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122573) ((-883 . -464) T) ((-883 . -319) T) ((-883 . -1070) T) ((-883 . -1078) T) ((-883 . -1133) T) ((-883 . -746) T) ((-883 . -21) T) ((-883 . -666) 122545) ((-883 . -23) T) ((-883 . -1122) T) ((-883 . -630) 122527) ((-883 . -1238) T) ((-883 . -102) T) ((-883 . -25) T) ((-883 . -133) T) ((-883 . -668) 122514) ((-883 . -149) T) ((-880 . -1070) T) ((-880 . -1078) T) ((-880 . -1133) T) ((-880 . -746) T) ((-880 . -21) T) ((-880 . -666) 122459) ((-880 . -23) T) ((-880 . -1122) T) ((-880 . -630) 122421) ((-880 . -1238) T) ((-880 . -102) T) ((-880 . -25) T) ((-880 . -133) T) ((-880 . -668) 122381) ((-880 . -633) 122316) ((-880 . -502) 122293) ((-880 . -38) 122263) ((-880 . -111) 122228) ((-880 . -1072) 122198) ((-880 . -1077) 122168) ((-880 . -660) 122138) ((-880 . -737) 122108) ((-879 . -1122) T) ((-879 . -630) 122090) ((-879 . -1238) T) ((-879 . -102) T) ((-878 . -857) T) ((-878 . -864) T) ((-878 . -861) T) ((-878 . -1122) T) ((-878 . -630) 122072) ((-878 . -1238) T) ((-878 . -102) T) 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120122) ((-854 . -1238) T) ((-854 . -102) T) ((-851 . -849) 120104) ((-851 . -102) T) ((-851 . -1238) T) ((-851 . -630) 120086) ((-851 . -1122) T) ((-847 . -1070) T) ((-847 . -1078) T) ((-847 . -1133) T) ((-847 . -746) T) ((-847 . -21) T) ((-847 . -666) 120031) ((-847 . -23) T) ((-847 . -1122) T) ((-847 . -630) 120013) ((-847 . -1238) T) ((-847 . -102) T) ((-847 . -25) T) ((-847 . -133) T) ((-847 . -668) 119973) ((-847 . -633) 119927) ((-847 . -1059) 119896) ((-847 . -298) 119875) ((-847 . -149) 119854) ((-847 . -147) 119833) ((-847 . -38) 119803) ((-847 . -111) 119768) ((-847 . -1072) 119738) ((-847 . -1077) 119708) ((-847 . -660) 119678) ((-847 . -737) 119648) ((-845 . -1122) T) ((-845 . -630) 119630) ((-845 . -1238) T) ((-845 . -102) T) ((-845 . -424) 119614) ((-845 . -633) 119482) ((-845 . -1059) 119378) ((-845 . -21) 119330) ((-845 . -666) 119247) ((-845 . -23) 119199) ((-845 . -25) 119151) ((-845 . -133) 119103) ((-845 . -860) 119082) ((-845 . -668) 119055) ((-845 . -1078) 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. -234) 114768) ((-837 . -245) 114747) ((-837 . -1296) 114717) ((-837 . -819) 114696) ((-837 . -816) 114675) ((-837 . -864) 114626) ((-837 . -861) 114577) ((-837 . -814) 114556) ((-837 . -815) 114535) ((-837 . -737) 114477) ((-837 . -660) 114399) ((-837 . -300) 114376) ((-837 . -298) 114353) ((-837 . -501) 114337) ((-837 . -526) 114270) ((-837 . -321) 114208) ((-837 . -34) T) ((-837 . -616) 114185) ((-837 . -1059) 114012) ((-837 . -633) 113810) ((-837 . -424) 113779) ((-837 . -658) 113685) ((-837 . -668) 113518) ((-837 . -390) 113487) ((-837 . -381) 113466) ((-837 . -240) 113418) ((-837 . -666) 113197) ((-837 . -746) 113175) ((-837 . -1133) 113153) ((-837 . -1078) 113131) ((-837 . -1070) 113109) ((-837 . -236) 113000) ((-837 . -239) 112897) ((-837 . -274) 112866) ((-837 . -911) 112733) ((-837 . -919) 112602) ((-837 . -917) 112534) ((-837 . -234) 112503) ((-837 . -630) 112196) ((-837 . -1077) 112117) ((-837 . -1072) 112018) ((-837 . -111) 111934) ((-837 . -133) 111805) ((-837 . -25) 111638) ((-837 . -102) 111370) ((-837 . -1238) T) ((-837 . -1122) 111122) ((-837 . -23) 110974) ((-837 . -21) 110885) ((-830 . -1122) T) ((-830 . -630) 110867) ((-830 . -1238) T) ((-830 . -102) T) ((-820 . -818) 110851) ((-820 . -864) 110830) ((-820 . -861) 110809) ((-820 . -1059) 110589) ((-820 . -633) 110435) ((-820 . -424) 110398) ((-820 . -298) 110356) ((-820 . -321) 110321) ((-820 . -526) 110233) ((-820 . -351) 110217) ((-820 . -381) 110196) ((-820 . -631) 110157) ((-820 . -149) 110136) ((-820 . -147) 110115) ((-820 . -737) 110099) ((-820 . -660) 110083) ((-820 . -668) 110057) ((-820 . -666) 110016) ((-820 . -133) T) ((-820 . -25) T) ((-820 . -102) T) ((-820 . -1238) T) ((-820 . -630) 109998) ((-820 . -1122) T) ((-820 . -23) T) ((-820 . -21) T) ((-820 . -1077) 109982) ((-820 . -1072) 109966) ((-820 . -111) 109945) ((-820 . -1070) T) ((-820 . -1078) T) ((-820 . -1133) T) ((-820 . -746) T) ((-820 . -38) 109929) ((-801 . -1264) 109913) ((-801 . -1173) 109891) ((-801 . -631) NIL) 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107158) ((-801 . -1238) T) ((-801 . -239) T) ((-801 . -274) 107142) ((-801 . -234) 107126) ((-800 . -1086) 107093) ((-800 . -631) 106727) ((-800 . -321) 106714) ((-800 . -526) 106666) ((-800 . -338) 106638) ((-800 . -1059) 106495) ((-800 . -424) 106479) ((-800 . -38) 106328) ((-800 . -633) 106094) ((-800 . -668) 105983) ((-800 . -666) 105893) ((-800 . -746) T) ((-800 . -1133) T) ((-800 . -1078) T) ((-800 . -1070) T) ((-800 . -111) 105722) ((-800 . -1072) 105565) ((-800 . -1077) 105408) ((-800 . -21) T) ((-800 . -23) T) ((-800 . -1122) T) ((-800 . -630) 105322) ((-800 . -1238) T) ((-800 . -102) T) ((-800 . -25) T) ((-800 . -133) T) ((-800 . -660) 105171) ((-800 . -737) 105020) ((-800 . -147) 104999) ((-800 . -149) 104978) ((-800 . -175) 104889) ((-800 . -569) 104820) ((-800 . -302) 104751) ((-800 . -47) 104723) ((-800 . -390) 104707) ((-800 . -658) 104655) ((-800 . -464) 104606) ((-800 . -917) 104590) ((-800 . -911) 104572) ((-800 . -919) 104556) ((-800 . -901) 104415) ((-800 . -929) 104394) ((-800 . -1243) 104373) ((-800 . -969) 104340) ((-793 . -1122) T) ((-793 . -630) 104322) ((-793 . -1238) T) ((-793 . -102) T) ((-791 . -815) T) ((-791 . -133) T) ((-791 . -25) T) ((-791 . -102) T) ((-791 . -1238) T) ((-791 . -630) 104304) ((-791 . -1122) T) ((-791 . -23) T) ((-791 . -814) T) ((-791 . -861) T) ((-791 . -864) T) ((-791 . -816) T) ((-791 . -819) T) ((-791 . -746) T) ((-791 . -1133) T) ((-789 . -1122) T) ((-789 . -630) 104286) ((-789 . -1238) T) ((-789 . -102) T) ((-756 . -757) 104270) ((-756 . -1120) 104254) ((-756 . -242) 104238) ((-756 . -631) 104199) ((-756 . -153) 104183) ((-756 . -501) 104167) ((-756 . -1122) T) ((-756 . -526) 104100) ((-756 . -321) 104038) ((-756 . -630) 104020) ((-756 . -102) T) ((-756 . -1238) T) ((-756 . -34) T) ((-756 . -107) 104004) ((-756 . -715) 103988) ((-755 . -1070) T) ((-755 . -1078) T) ((-755 . -1133) T) ((-755 . -746) T) ((-755 . -21) T) ((-755 . -666) 103933) ((-755 . -23) T) ((-755 . -1122) T) ((-755 . -630) 103915) ((-755 . -1238) T) ((-755 . -102) T) ((-755 . -25) T) ((-755 . -133) T) ((-755 . -668) 103875) ((-755 . -633) 103831) ((-755 . -1059) 103802) ((-755 . -149) 103781) ((-755 . -147) 103760) ((-755 . -38) 103730) ((-755 . -111) 103695) ((-755 . -1072) 103665) ((-755 . -1077) 103635) ((-755 . -660) 103605) ((-755 . -737) 103575) ((-755 . -381) 103528) ((-751 . -969) 103481) ((-751 . -633) 103266) ((-751 . -1059) 103142) ((-751 . -1243) 103121) ((-751 . -929) 103100) ((-751 . -901) NIL) ((-751 . -919) 103077) ((-751 . -911) 103052) ((-751 . -917) 103029) ((-751 . -526) 102972) ((-751 . -464) 102923) ((-751 . -658) 102871) ((-751 . -668) 102760) ((-751 . -390) 102744) ((-751 . -47) 102709) ((-751 . -38) 102558) ((-751 . -660) 102407) ((-751 . -737) 102256) ((-751 . -302) 102187) ((-751 . -569) 102118) ((-751 . -111) 101947) ((-751 . -1072) 101790) ((-751 . -1077) 101633) ((-751 . -175) 101544) ((-751 . -149) 101523) ((-751 . -147) 101502) ((-751 . -666) 101412) ((-751 . -133) T) ((-751 . -25) T) 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-23) T) ((-119 . -21) T) ((-119 . -1070) T) ((-119 . -1078) T) ((-119 . -1133) T) ((-119 . -746) T) ((-118 . -884) 7760) ((-118 . -940) T) ((-118 . -569) T) ((-118 . -302) T) ((-118 . -175) T) ((-118 . -633) 7732) ((-118 . -737) 7719) ((-118 . -660) 7706) ((-118 . -1077) 7693) ((-118 . -1072) 7680) ((-118 . -111) 7665) ((-118 . -38) 7652) ((-118 . -464) T) ((-118 . -319) T) ((-118 . -1070) T) ((-118 . -1078) T) ((-118 . -1133) T) ((-118 . -746) T) ((-118 . -21) T) ((-118 . -666) 7624) ((-118 . -23) T) ((-118 . -1122) T) ((-118 . -630) 7606) ((-118 . -1238) T) ((-118 . -102) T) ((-118 . -25) T) ((-118 . -133) T) ((-118 . -668) 7593) ((-118 . -149) T) ((-115 . -861) T) ((-115 . -630) 7575) ((-115 . -1122) T) ((-115 . -102) T) ((-115 . -1238) T) ((-115 . -864) T) ((-115 . -849) 7556) ((-114 . -857) T) ((-114 . -864) T) ((-114 . -861) T) ((-114 . -1122) T) ((-114 . -630) 7538) ((-114 . -1238) T) ((-114 . -102) T) ((-114 . -381) T) ((-114 . -988) T) ((-114 . -682) T) ((-114 . -113) T) ((-114 . -631) 7520) ((-110 . -125) T) ((-110 . -385) 7502) ((-110 . -864) T) ((-110 . -861) T) ((-110 . -153) 7484) ((-110 . -34) T) ((-110 . -102) T) ((-110 . -630) 7466) ((-110 . -321) NIL) ((-110 . -526) NIL) ((-110 . -1122) T) ((-110 . -501) 7448) ((-110 . -631) 7430) ((-110 . -298) 7380) ((-110 . -616) 7355) ((-110 . -300) 7330) ((-110 . -671) 7312) ((-110 . -19) 7294) ((-110 . -682) T) ((-110 . -1238) T) ((-110 . -113) T) ((-109 . -630) 7276) ((-108 . -1012) 7258) ((-108 . -1173) T) ((-108 . -633) 7208) ((-108 . -1059) 7168) ((-108 . -631) 7098) ((-108 . -1041) T) ((-108 . -929) NIL) ((-108 . -899) 7080) ((-108 . -860) T) ((-108 . -819) T) ((-108 . -816) T) ((-108 . -864) T) ((-108 . -861) T) ((-108 . -814) T) ((-108 . -812) T) ((-108 . -842) T) ((-108 . -901) 7062) ((-108 . -412) 7044) ((-108 . -658) 7026) ((-108 . -390) 7008) ((-108 . -298) NIL) ((-108 . -321) NIL) ((-108 . -526) NIL) ((-108 . -351) 6990) ((-108 . -250) T) ((-108 . -111) 6924) ((-108 . -1072) 6874) ((-108 . -1077) 6824) ((-108 . -302) T) ((-108 . -737) 6774) ((-108 . -660) 6724) ((-108 . -668) 6674) ((-108 . -666) 6624) ((-108 . -38) 6574) ((-108 . -319) T) ((-108 . -464) T) ((-108 . -175) T) ((-108 . -569) T) ((-108 . -940) T) ((-108 . -1243) T) ((-108 . -376) T) ((-108 . -240) T) ((-108 . -236) 6561) ((-108 . -239) T) ((-108 . -274) 6543) ((-108 . -911) NIL) ((-108 . -919) NIL) ((-108 . -917) NIL) ((-108 . -234) 6525) ((-108 . -149) T) ((-108 . -147) NIL) ((-108 . -133) T) ((-108 . -25) T) ((-108 . -102) T) ((-108 . -1238) T) ((-108 . -630) 6467) ((-108 . -1122) T) ((-108 . -23) T) ((-108 . -21) T) ((-108 . -1070) T) ((-108 . -1078) T) ((-108 . -1133) T) ((-108 . -746) T) ((-105 . -1122) T) ((-105 . -630) 6449) ((-105 . -1238) T) ((-105 . -102) T) ((-103 . -127) 6433) ((-103 . -1031) 6417) ((-103 . -34) T) ((-103 . -1238) T) ((-103 . -102) 6367) ((-103 . -630) 6299) ((-103 . -321) 6237) ((-103 . -526) 6170) ((-103 . -1122) 6148) ((-103 . -501) 6132) ((-103 . -121) 6116) ((-99 . -485) T) ((-99 . -1133) T) ((-99 . -102) T) ((-99 . -1238) T) ((-99 . -630) 6098) ((-99 . -1122) T) ((-99 . -746) T) ((-99 . -298) 6077) ((-97 . -1122) T) ((-97 . -630) 6059) ((-97 . -1238) T) ((-97 . -102) T) ((-96 . -1104) T) ((-96 . -502) 6040) ((-96 . -630) 6006) ((-96 . -633) 5987) ((-96 . -1122) T) ((-96 . -1238) T) ((-96 . -102) T) ((-96 . -93) T) ((-91 . -1142) 5971) ((-91 . -501) 5955) ((-91 . -1122) 5933) ((-91 . -526) 5866) ((-91 . -321) 5804) ((-91 . -630) 5736) ((-91 . -102) 5686) ((-91 . -1238) T) ((-91 . -34) T) ((-91 . -107) 5670) ((-89 . -409) T) ((-89 . -630) 5652) ((-89 . -1238) T) ((-89 . -408) T) ((-88 . -398) T) ((-88 . -630) 5634) ((-88 . -1238) T) ((-88 . -408) T) ((-87 . -452) T) ((-87 . -630) 5616) ((-87 . -1238) T) ((-87 . -408) T) ((-86 . -453) T) ((-86 . -630) 5598) ((-86 . -1238) T) ((-86 . -408) T) ((-85 . -398) T) ((-85 . -630) 5580) ((-85 . -1238) T) ((-85 . -408) T) ((-84 . -398) T) ((-84 . -630) 5562) ((-84 . -1238) T) ((-84 . -408) T) ((-83 . -453) T) ((-83 . -630) 5544) ((-83 . -1238) T) ((-83 . -408) T) ((-82 . -453) T) ((-82 . -630) 5526) ((-82 . -1238) T) ((-82 . -408) T) ((-81 . -453) T) ((-81 . -630) 5508) ((-81 . -1238) T) ((-81 . -408) T) ((-81 . -633) 5449) ((-80 . -453) T) ((-80 . -630) 5431) ((-80 . -1238) T) ((-80 . -408) T) ((-79 . -453) T) ((-79 . -630) 5413) ((-79 . -1238) T) ((-79 . -408) T) ((-78 . -409) T) ((-78 . -630) 5395) ((-78 . -1238) T) ((-78 . -408) T) ((-77 . -453) T) ((-77 . -630) 5377) ((-77 . -1238) T) ((-77 . -408) T) ((-76 . -453) T) ((-76 . -630) 5359) ((-76 . -1238) T) ((-76 . -408) T) ((-75 . -409) T) ((-75 . -630) 5341) ((-75 . -1238) T) ((-75 . -408) T) ((-74 . -453) T) ((-74 . -630) 5323) ((-74 . -1238) T) ((-74 . -408) T) ((-73 . -396) T) ((-73 . -630) 5305) ((-73 . -1238) T) ((-73 . -408) T) ((-72 . -408) T) ((-72 . -1238) T) ((-72 . -630) 5287) ((-71 . -453) T) ((-71 . -630) 5269) ((-71 . -1238) T) ((-71 . -408) T) ((-70 . -396) T) ((-70 . -630) 5251) ((-70 . -1238) T) ((-70 . -408) T) ((-69 . -408) T) ((-69 . -1238) T) ((-69 . -630) 5233) ((-68 . -396) T) ((-68 . -630) 5215) ((-68 . -1238) T) ((-68 . -408) T) ((-67 . -396) T) ((-67 . -630) 5197) ((-67 . -1238) T) ((-67 . -408) T) ((-66 . -409) T) ((-66 . -630) 5179) ((-66 . -1238) T) ((-66 . -408) T) ((-65 . -398) T) ((-65 . -630) 5161) ((-65 . -1238) T) ((-65 . -408) T) ((-65 . -633) 5090) ((-64 . -453) T) ((-64 . -630) 5072) ((-64 . -1238) T) ((-64 . -408) T) ((-63 . -408) T) ((-63 . -1238) T) ((-63 . -630) 5054) ((-62 . -453) T) ((-62 . -630) 5036) ((-62 . -1238) T) ((-62 . -408) T) ((-61 . -409) T) ((-61 . -630) 5018) ((-61 . -1238) T) ((-61 . -408) T) ((-60 . -57) 4980) ((-60 . -34) T) ((-60 . -1238) T) ((-60 . -102) 4930) ((-60 . -630) 4862) ((-60 . -321) 4800) ((-60 . -526) 4733) ((-60 . -1122) 4711) ((-60 . -501) 4695) ((-58 . -19) 4679) ((-58 . -671) 4663) ((-58 . -300) 4640) ((-58 . -298) 4592) ((-58 . -616) 4569) ((-58 . -631) 4530) ((-58 . -501) 4514) ((-58 . -1122) 4464) ((-58 . -526) 4397) ((-58 . -321) 4335) ((-58 . -630) 4247) ((-58 . -102) 4177) ((-58 . -1238) T) ((-58 . -34) T) ((-58 . -153) 4161) ((-58 . -861) 4140) ((-58 . -864) 4119) ((-58 . -385) 4103) ((-55 . -1122) T) ((-55 . -630) 4085) ((-55 . -1238) T) ((-55 . -102) T) ((-55 . -1059) 4067) ((-55 . -633) 4049) ((-51 . -1122) T) ((-51 . -630) 4031) ((-51 . -1238) T) ((-51 . -102) T) ((-50 . -638) 4015) ((-50 . -633) 3984) ((-50 . -668) 3958) ((-50 . -666) 3917) ((-50 . -746) T) ((-50 . -1133) T) ((-50 . -1078) T) ((-50 . -1070) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1122) T) ((-50 . -630) 3899) ((-50 . -1238) T) ((-50 . -102) T) ((-50 . -25) T) ((-50 . -133) T) ((-50 . -1059) 3883) ((-49 . -1122) T) ((-49 . -630) 3865) ((-49 . -1238) T) ((-49 . -102) T) ((-48 . -310) T) ((-48 . -102) T) ((-48 . -1238) T) ((-48 . -630) 3847) ((-48 . -1122) T) ((-48 . -633) 3780) ((-48 . -1059) 3723) ((-48 . -526) 3689) ((-48 . -321) 3676) ((-48 . -27) T) ((-48 . -1023) T) ((-48 . -250) T) ((-48 . -111) 3632) ((-48 . -1072) 3597) ((-48 . -1077) 3562) ((-48 . -302) T) ((-48 . -737) 3527) ((-48 . -660) 3492) ((-48 . -668) 3442) ((-48 . -666) 3392) ((-48 . -133) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -1070) T) ((-48 . -1078) T) ((-48 . -1133) T) ((-48 . -746) T) ((-48 . -38) 3357) ((-48 . -319) T) ((-48 . -464) T) ((-48 . -175) T) ((-48 . -569) T) ((-48 . -940) T) ((-48 . -1243) T) ((-48 . -376) T) ((-48 . -658) 3317) ((-48 . -1041) T) ((-48 . -631) 3262) ((-48 . -149) T) ((-48 . -240) T) ((-48 . -236) 3249) ((-48 . -239) T) ((-45 . -36) 3228) ((-45 . -616) 3153) ((-45 . -321) 2957) ((-45 . -526) 2749) ((-45 . -501) 2686) ((-45 . -298) 2586) ((-45 . -300) 2511) ((-45 . -627) 2490) ((-45 . -242) 2440) ((-45 . -107) 2390) ((-45 . -233) 2340) ((-45 . -1215) 2319) ((-45 . -294) 2269) ((-45 . -153) 2219) ((-45 . -34) T) ((-45 . -1238) T) ((-45 . -102) T) ((-45 . -630) 2201) ((-45 . -1122) T) ((-45 . -631) NIL) ((-45 . -671) 2151) ((-45 . -385) 2101) ((-45 . -864) NIL) ((-45 . -861) NIL) ((-45 . -1171) 2051) ((-45 . -1031) 2001) ((-45 . -1277) 1951) ((-45 . -686) 1901) ((-44 . -430) 1885) ((-44 . -764) 1869) ((-44 . -740) T) ((-44 . -781) T) ((-44 . -111) 1848) ((-44 . -1072) 1832) ((-44 . -1077) 1816) ((-44 . -21) T) ((-44 . -666) 1759) ((-44 . -23) T) ((-44 . -1122) T) ((-44 . -630) 1741) ((-44 . -102) T) ((-44 . -25) T) ((-44 . -133) T) ((-44 . -668) 1699) ((-44 . -660) 1683) ((-44 . -737) 1667) ((-44 . -380) 1651) ((-44 . -1238) T) ((-44 . -298) 1628) ((-40 . -355) 1602) ((-40 . -175) T) ((-40 . -633) 1532) ((-40 . -746) T) ((-40 . -1133) T) ((-40 . -1078) T) ((-40 . -1070) T) ((-40 . -668) 1439) ((-40 . -666) 1369) ((-40 . -133) T) ((-40 . -25) T) ((-40 . -102) T) ((-40 . -1238) T) ((-40 . -630) 1351) ((-40 . -1122) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -1077) 1296) ((-40 . -1072) 1241) ((-40 . -111) 1170) ((-40 . -631) 1154) ((-40 . -234) 1131) ((-40 . -917) 1083) ((-40 . -919) 992) ((-40 . -911) 899) ((-40 . -274) 876) ((-40 . -239) 813) ((-40 . -236) 744) ((-40 . -240) 716) ((-40 . -376) T) ((-40 . -1243) T) ((-40 . -940) T) ((-40 . -569) T) ((-40 . -737) 661) ((-40 . -660) 606) ((-40 . -38) 551) ((-40 . -464) T) ((-40 . -319) T) ((-40 . -302) T) ((-40 . -250) T) ((-40 . -381) NIL) ((-40 . -363) NIL) ((-40 . -1173) NIL) ((-40 . -147) 523) ((-40 . -414) NIL) ((-40 . -422) 495) ((-40 . -149) 467) ((-40 . -383) 439) ((-40 . -390) 416) ((-40 . -658) 355) ((-40 . -424) 332) ((-40 . -1059) 220) ((-40 . -744) 192) ((-31 . -1104) T) ((-31 . -502) 173) ((-31 . -630) 139) ((-31 . -633) 120) ((-31 . -1122) T) ((-31 . -1238) T) ((-31 . -102) T) ((-31 . -93) T) ((-30 . -974) T) ((-30 . -630) 102) ((0 . |EnumerationCategory|) T) ((0 . -630) 84) ((0 . -1122) T) ((0 . -102) T) ((0 . -1238) T) ((-2 . |RecordCategory|) T) ((-2 . -630) 66) ((-2 . -1122) T) ((-2 . -102) T) ((-2 . -1238) T) ((-3 . |UnionCategory|) T) ((-3 . -630) 48) ((-3 . -1122) T) ((-3 . -102) T) ((-3 . -1238) T) ((-1 . -1122) T) ((-1 . -630) 30) ((-1 . -1238) T) ((-1 . -102) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index b8822bfa..4b7ef4f3 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3521929245)            
-(4505 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3521934607)            
+(4428 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -266,25 +266,23 @@
  |ReduceLODE| |RationalRicDE| |SystemODESolver| |ODETools|
  |OrderedDirectProduct| |OrderlyDifferentialPolynomial|
  |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid|
- |OrderedIntegralDomain| |OpenMath| |OpenMathConnection| |OpenMathDevice|
- |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |ExpressionToOpenMath|
- |OppositeMonogenicLinearOperator| |OpenMathPackage| |OrderedMultisetAggregate|
- |OnePointCompletion| |OnePointCompletionFunctions2| |Operator|
- |OperatorCategory&| |OperatorCategory| |OperationsQuery| |OperatorSignature|
- |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage|
- |NumericalOptimizationProblem| |OrderedCompletion|
- |OrderedCompletionFunctions2| |OrderedFinite| |OrderingFunctions|
- |OrderedMonoid| |OrderedRing| |OrderedSet| |OrderedStructure| |OrderedType&|
- |OrderedType| |UnivariateSkewPolynomialCategory&|
- |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps|
- |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial|
- |OrthogonalPolynomialFunctions| |OrderedSemiGroup| |OrdSetInts|
- |OutputPackage| |OutputByteConduit&| |OutputByteConduit| |OutputBinaryFile|
- |OutputForm| |OrderedVariableList| |OverloadSet| |OrdinaryWeightedPolynomials|
- |PadeApproximants| |PadeApproximantPackage| |PAdicInteger|
- |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| |Pair|
- |Palette| |PolynomialAN2Expression| |ParameterAst|
- |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve|
+ |OrderedIntegralDomain| |OppositeMonogenicLinearOperator|
+ |OrderedMultisetAggregate| |OnePointCompletion| |OnePointCompletionFunctions2|
+ |Operator| |OperatorCategory&| |OperatorCategory| |OperationsQuery|
+ |OperatorSignature| |NumericalOptimizationCategory|
+ |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem|
+ |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedFinite|
+ |OrderingFunctions| |OrderedMonoid| |OrderedRing| |OrderedSet|
+ |OrderedStructure| |OrderedType&| |OrderedType|
+ |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory|
+ |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial|
+ |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| |OrderedSemiGroup|
+ |OrdSetInts| |OutputPackage| |OutputByteConduit&| |OutputByteConduit|
+ |OutputBinaryFile| |OutputForm| |OrderedVariableList| |OverloadSet|
+ |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage|
+ |PAdicInteger| |PAdicIntegerCategory| |PAdicRational|
+ |PAdicRationalConstructor| |Pair| |Palette| |PolynomialAN2Expression|
+ |ParameterAst| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve|
  |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |Parser|
  |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations|
  |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch|
@@ -729,51 +727,38 @@
  |constantCoefficientRicDE| |changeVar| |ratDsolve|
  |indicialEquationAtInfinity| |reduceLODE| |singRicDE| |polyRicDE| |ricDsolve|
  |triangulate| |solveInField| |wronskianMatrix| |variationOfParameters|
- |lexico| |OMmakeConn| |OMcloseConn| |OMconnInDevice| |OMconnOutDevice|
- |OMconnectTCP| |OMbindTCP| |OMopenFile| |OMopenString| |OMclose|
- |OMsetEncoding| |OMputApp| |OMputAtp| |OMputAttr| |OMputBind| |OMputBVar|
- |OMputError| |OMputObject| |OMputEndApp| |OMputEndAtp| |OMputEndAttr|
- |OMputEndBind| |OMputEndBVar| |OMputEndError| |OMputEndObject| |OMputInteger|
- |OMputFloat| |OMputVariable| |OMputString| |OMputSymbol| |OMgetApp| |OMgetAtp|
- |OMgetAttr| |OMgetBind| |OMgetBVar| |OMgetError| |OMgetObject| |OMgetEndApp|
- |OMgetEndAtp| |OMgetEndAttr| |OMgetEndBind| |OMgetEndBVar| |OMgetEndError|
- |OMgetEndObject| |OMgetInteger| |OMgetFloat| |OMgetVariable| |OMgetString|
- |OMgetSymbol| |OMgetType| |OMencodingBinary| |OMencodingSGML| |OMencodingXML|
- |OMencodingUnknown| |omError| |errorInfo| |errorKind| |OMReadError?|
- |OMUnknownSymbol?| |OMUnknownCD?| |OMParseError?| |OMwrite| |po| |op| |OMread|
- |OMreadFile| |OMreadStr| |OMlistCDs| |OMlistSymbols| |OMsupportsCD?|
- |OMsupportsSymbol?| |OMunhandledSymbol| |infinity| |makeop| |opeval|
- |evaluateInverse| |evaluate| |conjug| |adjoint| |arity| |getDatabase|
- |numericalOptimization| |optimize| |goodnessOfFit| |whatInfinity| |infinite?|
- |finite?| |minusInfinity| |plusInfinity| |pureLex| |totalLex| |reverseLex|
- |min| |leftLcm| |rightExtendedGcd| |rightGcd| |rightExactQuotient|
- |rightRemainder| |rightQuotient| |rightLcm| |leftExtendedGcd| |leftGcd|
- |leftExactQuotient| |leftRemainder| |leftQuotient| |times| |apply|
- |monicLeftDivide| |monicRightDivide| |leftDivide| |rightDivide| |hermiteH|
- |laguerreL| |legendreP| |outputList| |writeBytes!| |writeUInt8!| |writeInt8!|
- |writeByte!| |isOpen?| |outputBinaryFile| |not| |or| |and| |quo| |rem| |div|
- >= > ~= |blankSeparate| |semicolonSeparate| |commaSeparate| |pile| |paren|
- |bracket| |prod| |overlabel| |overbar| |prime| |quote| |supersub| |presuper|
- |presub| |super| |sub| |rarrow| |assign| |slash| |over| |zag| |box| |label|
- |infix?| |postfix| |infix| |prefix| |vconcat| |hconcat| |rspace| |vspace|
- |hspace| |superHeight| |subHeight| |height| |width| |doubleFloatFormat|
- |messagePrint| |message| |members| |padecf| |pade| |root| |quotientByP|
- |moduloP| |modulus| |digits| |continuedFraction| |pair| |light| |pastel|
- |bright| |dim| |dark| |getSyntaxFormsFromFile| |surface| |coordinate|
- |conjugates| |shuffle| |shufflein| |sequences| |permutations| |lists|
- |makeResult| |is?| |Is| |addMatchRestricted| |insertMatch| |addMatch|
- |getMatch| |failed| |failed?| |optpair| |getBadValues| |resetBadValues|
- |hasTopPredicate?| |topPredicate| |setTopPredicate| |patternVariable|
- |withPredicates| |setPredicates| |predicates| |hasPredicate?| |optional?|
- |multiple?| |generic?| |quoted?| |inR?| |isList| |isQuotient| |isOp| |Zero|
- |satisfy?| |addBadValue| |badValues| |retractable?| |ListOfTerms| |One|
- |PDESolve| |leftFactor| |rightFactorCandidate| |measure| D |ptree|
- |coerceImages| |fixedPoints| |odd?| |even?| |numberOfCycles| |cyclePartition|
- |coerceListOfPairs| |coercePreimagesImages| |listRepresentation| |permanent|
- |cycles| |cycle| |initializeGroupForWordProblem| <= < |support|
- |wordInGenerators| |wordInStrongGenerators| |orbits| |orbit|
- |permutationGroup| |wordsForStrongGenerators| |strongGenerators| |base|
- |generators| |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion|
+ |lexico| |po| |op| |infinity| |makeop| |opeval| |evaluateInverse| |evaluate|
+ |conjug| |adjoint| |arity| |getDatabase| |numericalOptimization| |optimize|
+ |goodnessOfFit| |whatInfinity| |infinite?| |finite?| |minusInfinity|
+ |plusInfinity| |pureLex| |totalLex| |reverseLex| |min| |leftLcm|
+ |rightExtendedGcd| |rightGcd| |rightExactQuotient| |rightRemainder|
+ |rightQuotient| |rightLcm| |leftExtendedGcd| |leftGcd| |leftExactQuotient|
+ |leftRemainder| |leftQuotient| |times| |apply| |monicLeftDivide|
+ |monicRightDivide| |leftDivide| |rightDivide| |hermiteH| |laguerreL|
+ |legendreP| |outputList| |writeBytes!| |writeUInt8!| |writeInt8!| |writeByte!|
+ |isOpen?| |outputBinaryFile| |not| |or| |and| |quo| |rem| |div| >= > ~=
+ |blankSeparate| |semicolonSeparate| |commaSeparate| |pile| |paren| |bracket|
+ |prod| |overlabel| |overbar| |prime| |quote| |supersub| |presuper| |presub|
+ |super| |sub| |rarrow| |assign| |slash| |over| |zag| |box| |label| |infix?|
+ |postfix| |infix| |prefix| |vconcat| |hconcat| |rspace| |vspace| |hspace|
+ |superHeight| |subHeight| |height| |width| |doubleFloatFormat| |messagePrint|
+ |message| |members| |padecf| |pade| |root| |quotientByP| |moduloP| |modulus|
+ |digits| |continuedFraction| |pair| |light| |pastel| |bright| |dim| |dark|
+ |getSyntaxFormsFromFile| |surface| |coordinate| |conjugates| |shuffle|
+ |shufflein| |sequences| |permutations| |lists| |makeResult| |is?| |Is|
+ |addMatchRestricted| |insertMatch| |addMatch| |getMatch| |failed| |failed?|
+ |optpair| |getBadValues| |resetBadValues| |hasTopPredicate?| |topPredicate|
+ |setTopPredicate| |patternVariable| |withPredicates| |setPredicates|
+ |predicates| |hasPredicate?| |optional?| |multiple?| |generic?| |quoted?|
+ |inR?| |isList| |isQuotient| |isOp| |Zero| |satisfy?| |addBadValue|
+ |badValues| |retractable?| |ListOfTerms| |One| |PDESolve| |leftFactor|
+ |rightFactorCandidate| |measure| D |ptree| |coerceImages| |fixedPoints| |odd?|
+ |even?| |numberOfCycles| |cyclePartition| |coerceListOfPairs|
+ |coercePreimagesImages| |listRepresentation| |permanent| |cycles| |cycle|
+ |initializeGroupForWordProblem| <= < |support| |wordInGenerators|
+ |wordInStrongGenerators| |orbits| |orbit| |permutationGroup|
+ |wordsForStrongGenerators| |strongGenerators| |base| |generators|
+ |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion|
  |factorByRecursion| |factorSquareFreeByRecursion| |randomR| |factorSFBRlcUnit|
  |charthRoot| |conditionP| |solveLinearPolynomialEquation|
  |factorSquareFreePolynomial| |factorPolynomial| |squareFreePolynomial|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 0917fcc4..b5e11626 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5481 +1,5449 @@
 
-(3445357 . 3521929259)       
-((-1943 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-1941 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-4295 ((|#2| $ (-558) |#2|) NIL T ELT) ((|#2| $ (-1263 (-558)) |#2|) 44 T ELT)) (-2518 (($ $) 80 T ELT)) (-4349 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3916 (((-558) (-1 (-114) |#2|) $) 27 T ELT) (((-558) |#2| $) NIL T ELT) (((-558) |#2| $ (-558)) 96 T ELT)) (-3367 (((-661 |#2|) $) 13 T ELT)) (-4015 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2168 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-4465 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2525 (($ |#2| $ (-558)) NIL T ELT) (($ $ $ (-558)) 67 T ELT)) (-1476 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-2166 (((-114) (-1 (-114) |#2|) $) 23 T ELT)) (-4307 ((|#2| $ (-558) |#2|) NIL T ELT) ((|#2| $ (-558)) NIL T ELT) (($ $ (-1263 (-558))) 66 T ELT)) (-2526 (($ $ (-558)) 76 T ELT) (($ $ (-1263 (-558))) 75 T ELT)) (-2165 (((-791) (-1 (-114) |#2|) $) 34 T ELT) (((-791) |#2| $) NIL T ELT)) (-1942 (($ $ $ (-558)) 69 T ELT)) (-3897 (($ $) 68 T ELT)) (-4027 (($ (-661 |#2|)) 73 T ELT)) (-4309 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-661 $)) 85 T ELT)) (-4453 (((-885) $) 92 T ELT)) (-2167 (((-114) (-1 (-114) |#2|) $) 22 T ELT)) (-3531 (((-114) $ $) 95 T ELT)) (-3163 (((-114) $ $) 99 T ELT))) 
-(((-18 |#1| |#2|) (-10 -8 (-15 -3531 ((-114) |#1| |#1|)) (-15 -4453 ((-885) |#1|)) (-15 -3163 ((-114) |#1| |#1|)) (-15 -1941 (|#1| |#1|)) (-15 -1941 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -2518 (|#1| |#1|)) (-15 -1942 (|#1| |#1| |#1| (-558))) (-15 -1943 ((-114) |#1|)) (-15 -4015 (|#1| |#1| |#1|)) (-15 -3916 ((-558) |#2| |#1| (-558))) (-15 -3916 ((-558) |#2| |#1|)) (-15 -3916 ((-558) (-1 (-114) |#2|) |#1|)) (-15 -1943 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -4015 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -4295 (|#2| |#1| (-1263 (-558)) |#2|)) (-15 -2525 (|#1| |#1| |#1| (-558))) (-15 -2525 (|#1| |#2| |#1| (-558))) (-15 -2526 (|#1| |#1| (-1263 (-558)))) (-15 -2526 (|#1| |#1| (-558))) (-15 -4465 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4309 (|#1| (-661 |#1|))) (-15 -4309 (|#1| |#1| |#1|)) (-15 -4309 (|#1| |#2| |#1|)) (-15 -4309 (|#1| |#1| |#2|)) (-15 -4307 (|#1| |#1| (-1263 (-558)))) (-15 -4027 (|#1| (-661 |#2|))) (-15 -1476 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -4349 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -4349 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -4349 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4307 (|#2| |#1| (-558))) (-15 -4307 (|#2| |#1| (-558) |#2|)) (-15 -4295 (|#2| |#1| (-558) |#2|)) (-15 -2165 ((-791) |#2| |#1|)) (-15 -3367 ((-661 |#2|) |#1|)) (-15 -2165 ((-791) (-1 (-114) |#2|) |#1|)) (-15 -2166 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2167 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2168 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4465 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3897 (|#1| |#1|))) (-19 |#2|) (-1246)) (T -18)) 
+(3432501 . 3521934621)       
+((-1935 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-1933 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-4218 ((|#2| $ (-558) |#2|) NIL T ELT) ((|#2| $ (-1255 (-558)) |#2|) 44 T ELT)) (-2510 (($ $) 80 T ELT)) (-4272 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3839 (((-558) (-1 (-114) |#2|) $) 27 T ELT) (((-558) |#2| $) NIL T ELT) (((-558) |#2| $ (-558)) 96 T ELT)) (-3290 (((-661 |#2|) $) 13 T ELT)) (-3938 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2160 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-4388 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2517 (($ |#2| $ (-558)) NIL T ELT) (($ $ $ (-558)) 67 T ELT)) (-1468 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-2158 (((-114) (-1 (-114) |#2|) $) 23 T ELT)) (-4230 ((|#2| $ (-558) |#2|) NIL T ELT) ((|#2| $ (-558)) NIL T ELT) (($ $ (-1255 (-558))) 66 T ELT)) (-2518 (($ $ (-558)) 76 T ELT) (($ $ (-1255 (-558))) 75 T ELT)) (-2157 (((-791) (-1 (-114) |#2|) $) 34 T ELT) (((-791) |#2| $) NIL T ELT)) (-1934 (($ $ $ (-558)) 69 T ELT)) (-3820 (($ $) 68 T ELT)) (-3950 (($ (-661 |#2|)) 73 T ELT)) (-4232 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-661 $)) 85 T ELT)) (-4376 (((-877) $) 92 T ELT)) (-2159 (((-114) (-1 (-114) |#2|) $) 22 T ELT)) (-3454 (((-114) $ $) 95 T ELT)) (-3086 (((-114) $ $) 99 T ELT))) 
+(((-18 |#1| |#2|) (-10 -8 (-15 -3454 ((-114) |#1| |#1|)) (-15 -4376 ((-877) |#1|)) (-15 -3086 ((-114) |#1| |#1|)) (-15 -1933 (|#1| |#1|)) (-15 -1933 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -2510 (|#1| |#1|)) (-15 -1934 (|#1| |#1| |#1| (-558))) (-15 -1935 ((-114) |#1|)) (-15 -3938 (|#1| |#1| |#1|)) (-15 -3839 ((-558) |#2| |#1| (-558))) (-15 -3839 ((-558) |#2| |#1|)) (-15 -3839 ((-558) (-1 (-114) |#2|) |#1|)) (-15 -1935 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -3938 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -4218 (|#2| |#1| (-1255 (-558)) |#2|)) (-15 -2517 (|#1| |#1| |#1| (-558))) (-15 -2517 (|#1| |#2| |#1| (-558))) (-15 -2518 (|#1| |#1| (-1255 (-558)))) (-15 -2518 (|#1| |#1| (-558))) (-15 -4388 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4232 (|#1| (-661 |#1|))) (-15 -4232 (|#1| |#1| |#1|)) (-15 -4232 (|#1| |#2| |#1|)) (-15 -4232 (|#1| |#1| |#2|)) (-15 -4230 (|#1| |#1| (-1255 (-558)))) (-15 -3950 (|#1| (-661 |#2|))) (-15 -1468 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -4272 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -4272 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -4272 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4230 (|#2| |#1| (-558))) (-15 -4230 (|#2| |#1| (-558) |#2|)) (-15 -4218 (|#2| |#1| (-558) |#2|)) (-15 -2157 ((-791) |#2| |#1|)) (-15 -3290 ((-661 |#2|) |#1|)) (-15 -2157 ((-791) (-1 (-114) |#2|) |#1|)) (-15 -2158 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2159 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2160 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4388 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3820 (|#1| |#1|))) (-19 |#2|) (-1238)) (T -18)) 
 NIL 
-(-10 -8 (-15 -3531 ((-114) |#1| |#1|)) (-15 -4453 ((-885) |#1|)) (-15 -3163 ((-114) |#1| |#1|)) (-15 -1941 (|#1| |#1|)) (-15 -1941 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -2518 (|#1| |#1|)) (-15 -1942 (|#1| |#1| |#1| (-558))) (-15 -1943 ((-114) |#1|)) (-15 -4015 (|#1| |#1| |#1|)) (-15 -3916 ((-558) |#2| |#1| (-558))) (-15 -3916 ((-558) |#2| |#1|)) (-15 -3916 ((-558) (-1 (-114) |#2|) |#1|)) (-15 -1943 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -4015 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -4295 (|#2| |#1| (-1263 (-558)) |#2|)) (-15 -2525 (|#1| |#1| |#1| (-558))) (-15 -2525 (|#1| |#2| |#1| (-558))) (-15 -2526 (|#1| |#1| (-1263 (-558)))) (-15 -2526 (|#1| |#1| (-558))) (-15 -4465 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4309 (|#1| (-661 |#1|))) (-15 -4309 (|#1| |#1| |#1|)) (-15 -4309 (|#1| |#2| |#1|)) (-15 -4309 (|#1| |#1| |#2|)) (-15 -4307 (|#1| |#1| (-1263 (-558)))) (-15 -4027 (|#1| (-661 |#2|))) (-15 -1476 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -4349 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -4349 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -4349 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4307 (|#2| |#1| (-558))) (-15 -4307 (|#2| |#1| (-558) |#2|)) (-15 -4295 (|#2| |#1| (-558) |#2|)) (-15 -2165 ((-791) |#2| |#1|)) (-15 -3367 ((-661 |#2|) |#1|)) (-15 -2165 ((-791) (-1 (-114) |#2|) |#1|)) (-15 -2166 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2167 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2168 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4465 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3897 (|#1| |#1|))) 
-((-3044 (((-114) $ $) 19 (|has| |#1| (-102)) ELT)) (-2421 (((-1302) $ (-558) (-558)) 44 (|has| $ (-6 -4503)) ELT)) (-1943 (((-114) (-1 (-114) |#1| |#1|) $) 107 T ELT) (((-114) $) 101 (|has| |#1| (-869)) ELT)) (-1941 (($ (-1 (-114) |#1| |#1|) $) 98 (|has| $ (-6 -4503)) ELT) (($ $) 97 (-12 (|has| |#1| (-869)) (|has| $ (-6 -4503))) ELT)) (-3387 (($ (-1 (-114) |#1| |#1|) $) 108 T ELT) (($ $) 102 (|has| |#1| (-869)) ELT)) (-4295 ((|#1| $ (-558) |#1|) 56 (|has| $ (-6 -4503)) ELT) ((|#1| $ (-1263 (-558)) |#1|) 64 (|has| $ (-6 -4503)) ELT)) (-4217 (($ (-1 (-114) |#1|) $) 81 (|has| $ (-6 -4502)) ELT)) (-4231 (($) 7 T CONST)) (-2518 (($ $) 99 (|has| $ (-6 -4503)) ELT)) (-2519 (($ $) 109 T ELT)) (-1475 (($ $) 84 (-12 (|has| |#1| (-1130)) (|has| $ (-6 -4502))) ELT)) (-3903 (($ |#1| $) 83 (-12 (|has| |#1| (-1130)) (|has| $ (-6 -4502))) ELT) (($ (-1 (-114) |#1|) $) 80 (|has| $ (-6 -4502)) ELT)) (-4349 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) 82 (-12 (|has| |#1| (-1130)) (|has| $ (-6 -4502))) ELT) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) 79 (|has| $ (-6 -4502)) ELT) ((|#1| (-1 |#1| |#1| |#1|) $) 78 (|has| $ (-6 -4502)) ELT)) (-1727 ((|#1| $ (-558) |#1|) 57 (|has| $ (-6 -4503)) ELT)) (-3592 ((|#1| $ (-558)) 55 T ELT)) (-3916 (((-558) (-1 (-114) |#1|) $) 106 T ELT) (((-558) |#1| $) 105 (|has| |#1| (-1130)) ELT) (((-558) |#1| $ (-558)) 104 (|has| |#1| (-1130)) ELT)) (-3367 (((-661 |#1|) $) 30 (|has| $ (-6 -4502)) ELT)) (-4121 (($ (-791) |#1|) 74 T ELT)) (-2423 (((-558) $) 47 (|has| (-558) (-869)) ELT)) (-3007 (($ $ $) 91 (|has| |#1| (-869)) ELT)) (-4015 (($ (-1 (-114) |#1| |#1|) $ $) 110 T ELT) (($ $ $) 103 (|has| |#1| (-869)) ELT)) (-3084 (((-661 |#1|) $) 29 (|has| $ (-6 -4502)) ELT)) (-3740 (((-114) |#1| $) 27 (-12 (|has| |#1| (-1130)) (|has| $ (-6 -4502))) ELT)) (-2424 (((-558) $) 48 (|has| (-558) (-869)) ELT)) (-3335 (($ $ $) 92 (|has| |#1| (-869)) ELT)) (-2168 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4503)) ELT)) (-4465 (($ (-1 |#1| |#1|) $) 35 T ELT) (($ (-1 |#1| |#1| |#1|) $ $) 69 T ELT)) (-3737 (((-1188) $) 22 (|has| |#1| (-1130)) ELT)) (-2525 (($ |#1| $ (-558)) 66 T ELT) (($ $ $ (-558)) 65 T ELT)) (-2426 (((-661 (-558)) $) 50 T ELT)) (-2427 (((-114) (-558) $) 51 T ELT)) (-3738 (((-1149) $) 21 (|has| |#1| (-1130)) ELT)) (-4308 ((|#1| $) 46 (|has| (-558) (-869)) ELT)) (-1476 (((-3 |#1| "failed") (-1 (-114) |#1|) $) 77 T ELT)) (-2422 (($ $ |#1|) 45 (|has| $ (-6 -4503)) ELT)) (-2166 (((-114) (-1 (-114) |#1|) $) 32 (|has| $ (-6 -4502)) ELT)) (-4275 (($ $ (-661 (-305 |#1|))) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ELT) (($ $ (-305 |#1|)) 25 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ELT) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ELT) (($ $ (-661 |#1|) (-661 |#1|)) 23 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ELT)) (-1337 (((-114) $ $) 11 T ELT)) (-2425 (((-114) |#1| $) 49 (-12 (|has| $ (-6 -4502)) (|has| |#1| (-1130))) ELT)) (-2428 (((-661 |#1|) $) 52 T ELT)) (-3900 (((-114) $) 8 T ELT)) (-4070 (($) 9 T ELT)) (-4307 ((|#1| $ (-558) |#1|) 54 T ELT) ((|#1| $ (-558)) 53 T ELT) (($ $ (-1263 (-558))) 75 T ELT)) (-2526 (($ $ (-558)) 68 T ELT) (($ $ (-1263 (-558))) 67 T ELT)) (-2165 (((-791) (-1 (-114) |#1|) $) 31 (|has| $ (-6 -4502)) ELT) (((-791) |#1| $) 28 (-12 (|has| |#1| (-1130)) (|has| $ (-6 -4502))) ELT)) (-1942 (($ $ $ (-558)) 100 (|has| $ (-6 -4503)) ELT)) (-3897 (($ $) 10 T ELT)) (-4479 (((-547) $) 85 (|has| |#1| (-631 (-547))) ELT)) (-4027 (($ (-661 |#1|)) 76 T ELT)) (-4309 (($ $ |#1|) 73 T ELT) (($ |#1| $) 72 T ELT) (($ $ $) 71 T ELT) (($ (-661 $)) 70 T ELT)) (-4453 (((-885) $) 17 (|has| |#1| (-630 (-885))) ELT)) (-1386 (((-114) $ $) 20 (|has| |#1| (-102)) ELT)) (-2167 (((-114) (-1 (-114) |#1|) $) 33 (|has| $ (-6 -4502)) ELT)) (-3042 (((-114) $ $) 93 (|has| |#1| (-869)) ELT)) (-3043 (((-114) $ $) 95 (|has| |#1| (-869)) ELT)) (-3531 (((-114) $ $) 18 (|has| |#1| (-102)) ELT)) (-3162 (((-114) $ $) 94 (|has| |#1| (-869)) ELT)) (-3163 (((-114) $ $) 96 (|has| |#1| (-869)) ELT)) (-4464 (((-791) $) 6 (|has| $ (-6 -4502)) ELT))) 
-(((-19 |#1|) (-142) (-1246)) (T -19)) 
+(-10 -8 (-15 -3454 ((-114) |#1| |#1|)) (-15 -4376 ((-877) |#1|)) (-15 -3086 ((-114) |#1| |#1|)) (-15 -1933 (|#1| |#1|)) (-15 -1933 (|#1| (-1 (-114) |#2| |#2|) |#1|)) (-15 -2510 (|#1| |#1|)) (-15 -1934 (|#1| |#1| |#1| (-558))) (-15 -1935 ((-114) |#1|)) (-15 -3938 (|#1| |#1| |#1|)) (-15 -3839 ((-558) |#2| |#1| (-558))) (-15 -3839 ((-558) |#2| |#1|)) (-15 -3839 ((-558) (-1 (-114) |#2|) |#1|)) (-15 -1935 ((-114) (-1 (-114) |#2| |#2|) |#1|)) (-15 -3938 (|#1| (-1 (-114) |#2| |#2|) |#1| |#1|)) (-15 -4218 (|#2| |#1| (-1255 (-558)) |#2|)) (-15 -2517 (|#1| |#1| |#1| (-558))) (-15 -2517 (|#1| |#2| |#1| (-558))) (-15 -2518 (|#1| |#1| (-1255 (-558)))) (-15 -2518 (|#1| |#1| (-558))) (-15 -4388 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4232 (|#1| (-661 |#1|))) (-15 -4232 (|#1| |#1| |#1|)) (-15 -4232 (|#1| |#2| |#1|)) (-15 -4232 (|#1| |#1| |#2|)) (-15 -4230 (|#1| |#1| (-1255 (-558)))) (-15 -3950 (|#1| (-661 |#2|))) (-15 -1468 ((-3 |#2| "failed") (-1 (-114) |#2|) |#1|)) (-15 -4272 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -4272 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -4272 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4230 (|#2| |#1| (-558))) (-15 -4230 (|#2| |#1| (-558) |#2|)) (-15 -4218 (|#2| |#1| (-558) |#2|)) (-15 -2157 ((-791) |#2| |#1|)) (-15 -3290 ((-661 |#2|) |#1|)) (-15 -2157 ((-791) (-1 (-114) |#2|) |#1|)) (-15 -2158 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2159 ((-114) (-1 (-114) |#2|) |#1|)) (-15 -2160 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4388 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3820 (|#1| |#1|))) 
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+(((-19 |#1|) (-142) (-1238)) (T -19)) 
 NIL 
-(-13 (-385 |t#1|) (-10 -7 (-6 -4503))) 
-(((-34) . T) ((-102) -4034 (|has| |#1| (-1130)) (|has| |#1| (-869)) (|has| |#1| (-102))) ((-630 (-885)) -4034 (|has| |#1| (-1130)) (|has| |#1| (-869)) (|has| |#1| (-630 (-885)))) ((-153 |#1|) . T) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-298 #1=(-558) |#1|) . T) ((-298 (-1263 (-558)) $) . T) ((-300 #1# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ((-385 |#1|) . T) ((-501 |#1|) . T) ((-616 #1# |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ((-671 |#1|) . T) ((-869) |has| |#1| (-869)) ((-872) |has| |#1| (-869)) ((-1130) -4034 (|has| |#1| (-1130)) (|has| |#1| (-869))) ((-1246) . T)) 
-((-1434 (((-3 $ "failed") $ $) 12 T ELT)) (-4344 (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (-946) $) NIL T ELT) (($ (-791) $) 16 T ELT) (($ (-558) $) 25 T ELT))) 
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+(-13 (-385 |t#1|) (-10 -7 (-6 -4426))) 
+(((-34) . T) ((-102) -3957 (|has| |#1| (-1122)) (|has| |#1| (-861)) (|has| |#1| (-102))) ((-630 (-877)) -3957 (|has| |#1| (-1122)) (|has| |#1| (-861)) (|has| |#1| (-630 (-877)))) ((-153 |#1|) . T) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-298 #1=(-558) |#1|) . T) ((-298 (-1255 (-558)) $) . T) ((-300 #1# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1122))) ((-385 |#1|) . T) ((-501 |#1|) . T) ((-616 #1# |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1122))) ((-671 |#1|) . T) ((-861) |has| |#1| (-861)) ((-864) |has| |#1| (-861)) ((-1122) -3957 (|has| |#1| (-1122)) (|has| |#1| (-861))) ((-1238) . T)) 
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 NIL 
-(-10 -8 (-15 -4344 (|#1| |#1| |#1|)) (-15 -4344 (|#1| |#1|)) (-15 * (|#1| (-558) |#1|)) (-15 -1434 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-791) |#1|)) (-15 * (|#1| (-946) |#1|))) 
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 (((-21) (-142)) (T -21)) 
-((-4344 (*1 *1 *1) (-4 *1 (-21))) (-4344 (*1 *1 *1 *1) (-4 *1 (-21)))) 
-(-13 (-133) (-666 (-558)) (-10 -8 (-15 -4344 ($ $)) (-15 -4344 ($ $ $)))) 
-(((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-630 (-885)) . T) ((-666 (-558)) . T) ((-1130) . T) ((-1246) . T)) 
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-NIL 
-(-10 -8 (-15 * (|#1| (-791) |#1|)) (-15 -3683 ((-114) |#1|)) (-15 -4231 (|#1|)) (-15 * (|#1| (-946) |#1|))) 
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+NIL 
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 (((-23) (-142)) (T -23)) 
-((-3136 (*1 *1) (-4 *1 (-23))) (-4231 (*1 *1) (-4 *1 (-23))) (-3683 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-114)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-791))))) 
-(-13 (-25) (-10 -8 (-15 (-3136) ($) -4459) (-15 -4231 ($) -4459) (-15 -3683 ((-114) $)) (-15 * ($ (-791) $)))) 
-(((-25) . T) ((-102) . T) ((-630 (-885)) . T) ((-1130) . T) ((-1246) . T)) 
-((* (($ (-946) $) 10 T ELT))) 
-(((-24 |#1|) (-10 -8 (-15 * (|#1| (-946) |#1|))) (-25)) (T -24)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-946) |#1|))) 
-((-3044 (((-114) $ $) 7 T ELT)) (-3737 (((-1188) $) 11 T ELT)) (-3738 (((-1149) $) 12 T ELT)) (-4453 (((-885) $) 13 T ELT)) (-1386 (((-114) $ $) 6 T ELT)) (-3531 (((-114) $ $) 8 T ELT)) (-4346 (($ $ $) 18 T ELT)) (* (($ (-946) $) 17 T ELT))) 
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+(-13 (-25) (-10 -8 (-15 (-3059) ($) -4382) (-15 -4154 ($) -4382) (-15 -3606 ((-114) $)) (-15 * ($ (-791) $)))) 
+(((-25) . T) ((-102) . T) ((-630 (-877)) . T) ((-1122) . T) ((-1238) . T)) 
+((* (($ (-938) $) 10 T ELT))) 
+(((-24 |#1|) (-10 -8 (-15 * (|#1| (-938) |#1|))) (-25)) (T -24)) 
+NIL 
+(-10 -8 (-15 * (|#1| (-938) |#1|))) 
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 (((-25) (-142)) (T -25)) 
-((-4346 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-946))))) 
-(-13 (-1130) (-10 -8 (-15 -4346 ($ $ $)) (-15 * ($ (-946) $)))) 
-(((-102) . T) ((-630 (-885)) . T) ((-1130) . T) ((-1246) . T)) 
-((-1758 (((-661 $) (-973 $)) 32 T ELT) (((-661 $) (-1200 $)) 16 T ELT) (((-661 $) (-1200 $) (-1206)) 20 T ELT)) (-1331 (($ (-973 $)) 30 T ELT) (($ (-1200 $)) 11 T ELT) (($ (-1200 $) (-1206)) 60 T ELT)) (-1332 (((-661 $) (-973 $)) 33 T ELT) (((-661 $) (-1200 $)) 18 T ELT) (((-661 $) (-1200 $) (-1206)) 19 T ELT)) (-3678 (($ (-973 $)) 31 T ELT) (($ (-1200 $)) 13 T ELT) (($ (-1200 $) (-1206)) NIL T ELT))) 
-(((-26 |#1|) (-10 -8 (-15 -1758 ((-661 |#1|) (-1200 |#1|) (-1206))) (-15 -1758 ((-661 |#1|) (-1200 |#1|))) (-15 -1758 ((-661 |#1|) (-973 |#1|))) (-15 -1331 (|#1| (-1200 |#1|) (-1206))) (-15 -1331 (|#1| (-1200 |#1|))) (-15 -1331 (|#1| (-973 |#1|))) (-15 -1332 ((-661 |#1|) (-1200 |#1|) (-1206))) (-15 -1332 ((-661 |#1|) (-1200 |#1|))) (-15 -1332 ((-661 |#1|) (-973 |#1|))) (-15 -3678 (|#1| (-1200 |#1|) (-1206))) (-15 -3678 (|#1| (-1200 |#1|))) (-15 -3678 (|#1| (-973 |#1|)))) (-27)) (T -26)) 
-NIL 
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+NIL 
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-NIL 
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-NIL 
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+((-1330 (*1 *2 *3 *1) (|partial| -12 (-4 *1 (-36 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122)) (-5 *2 (-2 (|:| -4290 *3) (|:| -2286 *4)))))) 
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+(((-34) . T) ((-107 #1=(-2 (|:| -4290 |#1|) (|:| -2286 |#2|))) . T) ((-102) -3957 (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-1122)) (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-861)) (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-102)) (|has| |#2| (-1122)) (|has| |#2| (-102))) ((-630 (-877)) -3957 (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-1122)) (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-861)) (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-630 (-877))) (|has| |#2| (-1122)) (|has| |#2| (-630 (-877)))) ((-153 #2=(-2 (|:| -4290 |#1|) (|:| -2286 |#2|))) . T) ((-631 (-547)) |has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-631 (-547))) ((-233 #1#) . T) ((-242 #1#) . T) ((-298 #3=(-558) #2#) . T) ((-298 (-1255 (-558)) $) . T) ((-298 |#1| |#2|) . T) ((-300 #3# #2#) . T) ((-300 |#1| |#2|) . T) ((-321 #2#) -12 (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-321 (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)))) (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-1122))) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ((-294 #2#) . T) ((-385 #2#) . T) ((-501 #2#) . T) ((-501 |#2|) . T) ((-616 #3# #2#) . T) ((-616 |#1| |#2|) . T) ((-526 #2# #2#) -12 (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-321 (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)))) (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-1122))) ((-526 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ((-627 |#1| |#2|) . T) ((-671 #2#) . T) ((-686 #2#) . T) ((-861) |has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-861)) ((-864) |has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-861)) ((-1031 #2#) . T) ((-1122) -3957 (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-1122)) (|has| (-2 (|:| -4290 |#1|) (|:| -2286 |#2|)) (-861)) (|has| |#2| (-1122))) ((-1171 #2#) . T) ((-1215 |#1| |#2|) . T) ((-1238) . T) ((-1277 #2#) . T)) 
+((-4376 (((-877) $) NIL T ELT) (($ (-558)) NIL T ELT) (($ |#2|) 10 T ELT))) 
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+NIL 
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 (((-38 |#1|) (-142) (-175)) (T -38)) 
 NIL 
-(-13 (-1078) (-737 |t#1|) (-633 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-630 (-885)) . T) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-660 |#1|) . T) ((-737 |#1|) . T) ((-746) . T) ((-1080 |#1|) . T) ((-1085 |#1|) . T) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1246) . T)) 
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-NIL 
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 NIL 
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 NIL 
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 NIL 
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 NIL 
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 (((-93) (-142)) (T -93)) 
 NIL 
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 NIL 
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 NIL 
 (((-98) (-142)) (T -98)) 
 NIL 
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-NIL 
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-NIL 
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+(((-194) (-10 -7 (-15 -1555 ((-661 (-1192 (-558))) (-558))) (-15 -3202 ((-1192 (-558)) (-558))) (-15 -1556 ((-417 (-1192 (-558))) (-558))))) (T -194)) 
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+(-10 -7 (-15 -1555 ((-661 (-1192 (-558))) (-558))) (-15 -3202 ((-1192 (-558)) (-558))) (-15 -1556 ((-417 (-1192 (-558))) (-558)))) 
+((-1751 (((-1176 (-229)) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 133 T ELT)) (-1772 (((-661 (-1180)) (-1176 (-229))) NIL T ELT)) (-1557 (((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 110 T ELT)) (-1749 (((-661 (-229)) (-326 (-229)) (-1198) (-1110 (-855 (-229)))) NIL T ELT)) (-1771 (((-661 (-1180)) (-661 (-229))) NIL T ELT)) (-1773 (((-229) (-1110 (-855 (-229)))) 31 T ELT)) (-1774 (((-229) (-1110 (-855 (-229)))) 32 T ELT)) (-1559 (((-391) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 127 T ELT)) (-1558 (((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 67 T ELT)) (-1769 (((-1180) (-229)) NIL T ELT)) (-2970 (((-1180) (-661 (-1180))) 27 T ELT)) (-1560 (((-1056) (-1198) (-1198) (-1056)) 13 T ELT))) 
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+((-1560 (*1 *2 *3 *3 *2) (-12 (-5 *2 (-1056)) (-5 *3 (-1198)) (-5 *1 (-195)))) (-2970 (*1 *2 *3) (-12 (-5 *3 (-661 (-1180))) (-5 *2 (-1180)) (-5 *1 (-195)))) (-1772 (*1 *2 *3) (-12 (-5 *3 (-1176 (-229))) (-5 *2 (-661 (-1180))) (-5 *1 (-195)))) (-1771 (*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-661 (-1180))) (-5 *1 (-195)))) (-1769 (*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1180)) (-5 *1 (-195)))) (-1751 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-1176 (-229))) (-5 *1 (-195)))) (-1749 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1198)) (-5 *5 (-1110 (-855 (-229)))) (-5 *2 (-661 (-229))) (-5 *1 (-195)))) (-1559 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-391)) (-5 *1 (-195)))) (-1774 (*1 *2 *3) (-12 (-5 *3 (-1110 (-855 (-229)))) (-5 *2 (-229)) (-5 *1 (-195)))) (-1773 (*1 *2 *3) (-12 (-5 *3 (-1110 (-855 (-229)))) (-5 *2 (-229)) (-5 *1 (-195)))) (-1558 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (-5 *1 (-195)))) (-1557 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))) (-5 *1 (-195))))) 
+(-10 -7 (-15 -1557 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1558 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1773 ((-229) (-1110 (-855 (-229))))) (-15 -1774 ((-229) (-1110 (-855 (-229))))) (-15 -1559 ((-391) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1749 ((-661 (-229)) (-326 (-229)) (-1198) (-1110 (-855 (-229))))) (-15 -1751 ((-1176 (-229)) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -1769 ((-1180) (-229))) (-15 -1771 ((-661 (-1180)) (-661 (-229)))) (-15 -1772 ((-661 (-1180)) (-1176 (-229)))) (-15 -2970 ((-1180) (-661 (-1180)))) (-15 -1560 ((-1056) (-1198) (-1198) (-1056)))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-2859 (((-1056) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) 61 T ELT) (((-1056) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) NIL T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 33 T ELT) (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3660 (((-1180) $) NIL T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) NIL T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) NIL T ELT))) 
 (((-196) (-807)) (T -196)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 66 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-2859 (((-1056) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) 66 T ELT) (((-1056) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) NIL T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3660 (((-1180) $) NIL T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) NIL T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) NIL T ELT))) 
 (((-197) (-807)) (T -197)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 80 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 46 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-2859 (((-1056) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) 80 T ELT) (((-1056) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) NIL T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 46 T ELT) (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3660 (((-1180) $) NIL T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) NIL T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) NIL T ELT))) 
 (((-198) (-807)) (T -198)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 63 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-2859 (((-1056) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) 63 T ELT) (((-1056) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) NIL T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3660 (((-1180) $) NIL T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) NIL T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) NIL T ELT))) 
 (((-199) (-807)) (T -199)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 76 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-2859 (((-1056) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) 76 T ELT) (((-1056) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) NIL T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3660 (((-1180) $) NIL T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) NIL T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) NIL T ELT))) 
 (((-200) (-807)) (T -200)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 93 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-2859 (((-1056) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) 93 T ELT) (((-1056) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) NIL T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3660 (((-1180) $) NIL T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) NIL T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) NIL T ELT))) 
 (((-201) (-807)) (T -201)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 90 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 51 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-2859 (((-1056) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) 90 T ELT) (((-1056) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) NIL T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 51 T ELT) (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3660 (((-1180) $) NIL T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) NIL T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) NIL T ELT))) 
 (((-202) (-807)) (T -202)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 78 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-2859 (((-1056) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) 78 T ELT) (((-1056) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1056)) NIL T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180)) (|:| |extra| (-1056))) (-1084) (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3660 (((-1180) $) NIL T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) NIL T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) NIL T ELT))) 
 (((-203) (-807)) (T -203)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 76 T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 35 T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
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 (((-204) (-807)) (T -204)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 77 T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 42 T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
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 (((-205) (-807)) (T -205)) 
 NIL 
 (-807) 
-((-3044 (((-114) $ $) NIL T ELT)) (-2867 (((-1064) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) 105 T ELT) (((-1064) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1064)) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 86 T ELT) (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)) (|:| |extra| (-1064))) (-1092) (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
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 (((-206) (-807)) (T -206)) 
 NIL 
 (-807) 
-((-1569 (((-3 (-2 (|:| -2978 (-115)) (|:| |w| (-229))) "failed") (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 110 T ELT)) (-1571 (((-558) (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 59 T ELT)) (-1570 (((-3 (-661 (-229)) "failed") (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229))) (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 91 T ELT))) 
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 (((-209) (-822)) (T -209)) 
 NIL 
 (-822) 
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 (((-210) (-822)) (T -210)) 
 NIL 
 (-822) 
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 (((-211) (-822)) (T -211)) 
 NIL 
 (-822) 
-((-3044 (((-114) $ $) NIL T ELT)) (-3146 (((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188))) (-1092) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 48 T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) NIL T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-2888 (((-1064) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 87 T ELT)) (-3531 (((-114) $ $) NIL T ELT))) 
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 (((-212) (-822)) (T -212)) 
 NIL 
 (-822) 
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-NIL 
-(-920) 
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-NIL 
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+NIL 
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+(((-233 |#1|) (-142) (-1122)) (T -233)) 
 NIL 
 (-13 (-242 |t#1|)) 
-(((-34) . T) ((-107 |#1|) . T) ((-102) -4034 (|has| |#1| (-1130)) (|has| |#1| (-102))) ((-630 (-885)) -4034 (|has| |#1| (-1130)) (|has| |#1| (-630 (-885)))) ((-153 |#1|) . T) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-242 |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ((-501 |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ((-1130) |has| |#1| (-1130)) ((-1246) . T)) 
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-(((-234 |#1|) (-142) (-1078)) (T -234)) 
-NIL 
-(-13 (-1078) (-274 |t#1|) (-10 -7 (IF (|has| |t#1| (-240)) (-6 (-240)) |%noBranch|) (IF (|has| |t#1| (-925 (-1206))) (-6 (-925 (-1206))) |%noBranch|))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-633 (-558)) . T) ((-630 (-885)) . T) ((-236 $) -4034 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-240) |has| |#1| (-240)) ((-239) -4034 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-666 (-558)) . T) ((-666 $) . T) ((-668 $) . T) ((-746) . T) ((-919 $ #1=(-1206)) -4034 (|has| |#1| (-927 (-1206))) (|has| |#1| (-925 (-1206)))) ((-925 (-1206)) |has| |#1| (-925 (-1206))) ((-927 #1#) -4034 (|has| |#1| (-927 (-1206))) (|has| |#1| (-925 (-1206)))) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1246) . T)) 
-((-3147 ((|#2| $) 9 T ELT))) 
-(((-235 |#1| |#2|) (-10 -8 (-15 -3147 (|#2| |#1|))) (-236 |#2|) (-1246)) (T -235)) 
-NIL 
-(-10 -8 (-15 -3147 (|#2| |#1|))) 
-((-4265 ((|#1| $) 7 T ELT)) (-3147 ((|#1| $) 6 T ELT))) 
-(((-236 |#1|) (-142) (-1246)) (T -236)) 
-((-4265 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1246)))) (-3147 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1246))))) 
-(-13 (-1246) (-10 -8 (-15 -4265 (|t#1| $)) (-15 -3147 (|t#1| $)))) 
-(((-1246) . T)) 
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-(((-237 |#1|) (-142) (-1078)) (T -237)) 
+(((-34) . T) ((-107 |#1|) . T) ((-102) -3957 (|has| |#1| (-1122)) (|has| |#1| (-102))) ((-630 (-877)) -3957 (|has| |#1| (-1122)) (|has| |#1| (-630 (-877)))) ((-153 |#1|) . T) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-242 |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1122))) ((-501 |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1122))) ((-1122) |has| |#1| (-1122)) ((-1238) . T)) 
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+(((-234 |#1|) (-142) (-1070)) (T -234)) 
+NIL 
+(-13 (-1070) (-274 |t#1|) (-10 -7 (IF (|has| |t#1| (-240)) (-6 (-240)) |%noBranch|) (IF (|has| |t#1| (-917 (-1198))) (-6 (-917 (-1198))) |%noBranch|))) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-633 (-558)) . T) ((-630 (-877)) . T) ((-236 $) -3957 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-240) |has| |#1| (-240)) ((-239) -3957 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-666 (-558)) . T) ((-666 $) . T) ((-668 $) . T) ((-746) . T) ((-911 $ #1=(-1198)) -3957 (|has| |#1| (-919 (-1198))) (|has| |#1| (-917 (-1198)))) ((-917 (-1198)) |has| |#1| (-917 (-1198))) ((-919 #1#) -3957 (|has| |#1| (-919 (-1198))) (|has| |#1| (-917 (-1198)))) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1238) . T)) 
+((-3070 ((|#2| $) 9 T ELT))) 
+(((-235 |#1| |#2|) (-10 -8 (-15 -3070 (|#2| |#1|))) (-236 |#2|) (-1238)) (T -235)) 
+NIL 
+(-10 -8 (-15 -3070 (|#2| |#1|))) 
+((-4188 ((|#1| $) 7 T ELT)) (-3070 ((|#1| $) 6 T ELT))) 
+(((-236 |#1|) (-142) (-1238)) (T -236)) 
+((-4188 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1238)))) (-3070 (*1 *2 *1) (-12 (-4 *1 (-236 *2)) (-4 *2 (-1238))))) 
+(-13 (-1238) (-10 -8 (-15 -4188 (|t#1| $)) (-15 -3070 (|t#1| $)))) 
+(((-1238) . T)) 
+((-2967 (((-114) $ $) 7 T ELT)) (-3606 (((-114) $) 21 T ELT)) (-1426 (((-3 $ "failed") $ $) 25 T ELT)) (-4154 (($) 22 T CONST)) (-3660 (((-1180) $) 11 T ELT)) (-3661 (((-1141) $) 12 T ELT)) (-4188 (($ $ (-791)) 42 T ELT) (($ $) 40 T ELT)) (-4376 (((-877) $) 13 T ELT)) (-1378 (((-114) $ $) 6 T ELT)) (-3059 (($) 23 T CONST)) (-3070 (($ $ (-791)) 43 T ELT) (($ $) 41 T ELT)) (-3454 (((-114) $ $) 8 T ELT)) (-4267 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-4269 (($ $ $) 18 T ELT)) (* (($ (-938) $) 17 T ELT) (($ (-791) $) 20 T ELT) (($ (-558) $) 29 T ELT) (($ |#1| $) 32 T ELT) (($ $ |#1|) 36 T ELT))) 
+(((-237 |#1|) (-142) (-1070)) (T -237)) 
 NIL 
 (-13 (-111 |t#1| |t#1|) (-239) (-10 -7 (IF (|has| |t#1| (-175)) (-6 (-737 |t#1|)) |%noBranch|))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-630 (-885)) . T) ((-236 $) . T) ((-239) . T) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-668 |#1|) . T) ((-660 |#1|) |has| |#1| (-175)) ((-737 |#1|) |has| |#1| (-175)) ((-1080 |#1|) . T) ((-1085 |#1|) . T) ((-1130) . T) ((-1246) . T)) 
-((-4265 (($ $) NIL T ELT) (($ $ (-791)) 9 T ELT)) (-3147 (($ $) NIL T ELT) (($ $ (-791)) 11 T ELT))) 
-(((-238 |#1|) (-10 -8 (-15 -3147 (|#1| |#1| (-791))) (-15 -4265 (|#1| |#1| (-791))) (-15 -3147 (|#1| |#1|)) (-15 -4265 (|#1| |#1|))) (-239)) (T -238)) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-630 (-877)) . T) ((-236 $) . T) ((-239) . T) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-668 |#1|) . T) ((-660 |#1|) |has| |#1| (-175)) ((-737 |#1|) |has| |#1| (-175)) ((-1072 |#1|) . T) ((-1077 |#1|) . T) ((-1122) . T) ((-1238) . T)) 
+((-4188 (($ $) NIL T ELT) (($ $ (-791)) 9 T ELT)) (-3070 (($ $) NIL T ELT) (($ $ (-791)) 11 T ELT))) 
+(((-238 |#1|) (-10 -8 (-15 -3070 (|#1| |#1| (-791))) (-15 -4188 (|#1| |#1| (-791))) (-15 -3070 (|#1| |#1|)) (-15 -4188 (|#1| |#1|))) (-239)) (T -238)) 
 NIL 
-(-10 -8 (-15 -3147 (|#1| |#1| (-791))) (-15 -4265 (|#1| |#1| (-791))) (-15 -3147 (|#1| |#1|)) (-15 -4265 (|#1| |#1|))) 
-((-4265 (($ $) 7 T ELT) (($ $ (-791)) 10 T ELT)) (-3147 (($ $) 6 T ELT) (($ $ (-791)) 9 T ELT))) 
+(-10 -8 (-15 -3070 (|#1| |#1| (-791))) (-15 -4188 (|#1| |#1| (-791))) (-15 -3070 (|#1| |#1|)) (-15 -4188 (|#1| |#1|))) 
+((-4188 (($ $) 7 T ELT) (($ $ (-791)) 10 T ELT)) (-3070 (($ $) 6 T ELT) (($ $ (-791)) 9 T ELT))) 
 (((-239) (-142)) (T -239)) 
-((-4265 (*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-791)))) (-3147 (*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-791))))) 
-(-13 (-236 $) (-10 -8 (-15 -4265 ($ $ (-791))) (-15 -3147 ($ $ (-791))))) 
-(((-236 $) . T) ((-1246) . T)) 
-((-3044 (((-114) $ $) 7 T ELT)) (-3683 (((-114) $) 21 T ELT)) (-1434 (((-3 $ "failed") $ $) 25 T ELT)) (-4231 (($) 22 T CONST)) (-3964 (((-3 $ "failed") $) 42 T ELT)) (-2649 (((-114) $) 40 T ELT)) (-3737 (((-1188) $) 11 T ELT)) (-3738 (((-1149) $) 12 T ELT)) (-4265 (($ $ (-791)) 47 T ELT) (($ $) 45 T ELT)) (-4453 (((-885) $) 13 T ELT) (($ (-558)) 38 T ELT)) (-3605 (((-791)) 37 T CONST)) (-1386 (((-114) $ $) 6 T ELT)) (-3136 (($) 23 T CONST)) (-3142 (($) 39 T CONST)) (-3147 (($ $ (-791)) 48 T ELT) (($ $) 46 T ELT)) (-3531 (((-114) $ $) 8 T ELT)) (-4344 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-4346 (($ $ $) 18 T ELT)) (** (($ $ (-946)) 33 T ELT) (($ $ (-791)) 41 T ELT)) (* (($ (-946) $) 17 T ELT) (($ (-791) $) 20 T ELT) (($ (-558) $) 29 T ELT) (($ $ $) 32 T ELT))) 
+((-4188 (*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-791)))) (-3070 (*1 *1 *1 *2) (-12 (-4 *1 (-239)) (-5 *2 (-791))))) 
+(-13 (-236 $) (-10 -8 (-15 -4188 ($ $ (-791))) (-15 -3070 ($ $ (-791))))) 
+(((-236 $) . T) ((-1238) . T)) 
+((-2967 (((-114) $ $) 7 T ELT)) (-3606 (((-114) $) 21 T ELT)) (-1426 (((-3 $ "failed") $ $) 25 T ELT)) (-4154 (($) 22 T CONST)) (-3887 (((-3 $ "failed") $) 42 T ELT)) (-2641 (((-114) $) 40 T ELT)) (-3660 (((-1180) $) 11 T ELT)) (-3661 (((-1141) $) 12 T ELT)) (-4188 (($ $ (-791)) 47 T ELT) (($ $) 45 T ELT)) (-4376 (((-877) $) 13 T ELT) (($ (-558)) 38 T ELT)) (-3528 (((-791)) 37 T CONST)) (-1378 (((-114) $ $) 6 T ELT)) (-3059 (($) 23 T CONST)) (-3065 (($) 39 T CONST)) (-3070 (($ $ (-791)) 48 T ELT) (($ $) 46 T ELT)) (-3454 (((-114) $ $) 8 T ELT)) (-4267 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-4269 (($ $ $) 18 T ELT)) (** (($ $ (-938)) 33 T ELT) (($ $ (-791)) 41 T ELT)) (* (($ (-938) $) 17 T ELT) (($ (-791) $) 20 T ELT) (($ (-558) $) 29 T ELT) (($ $ $) 32 T ELT))) 
 (((-240) (-142)) (T -240)) 
 NIL 
-(-13 (-1078) (-239)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-633 (-558)) . T) ((-630 (-885)) . T) ((-236 $) . T) ((-239) . T) ((-666 (-558)) . T) ((-666 $) . T) ((-668 $) . T) ((-746) . T) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1246) . T)) 
-((-1606 (($) 12 T ELT) (($ (-661 |#2|)) NIL T ELT)) (-3897 (($ $) 14 T ELT)) (-4027 (($ (-661 |#2|)) 10 T ELT)) (-4453 (((-885) $) 21 T ELT))) 
-(((-241 |#1| |#2|) (-10 -8 (-15 -4453 ((-885) |#1|)) (-15 -1606 (|#1| (-661 |#2|))) (-15 -1606 (|#1|)) (-15 -4027 (|#1| (-661 |#2|))) (-15 -3897 (|#1| |#1|))) (-242 |#2|) (-1130)) (T -241)) 
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-(((-246 |#1| |#2|) (-245 |#1| |#2|) (-791) (-1246)) (T -246)) 
+(-13 (-1070) (-239)) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-633 (-558)) . T) ((-630 (-877)) . T) ((-236 $) . T) ((-239) . T) ((-666 (-558)) . T) ((-666 $) . T) ((-668 $) . T) ((-746) . T) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1238) . T)) 
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+NIL 
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+(((-21) -3957 (|has| |#2| (-1070)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-23) -3957 (|has| |#2| (-1070)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -3957 (|has| |#2| (-1070)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -3957 (|has| |#2| (-1122)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -3957 (|has| |#2| (-1070)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -3957 (|has| |#2| (-1070)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-633 #1=(-419 (-558))) -12 (|has| |#2| (-1059 (-419 (-558)))) (|has| |#2| (-1122))) ((-633 (-558)) -3957 (|has| |#2| (-1070)) (-12 (|has| |#2| (-1059 (-558))) (|has| |#2| (-1122)))) ((-633 |#2|) |has| |#2| (-1122)) ((-630 (-877)) -3957 (|has| |#2| (-1122)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-630 (-877))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-630 (-1288 |#2|)) . T) ((-236 $) -3957 (-12 (|has| |#2| (-239)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1070)))) ((-234 |#2|) |has| |#2| (-1070)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1070))) ((-239) -3957 (-12 (|has| |#2| (-239)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1070)))) ((-274 |#2|) |has| |#2| (-1070)) ((-298 #2=(-558) |#2|) . T) ((-300 #2# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1070)) ((-424 |#2|) |has| |#2| (-1122)) ((-501 |#2|) . T) ((-616 #2# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ((-666 (-558)) -3957 (|has| |#2| (-1070)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-666 |#2|) -3957 (|has| |#2| (-1070)) (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-666 $) |has| |#2| (-1070)) ((-668 #3=(-558)) -12 (|has| |#2| (-658 (-558))) (|has| |#2| (-1070))) ((-668 |#2|) -3957 (|has| |#2| (-1070)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1070)) ((-660 |#2|) -3957 (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-658 #3#) -12 (|has| |#2| (-658 (-558))) (|has| |#2| (-1070))) ((-658 |#2|) |has| |#2| (-1070)) ((-737 |#2|) -3957 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-746) |has| |#2| (-1070)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-819) |has| |#2| (-815)) ((-861) -3957 (|has| |#2| (-861)) (|has| |#2| (-815))) ((-864) -3957 (|has| |#2| (-861)) (|has| |#2| (-815))) ((-911 $ #4=(-1198)) -3957 (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1198))) (|has| |#2| (-1070)))) ((-917 (-1198)) -12 (|has| |#2| (-917 (-1198))) (|has| |#2| (-1070))) ((-919 #4#) -3957 (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1198))) (|has| |#2| (-1070)))) ((-1059 #1#) -12 (|has| |#2| (-1059 (-419 (-558)))) (|has| |#2| (-1122))) ((-1059 (-558)) -12 (|has| |#2| (-1059 (-558))) (|has| |#2| (-1122))) ((-1059 |#2|) |has| |#2| (-1122)) ((-1072 |#2|) -3957 (|has| |#2| (-1070)) (|has| |#2| (-746)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1077 |#2|) -3957 (|has| |#2| (-1070)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1070) |has| |#2| (-1070)) ((-1078) |has| |#2| (-1070)) ((-1133) |has| |#2| (-1070)) ((-1122) -3957 (|has| |#2| (-1122)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-815)) (|has| |#2| (-746)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1238) . T) ((-1296 |#2|) |has| |#2| (-376))) 
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(-1070))) ELT) (((-2 (|:| -1783 (-709 (-558))) (|:| |vec| (-1288 (-558)))) (-709 $) (-1288 $)) NIL (-12 (|has| |#2| (-658 (-558))) (|has| |#2| (-1070))) ELT) (((-2 (|:| -1783 (-709 |#2|)) (|:| |vec| (-1288 |#2|))) (-709 $) (-1288 $)) NIL (|has| |#2| (-1070)) ELT) (((-709 |#2|) (-709 $)) NIL (|has| |#2| (-1070)) ELT)) (-3887 (((-3 $ "failed") $) 59 (|has| |#2| (-1070)) ELT)) (-3395 (($) NIL (|has| |#2| (-381)) ELT)) (-1719 ((|#2| $ (-558) |#2|) NIL (|has| $ (-6 -4426)) ELT)) (-3515 ((|#2| $ (-558)) 57 T ELT)) (-3604 (((-114) $) NIL (|has| |#2| (-815)) ELT)) (-3290 (((-661 |#2|) $) 14 (|has| $ (-6 -4425)) ELT)) (-2641 (((-114) $) NIL (|has| |#2| (-1070)) ELT)) (-2415 (((-558) $) 20 (|has| (-558) (-861)) ELT)) (-2930 (($ $ $) NIL (|has| |#2| (-861)) ELT)) (-3007 (((-661 |#2|) $) NIL (|has| $ (-6 -4425)) ELT)) (-3663 (((-114) |#2| $) NIL (-12 (|has| $ (-6 -4425)) (|has| |#2| (-1122))) ELT)) (-2416 (((-558) $) NIL (|has| (-558) (-861)) ELT)) (-3258 (($ $ $) NIL (|has| |#2| (-861)) ELT)) 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(|has| |#2| (-1122))) ELT) (($ $ (-305 |#2|)) NIL (-12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ELT) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ELT) (($ $ (-661 |#2|) (-661 |#2|)) NIL (-12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ELT)) (-1329 (((-114) $ $) NIL T ELT)) (-2417 (((-114) |#2| $) NIL (-12 (|has| $ (-6 -4425)) (|has| |#2| (-1122))) ELT)) (-2420 (((-661 |#2|) $) NIL T ELT)) (-3823 (((-114) $) NIL T ELT)) (-3993 (($) NIL T ELT)) (-4230 ((|#2| $ (-558) |#2|) NIL T ELT) ((|#2| $ (-558)) 21 T ELT)) (-4266 ((|#2| $ $) NIL (|has| |#2| (-1070)) ELT)) (-1600 (($ (-1288 |#2|)) 18 T ELT)) (-4341 (((-136)) NIL (|has| |#2| (-376)) ELT)) (-4188 (($ $ (-791)) NIL (-12 (|has| |#2| (-239)) (|has| |#2| (-1070))) ELT) (($ $) NIL (-12 (|has| |#2| (-239)) (|has| |#2| (-1070))) ELT) (($ $ (-661 (-1198)) (-661 (-791))) NIL (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) ELT) (($ $ (-1198) (-791)) NIL (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) ELT) (($ $ (-661 (-1198))) NIL (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) ELT) (($ $ (-1198)) NIL (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1070)) ELT) (($ $ (-1 |#2| |#2|) (-791)) NIL (|has| |#2| (-1070)) ELT)) (-2157 (((-791) (-1 (-114) |#2|) $) NIL (|has| $ (-6 -4425)) ELT) (((-791) |#2| $) NIL (-12 (|has| $ (-6 -4425)) (|has| |#2| (-1122))) ELT)) (-3820 (($ $) NIL T ELT)) (-4376 (((-1288 |#2|) $) 9 T ELT) (($ (-558)) NIL (-3957 (-12 (|has| |#2| (-1059 (-558))) (|has| |#2| (-1122))) (|has| |#2| (-1070))) ELT) (($ (-419 (-558))) NIL (-12 (|has| |#2| (-1059 (-419 (-558)))) (|has| |#2| (-1122))) ELT) (($ |#2|) 12 (|has| |#2| (-1122)) ELT) (((-877) $) NIL (|has| |#2| (-630 (-877))) ELT)) (-3528 (((-791)) NIL (|has| |#2| (-1070)) CONST)) (-1378 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-2159 (((-114) (-1 (-114) |#2|) $) NIL (|has| $ (-6 -4425)) ELT)) (-3059 (($) 37 (|has| |#2| (-23)) CONST)) (-3065 (($) 41 (|has| |#2| (-1070)) CONST)) (-3070 (($ $ (-791)) NIL (-12 (|has| |#2| (-239)) (|has| |#2| (-1070))) ELT) (($ $) NIL (-12 (|has| |#2| (-239)) (|has| |#2| (-1070))) ELT) (($ $ (-661 (-1198)) (-661 (-791))) NIL (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) ELT) (($ $ (-1198) (-791)) NIL (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) ELT) (($ $ (-661 (-1198))) NIL (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) ELT) (($ $ (-1198)) NIL (-12 (|has| |#2| (-919 (-1198))) (|has| |#2| (-1070))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1070)) ELT) (($ $ (-1 |#2| |#2|) (-791)) NIL (|has| |#2| (-1070)) ELT)) (-2965 (((-114) $ $) NIL (|has| |#2| (-861)) ELT)) (-2966 (((-114) $ $) NIL (|has| |#2| (-861)) ELT)) (-3454 (((-114) $ $) 28 (|has| |#2| (-102)) ELT)) (-3085 (((-114) $ $) NIL (|has| |#2| (-861)) ELT)) (-3086 (((-114) $ $) 67 (|has| |#2| (-861)) ELT)) (-4379 (($ $ |#2|) NIL (|has| |#2| (-376)) ELT)) (-4267 (($ $ $) NIL (|has| |#2| (-21)) ELT) (($ $) NIL (|has| |#2| (-21)) ELT)) (-4269 (($ $ $) 35 (|has| |#2| (-25)) ELT)) (** (($ $ (-791)) NIL (|has| |#2| (-1070)) ELT) (($ $ (-938)) NIL (|has| |#2| (-1070)) ELT)) (* (($ $ $) 47 (|has| |#2| (-1070)) ELT) (($ $ |#2|) 45 (|has| |#2| (-746)) ELT) (($ |#2| $) 46 (|has| |#2| (-746)) ELT) (($ (-558) $) NIL (|has| |#2| (-21)) ELT) (($ (-791) $) NIL (|has| |#2| (-23)) ELT) (($ (-938) $) NIL (|has| |#2| (-25)) ELT)) (-4387 (((-791) $) NIL (|has| $ (-6 -4425)) ELT))) 
+(((-246 |#1| |#2|) (-245 |#1| |#2|) (-791) (-1238)) (T -246)) 
 NIL 
 (-245 |#1| |#2|) 
-((-4348 (((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 21 T ELT)) (-4349 ((|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 23 T ELT)) (-4465 (((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)) 18 T ELT))) 
-(((-247 |#1| |#2| |#3|) (-10 -7 (-15 -4348 ((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -4349 (|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -4465 ((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)))) (-791) (-1246) (-1246)) (T -247)) 
-((-4465 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-246 *5 *6)) (-14 *5 (-791)) (-4 *6 (-1246)) (-4 *7 (-1246)) (-5 *2 (-246 *5 *7)) (-5 *1 (-247 *5 *6 *7)))) (-4349 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-246 *5 *6)) (-14 *5 (-791)) (-4 *6 (-1246)) (-4 *2 (-1246)) (-5 *1 (-247 *5 *6 *2)))) (-4348 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-246 *6 *7)) (-14 *6 (-791)) (-4 *7 (-1246)) (-4 *5 (-1246)) (-5 *2 (-246 *6 *5)) (-5 *1 (-247 *6 *7 *5))))) 
-(-10 -7 (-15 -4348 ((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -4349 (|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -4465 ((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)))) 
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-(((-248) (-10 -7 (-15 -3096 ((-661 (-1188)) (-1188))) (-15 -3096 ((-661 (-1188)) (-661 (-1188)))) (-15 -1609 ((-1188))) (-15 -1610 ((-1188) (-558) (-1188))) (-15 -4280 ((-1188) (-1188) (-558) (-1188))) (-15 -4280 ((-661 (-1188)) (-661 (-1188)) (-558) (-1188))) (-15 -1611 ((-1302) (-1188))) (-15 -1611 ((-1302) (-661 (-1188)))) (-15 -1612 ((-558) (-1188))) (-15 -1612 ((-558) (-661 (-1188)))))) (T -248)) 
-((-1612 (*1 *2 *3) (-12 (-5 *3 (-661 (-1188))) (-5 *2 (-558)) (-5 *1 (-248)))) (-1612 (*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-558)) (-5 *1 (-248)))) (-1611 (*1 *2 *3) (-12 (-5 *3 (-661 (-1188))) (-5 *2 (-1302)) (-5 *1 (-248)))) (-1611 (*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-248)))) (-4280 (*1 *2 *2 *3 *4) (-12 (-5 *2 (-661 (-1188))) (-5 *3 (-558)) (-5 *4 (-1188)) (-5 *1 (-248)))) (-4280 (*1 *2 *2 *3 *2) (-12 (-5 *2 (-1188)) (-5 *3 (-558)) (-5 *1 (-248)))) (-1610 (*1 *2 *3 *2) (-12 (-5 *2 (-1188)) (-5 *3 (-558)) (-5 *1 (-248)))) (-1609 (*1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-248)))) (-3096 (*1 *2 *2) (-12 (-5 *2 (-661 (-1188))) (-5 *1 (-248)))) (-3096 (*1 *2 *3) (-12 (-5 *2 (-661 (-1188))) (-5 *1 (-248)) (-5 *3 (-1188))))) 
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-NIL 
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 (((-250) (-142)) (T -250)) 
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 NIL 
 (-13 (-245 |#1| |#3|) (-668 |#2|)) 
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-NIL 
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-NIL 
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-NIL 
-(-860) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+(-13 (-1070) (-111 $ $) (-10 -7 (-6 -4418))) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 $ $) . T) ((-133) . T) ((-633 (-558)) . T) ((-630 (-877)) . T) ((-666 (-558)) . T) ((-666 $) . T) ((-668 $) . T) ((-746) . T) ((-1072 $) . T) ((-1077 $) . T) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1238) . T)) 
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+(-13 (-630 (-877)) (-10 -8 (-15 -3993 ($)) (-15 -1727 ((-661 (-1106)) $)) (-15 -1726 ((-711 (-1124)) (-518) (-518) $)) (-15 -1725 ($ (-518) (-518) (-1124) $)) (-15 -1724 ((-661 (-984)) (-518) $)) (-15 -1723 ($ (-518) (-661 (-984)) $)) (-15 -1722 ($)) (-15 -1721 ($)) (-15 -1720 ($)))) 
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+((-1784 (((-661 |#1|) (-661 |#1|)) 10 T ELT))) 
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+(-10 -7 (-15 -4388 ((-709 |#2|) (-1 |#2| |#1|) (-709 |#1|)))) 
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+NIL 
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-NIL 
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+NIL 
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 (((-526 |#1| |#1|) . T)) 
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-NIL 
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 NIL 
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-NIL 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
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-(((-34) . T) ((-102) -4034 (|has| |#1| (-1130)) (|has| |#1| (-869)) (|has| |#1| (-102))) ((-630 (-885)) -4034 (|has| |#1| (-1130)) (|has| |#1| (-869)) (|has| |#1| (-630 (-885)))) ((-153 |#1|) . T) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-298 #1=(-558) |#1|) . T) ((-298 (-1263 (-558)) $) . T) ((-300 #1# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ((-501 |#1|) . T) ((-616 #1# |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1130))) ((-671 |#1|) . T) ((-869) |has| |#1| (-869)) ((-872) |has| |#1| (-869)) ((-1130) -4034 (|has| |#1| (-1130)) (|has| |#1| (-869))) ((-1246) . T)) 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#2| |#2|) . T) ((-133) . T) ((-630 (-885)) . T) ((-666 (-558)) . T) ((-666 |#2|) . T) ((-668 |#2|) . T) ((-652 |#2|) . T) ((-660 |#2|) . T) ((-737 |#2|) . T) ((-1080 |#2|) . T) ((-1085 |#2|) . T) ((-1130) . T) ((-1246) . T)) 
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-NIL 
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+NIL 
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+NIL 
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+(((-34) . T) ((-102) -3957 (|has| |#1| (-1122)) (|has| |#1| (-861)) (|has| |#1| (-102))) ((-630 (-877)) -3957 (|has| |#1| (-1122)) (|has| |#1| (-861)) (|has| |#1| (-630 (-877)))) ((-153 |#1|) . T) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-298 #1=(-558) |#1|) . T) ((-298 (-1255 (-558)) $) . T) ((-300 #1# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1122))) ((-501 |#1|) . T) ((-616 #1# |#1|) . T) ((-526 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1122))) ((-671 |#1|) . T) ((-861) |has| |#1| (-861)) ((-864) |has| |#1| (-861)) ((-1122) -3957 (|has| |#1| (-1122)) (|has| |#1| (-861))) ((-1238) . T)) 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 |#2| |#2|) . T) ((-133) . T) ((-630 (-877)) . T) ((-666 (-558)) . T) ((-666 |#2|) . T) ((-668 |#2|) . T) ((-652 |#2|) . T) ((-660 |#2|) . T) ((-737 |#2|) . T) ((-1072 |#2|) . T) ((-1077 |#2|) . T) ((-1122) . T) ((-1238) . T)) 
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+NIL 
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+(((-390 |#1|) (-142) (-1070)) (T -390)) 
 NIL 
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-NIL 
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+NIL 
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-NIL 
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+((-2129 (((-3 |#5| "failed") |#5| |#2| (-1 |#2|)) 39 T ELT))) 
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+((-4402 (*1 *1 *2) (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-1070)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-475 *3 *4 *5 *6))))) 
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+NIL 
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-NIL 
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+NIL 
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 NIL 
 (-349 |#1| |#2| |#3| |#4|) 
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 NIL 
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 NIL 
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 NIL 
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ELT) (($ (-419 (-558)) $) NIL T ELT) (($ $ (-593 |#1|)) NIL T ELT) (($ (-593 |#1|) $) NIL T ELT))) 
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 NIL 
 (-341 (-593 |#1|)) 
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 NIL 
 (-57 |#1| |#4| |#5|) 
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 NIL 
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 NIL 
 (-706 |#1| (-614 |#1| |#3|) (-614 |#1| |#2|)) 
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-NIL 
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+NIL 
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 (((-539) (-142)) (T -539)) 
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 (((-176) . T)) 
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 NIL 
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+((-2286 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| -1638 (-3 (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated"))))) (-5 *1 (-572)))) (-2420 (*1 *2 *1) (-12 (-5 *2 (-661 (-2 (|:| -4290 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2286 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6#))) (|:| -1638 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) (-5 *1 (-572)))) (-2285 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6#))) (|:| -1638 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))) (-5 *1 (-572)))) (-4037 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -4290 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2286 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6#))) (|:| -1638 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) (-5 *1 (-572)))) (-2284 (*1 *1 *2) (-12 (-5 *2 (-661 (-2 (|:| -4290 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2286 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6#))) (|:| -1638 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) (-5 *1 (-572)))) (-2884 (*1 *2 *1) (-12 (-5 *2 (-661 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-5 *1 (-572)))) (-2283 (*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-572)))) (-2282 (*1 *1) (-5 *1 (-572)))) 
+(-10 -8 (-15 -2282 ($)) (-15 -2283 ((-1294))) (-15 -2884 ((-661 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) $)) (-15 -2284 ($ (-661 (-2 (|:| -4290 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2286 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| -1638 (-3 (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated"))))))))) (-15 -4037 ($ (-2 (|:| -4290 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2286 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6#))) (|:| -1638 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) (-15 -2285 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6#))) (|:| -1638 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2420 ((-661 (-2 (|:| -4290 (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| -2286 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6#))) (|:| -1638 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $)) (-15 -2286 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (-3 (|:| |str| (-1176 (-229))) (|:| |notEvaluated| #6#))) (|:| -1638 (-3 (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229))) (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) 
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 NIL 
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-NIL 
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 NIL 
 (-678 |#1|) 
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 (((-675 |#1|) (-678 |#1|) (-240)) (T -675)) 
 NIL 
 (-678 |#1|) 
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 NIL 
 (-13 (-678 |#1|) (-298 |#2| |#2|)) 
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-NIL 
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-NIL 
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+NIL 
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-NIL 
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-NIL 
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+NIL 
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 (((-737 |#1|) (-142) (-175)) (T -737)) 
 NIL 
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-NIL 
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+NIL 
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-NIL 
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+NIL 
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-NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 #1=(-419 (-558))) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -3957 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-633 #1#) -3957 (|has| |#1| (-1059 (-419 (-558)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-633 $) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-630 (-877)) . T) ((-175) . T) ((-631 |#2|) . T) ((-236 $) -3957 (|has| |#1| (-363)) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-234 |#1|) |has| |#1| (-376)) ((-240) -3957 (|has| |#1| (-363)) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-239) -3957 (|has| |#1| (-363)) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (-12 (|has| |#1| (-240)) (|has| |#1| (-376)))) ((-274 |#1|) |has| |#1| (-376)) ((-250) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-302) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-319) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-376) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-414) |has| |#1| (-363)) ((-381) -3957 (|has| |#1| (-363)) (|has| |#1| (-381))) ((-363) |has| |#1| (-363)) ((-383 |#1| |#2|) . T) ((-422 |#1| |#2|) . T) ((-390 |#1|) . T) ((-424 |#1|) . T) ((-464) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-569) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-666 #1#) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #1#) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 #2=(-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #1#) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-660 |#1|) . T) ((-660 $) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-658 #2#) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 #1#) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-737 |#1|) . T) ((-737 $) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-746) . T) ((-911 $ #3=(-1198)) -3957 (-12 (|has| |#1| (-376)) (|has| |#1| (-919 (-1198)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-917 (-1198))))) ((-917 (-1198)) -12 (|has| |#1| (-376)) (|has| |#1| (-917 (-1198)))) ((-919 #3#) -3957 (-12 (|has| |#1| (-376)) (|has| |#1| (-919 (-1198)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-917 (-1198))))) ((-940) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1059 (-419 (-558))) |has| |#1| (-1059 (-419 (-558)))) ((-1059 (-558)) |has| |#1| (-1059 (-558))) ((-1059 |#1|) . T) ((-1072 #1#) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1072 |#1|) . T) ((-1072 $) . T) ((-1077 #1#) -3957 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1077 |#1|) . T) ((-1077 $) . T) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1173) |has| |#1| (-363)) ((-1238) . T) ((-1243) -3957 (|has| |#1| (-363)) (|has| |#1| (-376)))) 
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+NIL 
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-NIL 
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-NIL 
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+NIL 
+(-10 -8 (-15 -2823 (|#1| |#1| |#1|)) (-15 -2824 (|#1| |#1| |#1|)) (-15 -2825 (|#1| |#1| |#1| |#1|))) 
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 (((-781) (-142)) (T -781)) 
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-(-13 (-21) (-740) (-10 -8 (-15 -2833 ($ $ $ $)) (-15 -2832 ($ $ $)) (-15 -2831 ($ $ $)))) 
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-((-4453 (((-885) $) NIL T ELT) (($ (-558)) 10 T ELT))) 
-(((-782 |#1|) (-10 -8 (-15 -4453 (|#1| (-558))) (-15 -4453 ((-885) |#1|))) (-783)) (T -782)) 
-NIL 
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+(((-782 |#1|) (-10 -8 (-15 -4376 (|#1| (-558))) (-15 -4376 ((-877) |#1|))) (-783)) (T -782)) 
+NIL 
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 (((-783) (-142)) (T -783)) 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-102) . T) ((-111 |#1| |#1|) . T) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #1=(-419 (-558))) |has| |#1| (-1059 (-419 (-558)))) ((-633 (-558)) . T) ((-633 |#1|) . T) ((-630 (-877)) . T) ((-631 (-547)) |has| |#1| (-631 (-547))) ((-298 |#1| $) |has| |#1| (-298 |#1| |#1|)) ((-321 |#1|) |has| |#1| (-321 |#1|)) ((-381) |has| |#1| (-381)) ((-351 |#1|) . T) ((-424 |#1|) . T) ((-526 (-1198) |#1|) |has| |#1| (-526 (-1198) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-660 |#1|) . T) ((-737 |#1|) . T) ((-746) . T) ((-861) |has| |#1| (-861)) ((-864) |has| |#1| (-861)) ((-1059 #1#) |has| |#1| (-1059 (-419 (-558)))) ((-1059 (-558)) |has| |#1| (-1059 (-558))) ((-1059 |#1|) . T) ((-1072 |#1|) . T) ((-1077 |#1|) . T) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1238) . T)) 
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 (((-819) (-142)) (T -819)) 
 NIL 
 (-13 (-814) (-133)) 
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-((-4465 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-175)) (-4 *6 (-175)) (-4 *2 (-818 *6)) (-5 *1 (-821 *4 *5 *2 *6)) (-4 *4 (-818 *5))))) 
-(-10 -7 (-15 -4465 (|#3| (-1 |#4| |#2|) |#1|))) 
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+(((-23) . T) ((-25) . T) ((-102) . T) ((-133) . T) ((-630 (-877)) . T) ((-814) . T) ((-816) . T) ((-861) . T) ((-864) . T) ((-1122) . T) ((-1238) . T)) 
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+(((-820 |#1|) (-13 (-818 |#1|) (-424 (-1017 |#1|)) (-10 -8 (-15 -2879 ($ (-1017 |#1|) (-1017 |#1|))))) (-175)) (T -820)) 
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+((-4388 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-175)) (-4 *6 (-175)) (-4 *2 (-818 *6)) (-5 *1 (-821 *4 *5 *2 *6)) (-4 *4 (-818 *5))))) 
+(-10 -7 (-15 -4388 (|#3| (-1 |#4| |#2|) |#1|))) 
+((-2967 (((-114) $ $) 7 T ELT)) (-3069 (((-2 (|:| -3069 (-391)) (|:| |explanations| (-1180))) (-1084) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 18 T ELT)) (-3660 (((-1180) $) 11 T ELT)) (-3661 (((-1141) $) 12 T ELT)) (-4376 (((-877) $) 13 T ELT)) (-1378 (((-114) $ $) 6 T ELT)) (-2880 (((-1056) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 17 T ELT)) (-3454 (((-114) $ $) 8 T ELT))) 
 (((-822) (-142)) (T -822)) 
-((-3146 (*1 *2 *3 *4) (-12 (-4 *1 (-822)) (-5 *3 (-1092)) (-5 *4 (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-2 (|:| -3146 (-391)) (|:| |explanations| (-1188)))))) (-2888 (*1 *2 *3) (-12 (-4 *1 (-822)) (-5 *3 (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 (-1064))))) 
-(-13 (-1130) (-10 -7 (-15 -3146 ((-2 (|:| -3146 (-391)) (|:| |explanations| (-1188))) (-1092) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))) (-15 -2888 ((-1064) (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229))) (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229))) (|:| |abserr| (-229)) (|:| |relerr| (-229))))))) 
-(((-102) . T) ((-630 (-885)) . T) ((-1130) . T) ((-1246) . T)) 
-((-2889 (((-2 (|:| |particular| |#2|) (|:| -2230 (-661 |#2|))) |#3| |#2| (-1206)) 19 T ELT))) 
-(((-823 |#1| |#2| |#3|) (-10 -7 (-15 -2889 ((-2 (|:| |particular| |#2|) (|:| -2230 (-661 |#2|))) |#3| |#2| (-1206)))) (-13 (-319) (-1067 (-558)) (-658 (-558)) (-149)) (-13 (-29 |#1|) (-1232) (-987)) (-678 |#2|)) (T -823)) 
-((-2889 (*1 *2 *3 *4 *5) (-12 (-5 *5 (-1206)) (-4 *6 (-13 (-319) (-1067 (-558)) (-658 (-558)) (-149))) (-4 *4 (-13 (-29 *6) (-1232) (-987))) (-5 *2 (-2 (|:| |particular| *4) (|:| -2230 (-661 *4)))) (-5 *1 (-823 *6 *4 *3)) (-4 *3 (-678 *4))))) 
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 NIL 
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 NIL 
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 NIL 
 (-277 |#1|) 
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 (((-842) (-142)) (T -842)) 
 NIL 
-(-13 (-569) (-868)) 
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-NIL 
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-(((-879) (-142)) (T -879)) 
-NIL 
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-(((-102) . T) ((-630 (-885)) . T) ((-869) . T) ((-872) . T) ((-1141) . T) ((-1130) . T) ((-1246) . T)) 
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-NIL 
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+NIL 
+(-13 (-812) (-1070) (-746)) 
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+(((-861) (-142)) (T -861)) 
+NIL 
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+NIL 
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+((-2930 (($ $ $) 16 T ELT)) (-3258 (($ $ $) 15 T ELT)) (-1378 (((-114) $ $) 17 T ELT)) (-2965 (((-114) $ $) 12 T ELT)) (-2966 (((-114) $ $) 9 T ELT)) (-3454 (((-114) $ $) 14 T ELT)) (-3085 (((-114) $ $) 11 T ELT))) 
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+NIL 
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+(((-102) . T) ((-1238) . T)) 
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+NIL 
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 NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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-NIL 
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-NIL 
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 NIL 
 (-13 (-93)) 
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-NIL 
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+NIL 
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 NIL 
 (-277 |#1|) 
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-NIL 
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 NIL 
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-NIL 
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-(((-1129 |#1|) (-10 -8 (-15 -3737 ((-1188) |#1|)) (-15 -3738 ((-1149) |#1|))) (-1130)) (T -1129)) 
-NIL 
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-(((-1132) (-1133 (-1188) (-1206) (-558) (-229) (-885))) (T -1132)) 
-NIL 
-(-1133 (-1188) (-1206) (-558) (-229) (-885)) 
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-(((-1133 |#1| |#2| |#3| |#4| |#5|) (-142) (-1130) (-1130) (-1130) (-1130) (-1130)) (T -1133)) 
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-(((-102) . T) ((-630 (-885)) . T) ((-635 (-661 $)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 |#4|) . T) ((-635 |#5|) . T) ((-298 (-558) $) . T) ((-298 (-661 (-558)) $) . T) ((-1130) . T) ((-1246) . T)) 
-((-3044 (((-114) $ $) NIL T ELT)) (-3755 (((-114) $) 45 T ELT)) (-3751 ((|#2| $) 48 T ELT)) (-3756 (((-114) $) 20 T ELT)) (-4040 ((|#1| $) 21 T ELT)) (-3758 (((-114) $) 42 T ELT)) (-3760 (((-114) $) 14 T ELT)) (-3757 (((-114) $) 44 T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3754 (((-114) $) 46 T ELT)) (-3750 ((|#3| $) 50 T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-3753 (((-114) $) 47 T ELT)) (-3749 ((|#4| $) 49 T ELT)) (-3748 ((|#5| $) 51 T ELT)) (-3761 (((-114) $ $) 41 T ELT)) (-4307 (($ $ (-558)) 62 T ELT) (($ $ (-661 (-558))) 64 T ELT)) (-3752 (((-661 $) $) 27 T ELT)) (-4479 (($ |#1|) 53 T ELT) (($ |#2|) 54 T ELT) (($ |#3|) 55 T ELT) (($ |#4|) 56 T ELT) (($ |#5|) 57 T ELT) (($ (-661 $)) 52 T ELT)) (-4453 (((-885) $) 28 T ELT)) (-3746 (($ $) 26 T ELT)) (-3747 (($ $) 58 T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3759 (((-114) $) 23 T ELT)) (-3531 (((-114) $ $) 40 T ELT)) (-4464 (((-558) $) 60 T ELT))) 
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-NIL 
-(-1133 |#1| |#2| |#3| |#4| |#5|) 
-((-3877 (((-1302) $) 22 T ELT)) (-3762 (($ (-1206) (-446) |#2|) 11 T ELT)) (-4453 (((-885) $) 16 T ELT))) 
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-((-3762 (*1 *1 *2 *3 *4) (-12 (-5 *2 (-1206)) (-5 *3 (-446)) (-4 *5 (-1130)) (-5 *1 (-1135 *5 *4)) (-4 *4 (-433 *5))))) 
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-NIL 
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 NIL 
 (-245 |#1| |#3|) 
-((-3805 (((-661 (-1265 |#2| |#1|)) (-1265 |#2| |#1|) (-1265 |#2| |#1|)) 50 T ELT)) (-3811 (((-558) (-1265 |#2| |#1|)) 96 (|has| |#1| (-464)) ELT)) (-3809 (((-558) (-1265 |#2| |#1|)) 79 T ELT)) (-3806 (((-661 (-1265 |#2| |#1|)) (-1265 |#2| |#1|) (-1265 |#2| |#1|)) 58 T ELT)) (-3810 (((-558) (-1265 |#2| |#1|) (-1265 |#2| |#1|)) 95 (|has| |#1| (-464)) ELT)) (-3807 (((-661 |#1|) (-1265 |#2| |#1|) (-1265 |#2| |#1|)) 61 T ELT)) (-3808 (((-558) (-1265 |#2| |#1|) (-1265 |#2| |#1|)) 78 T ELT))) 
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-((-3044 (((-114) $ $) NIL T ELT)) (-3813 (((-1211) $) 12 T ELT)) (-3812 (((-661 (-1211)) $) 14 T ELT)) (-3814 (($ (-661 (-1211)) (-1211)) 10 T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4453 (((-885) $) 29 T ELT)) (-1386 (((-114) $ $) NIL T ELT)) (-3531 (((-114) $ $) 17 T ELT))) 
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-(-13 (-1130) (-10 -8 (-15 -3814 ($ (-661 (-1211)) (-1211))) (-15 -3813 ((-1211) $)) (-15 -3812 ((-661 (-1211)) $)))) 
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-(((-1145) (-13 (-1112) (-10 -8 (-15 -3815 ($ (-518) (-1144))) (-15 -4047 ((-518) $)) (-15 -3814 ((-1144) $))))) (T -1145)) 
-((-3815 (*1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-1144)) (-5 *1 (-1145)))) (-4047 (*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-1145)))) (-3814 (*1 *2 *1) (-12 (-5 *2 (-1144)) (-5 *1 (-1145))))) 
-(-13 (-1112) (-10 -8 (-15 -3815 ($ (-518) (-1144))) (-15 -4047 ((-518) $)) (-15 -3814 ((-1144) $)))) 
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-(((-1146 |#1| |#2|) (-10 -7 (-15 -4130 ((-3 (-558) #1="failed") |#2|)) (-15 -4130 ((-3 (-558) #1#) |#2| (-1206) (-863 |#2|))) (-15 -4130 ((-3 (-558) #1#) |#2| (-1206) |#2| (-1188)))) (-13 (-569) (-1067 (-558)) (-658 (-558)) (-464)) (-13 (-27) (-1232) (-433 |#1|))) (T -1146)) 
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-(((-1148) (-10 -7 (-15 -4156 ((-326 (-558)) (-48))))) (T -1148)) 
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-NIL 
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-NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-34) . T) ((-38 |#2|) |has| |#2| (-6 (-4427 #1="*"))) ((-102) . T) ((-111 |#2| |#2|) . T) ((-133) . T) ((-633 #2=(-419 (-558))) |has| |#2| (-1059 (-419 (-558)))) ((-633 (-558)) . T) ((-633 |#2|) . T) ((-630 (-877)) . T) ((-236 $) -3957 (|has| |#2| (-239)) (|has| |#2| (-240))) ((-234 |#2|) . T) ((-240) |has| |#2| (-240)) ((-239) -3957 (|has| |#2| (-239)) (|has| |#2| (-240))) ((-274 |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ((-390 |#2|) . T) ((-424 |#2|) . T) ((-501 |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1122))) ((-666 (-558)) . T) ((-666 |#2|) . T) ((-666 $) . T) ((-668 #3=(-558)) |has| |#2| (-658 (-558))) ((-668 |#2|) . T) ((-668 $) . T) ((-660 |#2|) -3957 (|has| |#2| (-175)) (|has| |#2| (-6 (-4427 #1#)))) ((-658 #3#) |has| |#2| (-658 (-558))) ((-658 |#2|) . T) ((-737 |#2|) -3957 (|has| |#2| (-175)) (|has| |#2| (-6 (-4427 #1#)))) ((-746) . T) ((-911 $ #4=(-1198)) -3957 (|has| |#2| (-919 (-1198))) (|has| |#2| (-917 (-1198)))) ((-917 (-1198)) |has| |#2| (-917 (-1198))) ((-919 #4#) -3957 (|has| |#2| (-919 (-1198))) (|has| |#2| (-917 (-1198)))) ((-1074 |#1| |#1| |#2| |#3| |#4|) . T) ((-1059 #2#) |has| |#2| (-1059 (-419 (-558)))) ((-1059 (-558)) |has| |#2| (-1059 (-558))) ((-1059 |#2|) . T) ((-1072 |#2|) . T) ((-1077 |#2|) . T) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1238) . T)) 
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 NIL 
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-NIL 
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-NIL 
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-(((-1232) (-142)) (T -1232)) 
-((-4134 (*1 *1) (-4 *1 (-1232)))) 
-(-13 (-1235) (-95) (-505) (-35) (-296) (-10 -8 (-15 -4134 ($)))) 
-(((-35) . T) ((-95) . T) ((-296) . T) ((-505) . T) ((-1235) . T)) 
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-NIL 
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-((-4146 (($ $) 11 T ELT)) (-4145 (($ $) 10 T ELT)) (-4144 (($ $) 9 T ELT)) (-4143 (($ $) 8 T ELT)) (-4142 (($ $) 7 T ELT)) (-4141 (($ $) 6 T ELT))) 
-(((-1235) (-142)) (T -1235)) 
-((-4146 (*1 *1 *1) (-4 *1 (-1235))) (-4145 (*1 *1 *1) (-4 *1 (-1235))) (-4144 (*1 *1 *1) (-4 *1 (-1235))) (-4143 (*1 *1 *1) (-4 *1 (-1235))) (-4142 (*1 *1 *1) (-4 *1 (-1235))) (-4141 (*1 *1 *1) (-4 *1 (-1235)))) 
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-((-4153 (*1 *2 *3) (-12 (-4 *4 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *2 (-171 *3)) (-5 *1 (-1236 *4 *3)) (-4 *3 (-13 (-27) (-1232) (-433 *4))))) (-4152 (*1 *2 *3) (-12 (-4 *4 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *2 (-114)) (-5 *1 (-1236 *4 *3)) (-4 *3 (-13 (-27) (-1232) (-433 *4))))) (-4151 (*1 *2 *2) (-12 (-4 *3 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-1236 *3 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *3))))) (-4150 (*1 *2 *2) (-12 (-4 *3 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-1236 *3 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *3))))) (-4149 (*1 *2 *2) (-12 (-4 *3 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-1236 *3 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *3))))) (-4148 (*1 *2 *2 *3) (-12 (-5 *3 (-1206)) (-4 *4 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-1236 *4 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *4))))) (-4148 (*1 *2 *2) (-12 (-4 *3 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-1236 *3 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *3))))) (-4147 (*1 *2 *2 *3) (-12 (-5 *3 (-1206)) (-4 *4 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-1236 *4 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *4))))) (-4147 (*1 *2 *2) (-12 (-4 *3 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-1236 *3 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *3)))))) 
-(-10 -7 (-15 -4147 (|#2| |#2|)) (-15 -4147 (|#2| |#2| (-1206))) (-15 -4148 (|#2| |#2|)) (-15 -4148 (|#2| |#2| (-1206))) (-15 -4149 (|#2| |#2|)) (-15 -4150 (|#2| |#2|)) (-15 -4151 (|#2| |#2|)) (-15 -4152 ((-114) |#2|)) (-15 -4153 ((-171 |#2|) |#2|))) 
-((-4154 ((|#4| |#4| |#1|) 31 T ELT)) (-4155 ((|#4| |#4| |#1|) 32 T ELT))) 
-(((-1237 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -4154 (|#4| |#4| |#1|)) (-15 -4155 (|#4| |#4| |#1|))) (-569) (-385 |#1|) (-385 |#1|) (-706 |#1| |#2| |#3|)) (T -1237)) 
-((-4155 (*1 *2 *2 *3) (-12 (-4 *3 (-569)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3)) (-5 *1 (-1237 *3 *4 *5 *2)) (-4 *2 (-706 *3 *4 *5)))) (-4154 (*1 *2 *2 *3) (-12 (-4 *3 (-569)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3)) (-5 *1 (-1237 *3 *4 *5 *2)) (-4 *2 (-706 *3 *4 *5))))) 
-(-10 -7 (-15 -4154 (|#4| |#4| |#1|)) (-15 -4155 (|#4| |#4| |#1|))) 
-((-4173 ((|#2| |#2|) 148 T ELT)) (-4175 ((|#2| |#2|) 145 T ELT)) (-4172 ((|#2| |#2|) 136 T ELT)) (-4174 ((|#2| |#2|) 133 T ELT)) (-4171 ((|#2| |#2|) 141 T ELT)) (-4170 ((|#2| |#2|) 129 T ELT)) (-4159 ((|#2| |#2|) 44 T ELT)) (-4158 ((|#2| |#2|) 105 T ELT)) (-4156 ((|#2| |#2|) 88 T ELT)) (-4169 ((|#2| |#2|) 143 T ELT)) (-4168 ((|#2| |#2|) 131 T ELT)) (-4181 ((|#2| |#2|) 153 T ELT)) (-4179 ((|#2| |#2|) 151 T ELT)) (-4180 ((|#2| |#2|) 152 T ELT)) (-4178 ((|#2| |#2|) 150 T ELT)) (-4157 ((|#2| |#2|) 163 T ELT)) (-4182 ((|#2| |#2|) 30 (-12 (|has| |#2| (-631 (-913 |#1|))) (|has| |#2| (-909 |#1|)) (|has| |#1| (-631 (-913 |#1|))) (|has| |#1| (-909 |#1|))) ELT)) (-4160 ((|#2| |#2|) 89 T ELT)) (-4161 ((|#2| |#2|) 154 T ELT)) (-4470 ((|#2| |#2|) 155 T ELT)) (-4167 ((|#2| |#2|) 142 T ELT)) (-4166 ((|#2| |#2|) 130 T ELT)) (-4165 ((|#2| |#2|) 149 T ELT)) (-4177 ((|#2| |#2|) 147 T ELT)) (-4164 ((|#2| |#2|) 137 T ELT)) (-4176 ((|#2| |#2|) 135 T ELT)) (-4163 ((|#2| |#2|) 139 T ELT)) (-4162 ((|#2| |#2|) 127 T ELT))) 
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-NIL 
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T) ((-175) -4034 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-631 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1049))) ((-631 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1049))) ((-631 (-547)) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-547)))) ((-631 (-913 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-913 (-391))))) ((-631 (-913 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-913 (-558))))) ((-236 $) -4034 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -4034 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-239) -4034 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-419 (-558)))) ((-298 #1# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-558) (-1141)) ((-302) -4034 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-412 |#2|) |has| |#1| (-376)) ((-464) |has| |#1| (-376)) ((-505) |has| |#1| (-38 (-419 (-558)))) ((-526 (-1206) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-526 (-1206) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-569) -4034 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-666 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 |#2|) |has| |#1| (-376)) ((-666 $) . T) ((-668 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-668 #4=(-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-660 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-660 |#1|) |has| |#1| (-175)) ((-660 |#2|) |has| |#1| (-376)) ((-660 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-658 #4#) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-658 |#2|) |has| |#1| (-376)) ((-737 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-737 |#1|) |has| |#1| (-175)) ((-737 |#2|) |has| |#1| (-376)) ((-737 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-746) . T) ((-812) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-819) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-868) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-869) -4034 (-12 (|has| |#1| (-376)) (|has| |#2| (-869))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-872) -4034 (-12 (|has| |#1| (-376)) (|has| |#2| (-869))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-919 $ #5=(-1206)) -4034 (-12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1206)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-925 (-1206))))) ((-925 (-1206)) -4034 (-12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-925 (-1206))))) ((-927 #5#) -4034 (-12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1206)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-925 (-1206))))) ((-909 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-909 (-391)))) ((-909 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-909 (-558)))) ((-907 |#2|) |has| |#1| (-376)) ((-937) -12 (|has| |#1| (-376)) (|has| |#2| (-937))) ((-1002 |#1| #1# (-1111)) . T) ((-948) |has| |#1| (-376)) ((-1020 |#2|) |has| |#1| (-376)) ((-1031) |has| |#1| (-38 (-419 (-558)))) ((-1049) -12 (|has| |#1| (-376)) (|has| |#2| (-1049))) ((-1067 (-419 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-1067 (-558)))) ((-1067 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-1067 (-558)))) ((-1067 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-1067 (-1206)))) ((-1067 |#2|) . T) ((-1080 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1080 |#1|) . T) ((-1080 |#2|) |has| |#1| (-376)) ((-1080 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1085 #2#) -4034 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1085 |#1|) . T) ((-1085 |#2|) |has| |#1| (-376)) ((-1085 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1181) -12 (|has| |#1| (-376)) (|has| |#2| (-1181))) ((-1232) |has| |#1| (-38 (-419 (-558)))) ((-1235) |has| |#1| (-38 (-419 (-558)))) ((-1246) . T) ((-1251) |has| |#1| (-376)) ((-1258 |#1|) . T) ((-1275 |#1| #1#) . T)) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| #1=(-791)) . T) ((-25) . T) ((-38 #2=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-102) . T) ((-111 #2# #2#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #2#) -4034 (|has| |#1| (-1067 (-419 (-558)))) (|has| |#1| (-38 (-419 (-558))))) ((-633 (-558)) . T) ((-633 #3=(-1111)) . T) ((-633 |#1|) . T) ((-633 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-630 (-885)) . T) ((-175) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-631 (-547)) -12 (|has| |#1| (-631 (-547))) (|has| (-1111) (-631 (-547)))) ((-631 (-913 (-391))) -12 (|has| |#1| (-631 (-913 (-391)))) (|has| (-1111) (-631 (-913 (-391))))) ((-631 (-913 (-558))) -12 (|has| |#1| (-631 (-913 (-558)))) (|has| (-1111) (-631 (-913 (-558))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-419 $) (-419 $)) |has| |#1| (-569)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #1#) . T) ((-390 |#1|) . T) ((-424 |#1|) . T) ((-464) -4034 (|has| |#1| (-937)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-526 #3# |#1|) . T) ((-526 #3# $) . T) ((-526 $ $) . T) ((-569) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-666 #2#) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #2#) |has| |#1| (-38 (-419 (-558)))) ((-668 #4=(-558)) |has| |#1| (-658 (-558))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #2#) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-658 #4#) |has| |#1| (-658 (-558))) ((-658 |#1|) . T) ((-737 #2#) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376))) ((-746) . T) ((-919 $ #3#) . T) ((-919 $ #5=(-1206)) -4034 (|has| |#1| (-927 (-1206))) (|has| |#1| (-925 (-1206)))) ((-925 #3#) . T) ((-925 (-1206)) |has| |#1| (-925 (-1206))) ((-927 #3#) . T) ((-927 #5#) -4034 (|has| |#1| (-927 (-1206))) (|has| |#1| (-925 (-1206)))) ((-909 (-391)) -12 (|has| |#1| (-909 (-391))) (|has| (-1111) (-909 (-391)))) ((-909 (-558)) -12 (|has| |#1| (-909 (-558))) (|has| (-1111) (-909 (-558)))) ((-977 |#1| #1# #3#) . T) ((-937) |has| |#1| (-937)) ((-948) |has| |#1| (-376)) ((-1067 (-419 (-558))) |has| |#1| (-1067 (-419 (-558)))) ((-1067 (-558)) |has| |#1| (-1067 (-558))) ((-1067 #3#) . T) ((-1067 |#1|) . T) ((-1080 #2#) |has| |#1| (-38 (-419 (-558)))) ((-1080 |#1|) . T) ((-1080 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1085 #2#) |has| |#1| (-38 (-419 (-558)))) ((-1085 |#1|) . T) ((-1085 $) -4034 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-464)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1181) |has| |#1| (-1181)) ((-1246) . T) ((-1251) |has| |#1| (-937))) 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-47 |#1| #1=(-791)) . T) ((-25) . T) ((-38 #2=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-569)) ((-35) |has| |#1| (-38 (-419 (-558)))) ((-95) |has| |#1| (-38 (-419 (-558)))) ((-102) . T) ((-111 #2# #2#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4034 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #2#) |has| |#1| (-38 (-419 (-558)))) ((-633 (-558)) . T) ((-633 |#1|) |has| |#1| (-175)) ((-633 $) |has| |#1| (-569)) ((-630 (-885)) . T) ((-175) -4034 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-791) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-791) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-791) |#1|))) ((-296) |has| |#1| (-38 (-419 (-558)))) ((-298 #1# |#1|) . T) ((-298 $ $) |has| (-791) (-1141)) ((-302) |has| |#1| (-569)) ((-505) |has| |#1| (-38 (-419 (-558)))) ((-569) |has| |#1| (-569)) ((-666 #2#) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #2#) |has| |#1| (-38 (-419 (-558)))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #2#) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) |has| |#1| (-569)) ((-737 #2#) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) |has| |#1| (-569)) ((-746) . T) ((-919 $ #3=(-1206)) -12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-791) |#1|)))) ((-925 #3#) -12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-791) |#1|)))) ((-927 #3#) -12 (|has| |#1| (-925 (-1206))) (|has| |#1| (-15 * (|#1| (-791) |#1|)))) ((-1002 |#1| #1# (-1111)) . T) ((-1031) |has| |#1| (-38 (-419 (-558)))) ((-1080 #2#) |has| |#1| (-38 (-419 (-558)))) ((-1080 |#1|) . T) ((-1080 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1085 #2#) |has| |#1| (-38 (-419 (-558)))) ((-1085 |#1|) . T) ((-1085 $) -4034 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1078) . T) ((-1086) . T) ((-1141) . T) ((-1130) . T) ((-1232) |has| |#1| (-38 (-419 (-558)))) ((-1235) |has| |#1| (-38 (-419 (-558)))) ((-1246) . T) ((-1275 |#1| #1#) . T)) 
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-NIL 
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-NIL 
-(-13 (-10 -7 (-6 -2509))) 
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-NIL 
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-(((-1325 |#1|) (-10 -7 (-15 -4480 ((-114) (-1296 |#1|))) (-15 -4481 ((-3 (-1296 (-558)) "failed") (-1296 |#1|))) (-15 -4482 ((-3 (-1296 (-419 (-558))) "failed") (-1296 |#1|) |#1|))) (-13 (-1078) (-658 (-558)))) (T -1325)) 
-((-4482 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1296 *4)) (-4 *4 (-13 (-1078) (-658 (-558)))) (-5 *2 (-1296 (-419 (-558)))) (-5 *1 (-1325 *4)))) (-4481 (*1 *2 *3) (|partial| -12 (-5 *3 (-1296 *4)) (-4 *4 (-13 (-1078) (-658 (-558)))) (-5 *2 (-1296 (-558))) (-5 *1 (-1325 *4)))) (-4480 (*1 *2 *3) (-12 (-5 *3 (-1296 *4)) (-4 *4 (-13 (-1078) (-658 (-558)))) (-5 *2 (-114)) (-5 *1 (-1325 *4))))) 
-(-10 -7 (-15 -4480 ((-114) (-1296 |#1|))) (-15 -4481 ((-3 (-1296 (-558)) "failed") (-1296 |#1|))) (-15 -4482 ((-3 (-1296 (-419 (-558))) "failed") (-1296 |#1|) |#1|))) 
-((-3044 (((-114) $ $) NIL T ELT)) (-3683 (((-114) $) 12 T ELT)) (-1434 (((-3 $ "failed") $ $) NIL T ELT)) (-3615 (((-791)) 9 T ELT)) (-4231 (($) NIL T CONST)) (-3964 (((-3 $ "failed") $) 57 T ELT)) (-3472 (($) 46 T ELT)) (-2649 (((-114) $) 38 T ELT)) (-3942 (((-711 $) $) 36 T ELT)) (-2228 (((-946) $) 14 T ELT)) (-3737 (((-1188) $) NIL T ELT)) (-3943 (($) 26 T CONST)) (-2639 (($ (-946)) 47 T ELT)) (-3738 (((-1149) $) NIL T ELT)) (-4479 (((-558) $) 16 T ELT)) (-4453 (((-885) $) 21 T ELT) (($ (-558)) 18 T ELT)) (-3605 (((-791)) 10 T CONST)) (-1386 (((-114) $ $) 59 T ELT)) (-3136 (($) 23 T CONST)) (-3142 (($) 25 T CONST)) (-3531 (((-114) $ $) 31 T ELT)) (-4344 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-4346 (($ $ $) 29 T ELT)) (** (($ $ (-946)) NIL T ELT) (($ $ (-791)) 52 T ELT)) (* (($ (-946) $) NIL T ELT) (($ (-791) $) NIL T ELT) (($ (-558) $) 41 T ELT) (($ $ $) 40 T ELT))) 
-(((-1326 |#1|) (-13 (-175) (-381) (-631 (-558)) (-1181)) (-946)) (T -1326)) 
-NIL 
-(-13 (-175) (-381) (-631 (-558)) (-1181)) 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-((-3 3445342 3445347 3445352 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3445327 3445332 3445337 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3445312 3445317 3445322 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3445297 3445302 3445307 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1326 3444290 3445172 3445249 "ZMOD" 3445254 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1325 3443326 3443508 3443731 "ZLINDEP" 3444122 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1324 3432488 3434394 3436366 "ZDSOLVE" 3441456 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1323 3431722 3431875 3432064 "YSTREAM" 3432334 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1322 3431082 3431391 3431506 "YDIAGRAM" 3431629 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1321 3428530 3430383 3430587 "XRPOLY" 3430925 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1320 3424797 3426401 3426976 "XPR" 3428002 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1319 3422128 3423804 3423859 "XPOLYC" 3424147 NIL XPOLYC (NIL T T) -9 NIL 3424260 NIL) (-1318 3419532 3421468 3421672 "XPOLY" 3421968 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1317 3415480 3418049 3418437 "XPBWPOLY" 3419190 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1316 3410372 3411951 3412006 "XFALG" 3414178 NIL XFALG (NIL T T) -9 NIL 3414967 NIL) (-1315 3405650 3408348 3408390 "XF" 3409011 NIL XF (NIL T) -9 NIL 3409411 NIL) (-1314 3405247 3405359 3405528 "XF-" 3405533 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1313 3404362 3404484 3404689 "XEXPPKG" 3405139 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1312 3402103 3404212 3404308 "XDPOLY" 3404313 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1311 3400758 3401496 3401539 "XALG" 3401544 NIL XALG (NIL T) -9 NIL 3401655 NIL) (-1310 3393809 3398735 3399229 "WUTSET" 3400350 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1309 3391911 3392861 3393184 "WP" 3393620 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1308 3391459 3391733 3391803 "WHILEAST" 3391863 T WHILEAST (NIL) -8 NIL NIL NIL) (-1307 3390871 3391176 3391270 "WHEREAST" 3391387 T WHEREAST (NIL) -8 NIL NIL NIL) (-1306 3389745 3389955 3390250 "WFFINTBS" 3390668 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1305 3387613 3388076 3388538 "WEIER" 3389317 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1304 3386537 3387095 3387137 "VSPACE" 3387273 NIL VSPACE (NIL T) -9 NIL 3387347 NIL) (-1303 3386369 3386402 3386493 "VSPACE-" 3386498 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1302 3386166 3386220 3386288 "VOID" 3386323 T VOID (NIL) -8 NIL NIL NIL) (-1301 3382434 3383229 3383966 "VIEWDEF" 3385451 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1300 3371378 3373982 3376155 "VIEW3D" 3380283 T VIEW3D (NIL) -8 NIL NIL NIL) (-1299 3363395 3365289 3366868 "VIEW2D" 3369821 T VIEW2D (NIL) -8 NIL NIL NIL) (-1298 3361495 3361890 3362296 "VIEW" 3363011 T VIEW (NIL) -7 NIL NIL NIL) (-1297 3360048 3360331 3360649 "VECTOR2" 3361225 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1296 3355068 3359818 3359910 "VECTOR" 3359991 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1295 3348127 3352772 3352815 "VECTCAT" 3353810 NIL VECTCAT (NIL T) -9 NIL 3354397 NIL) (-1294 3347069 3347395 3347785 "VECTCAT-" 3347790 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1293 3346475 3346720 3346840 "VARIABLE" 3346984 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1292 3346408 3346413 3346443 "UTYPE" 3346448 T UTYPE (NIL) -9 NIL NIL NIL) (-1291 3345216 3345392 3345654 "UTSODETL" 3346234 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1290 3342608 3343116 3343640 "UTSODE" 3344757 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1289 3332618 3338541 3338584 "UTSCAT" 3339696 NIL UTSCAT (NIL T) -9 NIL 3340454 NIL) (-1288 3329744 3330688 3331677 "UTSCAT-" 3331682 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1287 3329365 3329414 3329547 "UTS2" 3329695 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1286 3320682 3327126 3327606 "UTS" 3328943 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1285 3314661 3317492 3317535 "URAGG" 3319605 NIL URAGG (NIL T) -9 NIL 3320328 NIL) (-1284 3311696 3312663 3313686 "URAGG-" 3313691 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1283 3307079 3310331 3310796 "UPXSSING" 3311360 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1282 3299510 3306983 3307055 "UPXSCONS" 3307060 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1281 3288270 3295712 3295774 "UPXSCCA" 3296348 NIL UPXSCCA (NIL T T) -9 NIL 3296581 NIL) (-1280 3287890 3287993 3288167 "UPXSCCA-" 3288172 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1279 3276550 3283717 3283760 "UPXSCAT" 3284408 NIL UPXSCAT (NIL T) -9 NIL 3285017 NIL) (-1278 3275974 3276059 3276238 "UPXS2" 3276465 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1277 3267470 3275356 3275620 "UPXS" 3275768 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1276 3266109 3266379 3266729 "UPSQFREE" 3267214 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1275 3258940 3262375 3262430 "UPSCAT" 3263510 NIL UPSCAT (NIL T T) -9 NIL 3264276 NIL) (-1274 3258096 3258351 3258678 "UPSCAT-" 3258683 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1273 3257717 3257766 3257899 "UPOLYC2" 3258047 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1272 3241893 3250844 3250887 "UPOLYC" 3252988 NIL UPOLYC (NIL T) -9 NIL 3254209 NIL) (-1271 3232798 3235685 3238813 "UPOLYC-" 3238818 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1270 3232119 3232244 3232408 "UPMP" 3232687 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1269 3231666 3231753 3231892 "UPDIVP" 3232032 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1268 3230204 3230483 3230799 "UPDECOMP" 3231415 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1267 3229417 3229547 3229733 "UPCDEN" 3230088 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1266 3228930 3229005 3229154 "UP2" 3229342 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1265 3219561 3228613 3228742 "UP" 3228849 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1264 3218766 3218903 3219108 "UNISEG2" 3219404 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1263 3217119 3217970 3218247 "UNISEG" 3218524 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1262 3216161 3216359 3216585 "UNIFACT" 3216935 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1261 3202908 3216065 3216137 "ULSCONS" 3216142 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1260 3182741 3195988 3196050 "ULSCCAT" 3196688 NIL ULSCCAT (NIL T T) -9 NIL 3196977 NIL) (-1259 3181773 3182060 3182436 "ULSCCAT-" 3182441 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1258 3170230 3177319 3177362 "ULSCAT" 3178225 NIL ULSCAT (NIL T) -9 NIL 3178956 NIL) (-1257 3169654 3169739 3169918 "ULS2" 3170145 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1256 3151501 3168966 3169208 "ULS" 3169470 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1255 3150420 3151120 3151234 "UINT8" 3151345 T UINT8 (NIL) -8 NIL NIL 3151437) (-1254 3149338 3150038 3150152 "UINT64" 3150263 T UINT64 (NIL) -8 NIL NIL 3150355) (-1253 3148256 3148956 3149070 "UINT32" 3149181 T UINT32 (NIL) -8 NIL NIL 3149273) (-1252 3147174 3147874 3147988 "UINT16" 3148099 T UINT16 (NIL) -8 NIL NIL 3148191) (-1251 3145253 3146420 3146450 "UFD" 3146662 T UFD (NIL) -9 NIL 3146776 NIL) (-1250 3145035 3145093 3145188 "UFD-" 3145193 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1249 3144093 3144300 3144516 "UDVO" 3144841 T UDVO (NIL) -7 NIL NIL NIL) (-1248 3141859 3142318 3142789 "UDPO" 3143657 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1247 3141571 3141814 3141845 "TYPEAST" 3141850 T TYPEAST (NIL) -8 NIL NIL NIL) (-1246 3141504 3141509 3141539 "TYPE" 3141544 T TYPE (NIL) -9 NIL NIL NIL) (-1245 3140457 3140677 3140917 "TWOFACT" 3141298 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1244 3139432 3139866 3140101 "TUPLE" 3140257 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1243 3137069 3137642 3138181 "TUBETOOL" 3138915 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1242 3135875 3136116 3136358 "TUBE" 3136862 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1241 3124124 3128632 3128729 "TSETCAT" 3133998 NIL TSETCAT (NIL T T T T) -9 NIL 3135530 NIL) (-1240 3118592 3120456 3122347 "TSETCAT-" 3122352 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1239 3112778 3117564 3117847 "TS" 3118344 NIL TS (NIL T) -8 NIL NIL NIL) (-1238 3107251 3108264 3109193 "TRMANIP" 3111914 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1237 3106680 3106755 3106918 "TRIMAT" 3107183 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1236 3104492 3104783 3105140 "TRIGMNIP" 3106429 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1235 3103976 3104125 3104155 "TRIGCAT" 3104368 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1234 3103621 3103724 3103865 "TRIGCAT-" 3103870 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1233 3100347 3102479 3102760 "TREE" 3103375 NIL TREE (NIL T) -8 NIL NIL NIL) (-1232 3099453 3100149 3100179 "TRANFUN" 3100214 T TRANFUN (NIL) -9 NIL 3100280 NIL) (-1231 3098672 3098923 3099203 "TRANFUN-" 3099208 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1230 3098470 3098508 3098569 "TOPSP" 3098633 T TOPSP (NIL) -7 NIL NIL NIL) (-1229 3097800 3097933 3098087 "TOOLSIGN" 3098351 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1228 3096314 3096977 3097216 "TEXTFILE" 3097583 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1227 3096089 3096126 3096198 "TEX1" 3096277 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1226 3093893 3094542 3094971 "TEX" 3095682 T TEX (NIL) -8 NIL NIL NIL) (-1225 3093529 3093604 3093694 "TEMUTL" 3093825 T TEMUTL (NIL) -7 NIL NIL NIL) (-1224 3091623 3091963 3092288 "TBCMPPK" 3093252 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1223 3083059 3089709 3089765 "TBAGG" 3090165 NIL TBAGG (NIL T T) -9 NIL 3090376 NIL) (-1222 3077943 3079617 3081371 "TBAGG-" 3081376 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1221 3077309 3077434 3077579 "TANEXP" 3077832 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1220 3076760 3077084 3077174 "TALGOP" 3077254 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1219 3076154 3076271 3076409 "TABLEAU" 3076657 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1218 3069284 3076011 3076104 "TABLE" 3076109 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1217 3063814 3065112 3066360 "TABLBUMP" 3068070 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1216 3063024 3063183 3063364 "SYSTEM" 3063655 T SYSTEM (NIL) -8 NIL NIL NIL) (-1215 3059429 3060182 3060965 "SYSSOLP" 3062275 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1214 3059191 3059384 3059415 "SYSPTR" 3059420 T SYSPTR (NIL) -8 NIL NIL NIL) (-1213 3058030 3058722 3058848 "SYSNNI" 3059034 NIL SYSNNI (NIL NIL) -8 NIL NIL 3059126) (-1212 3057237 3057792 3057871 "SYSINT" 3057931 NIL SYSINT (NIL NIL) -8 NIL NIL 3057976) (-1211 3053347 3054515 3055225 "SYNTAX" 3056549 T SYNTAX (NIL) -8 NIL NIL NIL) (-1210 3050427 3051107 3051739 "SYMTAB" 3052737 T SYMTAB (NIL) -8 NIL NIL NIL) (-1209 3045550 3046596 3047573 "SYMS" 3049472 T SYMS (NIL) -8 NIL NIL NIL) (-1208 3042468 3045006 3045239 "SYMPOLY" 3045357 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1207 3041973 3042060 3042183 "SYMFUNC" 3042380 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1206 3037916 3039299 3040105 "SYMBOL" 3041189 T SYMBOL (NIL) -8 NIL NIL NIL) (-1205 3031389 3033144 3034864 "SWITCH" 3036218 T SWITCH (NIL) -8 NIL NIL NIL) (-1204 3024150 3030345 3030639 "SUTS" 3031153 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3015646 3023532 3023796 "SUPXS" 3023944 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1202 3014793 3014932 3015149 "SUPFRACF" 3015514 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1201 3014408 3014473 3014586 "SUP2" 3014728 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1200 3004987 3014026 3014152 "SUP" 3014317 NIL SUP (NIL T) -8 NIL NIL NIL) (-1199 3003411 3003709 3004065 "SUMRF" 3004686 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1198 3002734 3002812 3003004 "SUMFS" 3003332 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1197 2984616 3002046 3002288 "SULS" 3002550 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1196 2984164 2984438 2984508 "SUCHTAST" 2984568 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1195 2983405 2983689 2983829 "SUCH" 2984072 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1194 2977044 2978311 2979270 "SUBSPACE" 2982493 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1193 2976464 2976564 2976728 "SUBRESP" 2976932 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1192 2970475 2971757 2972904 "STTFNC" 2975364 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1191 2963669 2965140 2966451 "STTF" 2969211 NIL STTF (NIL T) -7 NIL NIL NIL) (-1190 2954785 2956851 2958645 "STTAYLOR" 2961910 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1189 2947655 2954649 2954732 "STRTBL" 2954737 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1188 2942308 2947378 2947470 "STRING" 2947585 T STRING (NIL) -8 NIL NIL NIL) (-1187 2941812 2941895 2942039 "STREAM3" 2942225 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1186 2940776 2940977 2941212 "STREAM2" 2941625 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1185 2940458 2940516 2940609 "STREAM1" 2940718 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1184 2932574 2938077 2938688 "STREAM" 2939882 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1183 2931566 2931771 2932002 "STINPROD" 2932390 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1182 2930681 2931055 2931203 "STEPAST" 2931440 T STEPAST (NIL) -8 NIL NIL NIL) (-1181 2930177 2930422 2930452 "STEP" 2930546 T STEP (NIL) -9 NIL 2930617 NIL) (-1180 2923349 2930076 2930153 "STBL" 2930158 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1179 2917532 2922143 2922186 "STAGG" 2922618 NIL STAGG (NIL T) -9 NIL 2922797 NIL) (-1178 2915090 2915840 2916710 "STAGG-" 2916715 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1177 2913176 2914860 2914952 "STACK" 2915033 NIL STACK (NIL T) -8 NIL NIL NIL) (-1176 2912493 2913006 2913036 "SRING" 2913041 T SRING (NIL) -9 NIL 2913061 NIL) (-1175 2904642 2910634 2911090 "SREGSET" 2912123 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1174 2896989 2898436 2899949 "SRDCMPK" 2903248 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1173 2889403 2894348 2894378 "SRAGG" 2895681 T SRAGG (NIL) -9 NIL 2896289 NIL) (-1172 2888354 2888675 2889054 "SRAGG-" 2889059 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1171 2882056 2887301 2887722 "SQMATRIX" 2887980 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1170 2875583 2878774 2879501 "SPLTREE" 2881401 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1169 2871408 2872239 2872885 "SPLNODE" 2875009 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1168 2870383 2870688 2870718 "SPFCAT" 2871162 T SPFCAT (NIL) -9 NIL NIL NIL) (-1167 2869078 2869330 2869594 "SPECOUT" 2870141 T SPECOUT (NIL) -7 NIL NIL NIL) (-1166 2859730 2862046 2862076 "SPADXPT" 2866752 T SPADXPT (NIL) -9 NIL 2868916 NIL) (-1165 2859485 2859531 2859600 "SPADPRSR" 2859683 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1164 2857090 2859440 2859471 "SPADAST" 2859476 T SPADAST (NIL) -8 NIL NIL NIL) (-1163 2848691 2850794 2850837 "SPACEC" 2855210 NIL SPACEC (NIL T) -9 NIL 2857026 NIL) (-1162 2846491 2848623 2848672 "SPACE3" 2848677 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1161 2845223 2845414 2845705 "SORTPAK" 2846296 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1160 2843285 2843618 2844030 "SOLVETRA" 2844887 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1159 2842323 2842557 2842818 "SOLVESER" 2843058 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1158 2837555 2838515 2839510 "SOLVERAD" 2841375 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1157 2833280 2833979 2834708 "SOLVEFOR" 2836922 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1156 2827025 2832628 2832725 "SNTSCAT" 2832730 NIL SNTSCAT (NIL T T T T) -9 NIL 2832800 NIL) (-1155 2820576 2825348 2825739 "SMTS" 2826715 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1154 2814324 2820464 2820541 "SMP" 2820546 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1153 2812453 2812784 2813182 "SMITH" 2814021 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1152 2804090 2809026 2809129 "SMATCAT" 2810483 NIL SMATCAT (NIL NIL T T T) -9 NIL 2811033 NIL) (-1151 2800883 2801867 2803038 "SMATCAT-" 2803043 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1150 2798463 2800091 2800134 "SKAGG" 2800395 NIL SKAGG (NIL T) -9 NIL 2800530 NIL) (-1149 2794127 2797960 2798130 "SINT" 2798282 T SINT (NIL) -8 NIL NIL 2798430) (-1148 2793893 2793937 2794003 "SIMPAN" 2794083 T SIMPAN (NIL) -7 NIL NIL NIL) (-1147 2792734 2792966 2793234 "SIGNRF" 2793659 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1146 2791570 2791732 2792009 "SIGNEF" 2792570 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1145 2790810 2791153 2791277 "SIGAST" 2791468 T SIGAST (NIL) -8 NIL NIL NIL) (-1144 2790035 2790345 2790485 "SIG" 2790692 T SIG (NIL) -8 NIL NIL NIL) (-1143 2787687 2788179 2788685 "SHP" 2789576 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1142 2781132 2787588 2787664 "SHDP" 2787669 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1141 2780643 2780883 2780913 "SGROUP" 2781006 T SGROUP (NIL) -9 NIL 2781068 NIL) (-1140 2780495 2780527 2780600 "SGROUP-" 2780605 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1139 2777214 2777984 2778707 "SGCF" 2779794 T SGCF (NIL) -7 NIL NIL NIL) (-1138 2771057 2776660 2776757 "SFRTCAT" 2776762 NIL SFRTCAT (NIL T T T T) -9 NIL 2776801 NIL) (-1137 2764376 2765496 2766632 "SFRGCD" 2770040 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1136 2757394 2758575 2759761 "SFQCMPK" 2763309 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1135 2756996 2757103 2757214 "SFORT" 2757335 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1134 2755922 2756836 2756957 "SEXOF" 2756962 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1133 2751511 2752418 2752513 "SEXCAT" 2755135 NIL SEXCAT (NIL T T T T T) -9 NIL 2755695 NIL) (-1132 2750426 2751392 2751460 "SEX" 2751465 T SEX (NIL) -8 NIL NIL NIL) (-1131 2748554 2749143 2749446 "SETMN" 2750169 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1130 2748084 2748272 2748302 "SETCAT" 2748419 T SETCAT (NIL) -9 NIL 2748504 NIL) (-1129 2747852 2747916 2748015 "SETCAT-" 2748020 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1128 2744066 2746313 2746356 "SETAGG" 2747226 NIL SETAGG (NIL T) -9 NIL 2747566 NIL) (-1127 2743488 2743640 2743877 "SETAGG-" 2743882 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1126 2740411 2743422 2743470 "SET" 2743475 NIL SET (NIL T) -8 NIL NIL NIL) (-1125 2739794 2740107 2740208 "SEQAST" 2740332 T SEQAST (NIL) -8 NIL NIL NIL) (-1124 2738921 2739287 2739348 "SEGXCAT" 2739634 NIL SEGXCAT (NIL T T) -9 NIL 2739754 NIL) (-1123 2737846 2738114 2738157 "SEGCAT" 2738679 NIL SEGCAT (NIL T) -9 NIL 2738900 NIL) (-1122 2737461 2737526 2737639 "SEGBIND2" 2737781 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1121 2736351 2736824 2737032 "SEGBIND" 2737288 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1120 2735870 2736152 2736229 "SEGAST" 2736296 T SEGAST (NIL) -8 NIL NIL NIL) (-1119 2735079 2735215 2735419 "SEG2" 2735714 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1118 2733995 2734745 2734927 "SEG" 2734932 NIL SEG (NIL T) -8 NIL NIL NIL) (-1117 2733228 2733930 2733977 "SDVAR" 2733982 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1116 2724622 2732998 2733128 "SDPOL" 2733133 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1115 2723191 2723481 2723800 "SCPKG" 2724337 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1114 2722313 2722527 2722719 "SCOPE" 2723021 T SCOPE (NIL) -8 NIL NIL NIL) (-1113 2721509 2721667 2721846 "SCACHE" 2722168 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1112 2721093 2721327 2721357 "SASTCAT" 2721362 T SASTCAT (NIL) -9 NIL 2721375 NIL) (-1111 2720496 2720928 2721004 "SAOS" 2721039 T SAOS (NIL) -8 NIL NIL NIL) (-1110 2720055 2720096 2720269 "SAERFFC" 2720455 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1109 2719642 2719683 2719842 "SAEFACT" 2720014 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1108 2712699 2719539 2719619 "SAE" 2719624 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1107 2711002 2711334 2711735 "RURPK" 2712365 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1106 2709579 2709945 2710250 "RULESET" 2710836 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1105 2709149 2709373 2709456 "RULECOLD" 2709531 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1104 2706264 2706902 2707360 "RULE" 2708830 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1103 2706048 2706082 2706153 "RTVALUE" 2706215 T RTVALUE (NIL) -8 NIL NIL NIL) (-1102 2705459 2705765 2705859 "RSTRCAST" 2705976 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1101 2700229 2701102 2702022 "RSETGCD" 2704658 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1100 2688934 2694537 2694634 "RSETCAT" 2698753 NIL RSETCAT (NIL T T T T) -9 NIL 2699850 NIL) (-1099 2686753 2687400 2688224 "RSETCAT-" 2688229 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1098 2679061 2680515 2682035 "RSDCMPK" 2685352 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1097 2676930 2677493 2677567 "RRCC" 2678653 NIL RRCC (NIL T T) -9 NIL 2678997 NIL) (-1096 2676251 2676455 2676734 "RRCC-" 2676739 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1095 2675634 2675947 2676048 "RPTAST" 2676172 T RPTAST (NIL) -8 NIL NIL NIL) (-1094 2648046 2658746 2658813 "RPOLCAT" 2669479 NIL RPOLCAT (NIL T T T) -9 NIL 2672639 NIL) (-1093 2639052 2641908 2645018 "RPOLCAT-" 2645023 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1092 2629621 2637263 2637745 "ROUTINE" 2638592 T ROUTINE (NIL) -8 NIL NIL NIL) (-1091 2625686 2629247 2629387 "ROMAN" 2629503 T ROMAN (NIL) -8 NIL NIL NIL) (-1090 2623800 2624546 2624806 "ROIRC" 2625491 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1089 2619577 2622342 2622372 "RNS" 2622641 T RNS (NIL) -9 NIL 2622897 NIL) (-1088 2617984 2618469 2619003 "RNS-" 2619078 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1087 2616945 2617349 2617551 "RNGBIND" 2617835 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1086 2616238 2616742 2616772 "RNG" 2616777 T RNG (NIL) -9 NIL 2616798 NIL) (-1085 2615533 2616011 2616054 "RMODULE" 2616059 NIL RMODULE (NIL T) -9 NIL 2616086 NIL) (-1084 2614357 2614463 2614799 "RMCAT2" 2615434 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1083 2610973 2613703 2614000 "RMATRIX" 2614119 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1082 2603583 2606060 2606175 "RMATCAT" 2609534 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2610516 NIL) (-1081 2602922 2603105 2603412 "RMATCAT-" 2603417 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1080 2602495 2602709 2602752 "RLINSET" 2602814 NIL RLINSET (NIL T) -9 NIL 2602858 NIL) (-1079 2602056 2602137 2602265 "RINTERP" 2602414 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1078 2600980 2601654 2601684 "RING" 2601740 T RING (NIL) -9 NIL 2601832 NIL) (-1077 2600760 2600816 2600913 "RING-" 2600918 NIL RING- (NIL T) -8 NIL NIL NIL) (-1076 2599571 2599838 2600096 "RIDIST" 2600524 T RIDIST (NIL) -7 NIL NIL NIL) (-1075 2590337 2599039 2599245 "RGCHAIN" 2599419 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1074 2589595 2590079 2590120 "RGBCSPC" 2590178 NIL RGBCSPC (NIL T) -9 NIL 2590230 NIL) (-1073 2588661 2589120 2589161 "RGBCMDL" 2589393 NIL RGBCMDL (NIL T) -9 NIL 2589507 NIL) (-1072 2588301 2588370 2588473 "RFFACTOR" 2588592 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1071 2588020 2588061 2588158 "RFFACT" 2588260 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1070 2586071 2586501 2586883 "RFDIST" 2587660 T RFDIST (NIL) -7 NIL NIL NIL) (-1069 2583011 2583679 2584349 "RF" 2585435 NIL RF (NIL T) -7 NIL NIL NIL) (-1068 2582458 2582556 2582719 "RETSOL" 2582913 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1067 2582076 2582174 2582217 "RETRACT" 2582350 NIL RETRACT (NIL T) -9 NIL 2582437 NIL) (-1066 2581919 2581950 2582037 "RETRACT-" 2582042 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1065 2581467 2581741 2581811 "RETAST" 2581871 T RETAST (NIL) -8 NIL NIL NIL) (-1064 2573933 2581120 2581247 "RESULT" 2581362 T RESULT (NIL) -8 NIL NIL NIL) (-1063 2572368 2573202 2573401 "RESRING" 2573836 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1062 2571992 2572053 2572151 "RESLATC" 2572305 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1061 2571691 2571732 2571839 "REPSQ" 2571951 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1060 2571382 2571423 2571534 "REPDB" 2571650 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1059 2565214 2566671 2567894 "REP2" 2570194 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1058 2561517 2562272 2563080 "REP1" 2564441 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1057 2558897 2559519 2560121 "REP" 2560937 T REP (NIL) -7 NIL NIL NIL) (-1056 2551046 2557038 2557494 "REGSET" 2558527 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1055 2549755 2550194 2550444 "REF" 2550831 NIL REF (NIL T) -8 NIL NIL NIL) (-1054 2549120 2549235 2549402 "REDORDER" 2549639 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1053 2544522 2548333 2548560 "RECLOS" 2548948 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1052 2543556 2543755 2543970 "REALSOLV" 2544329 T REALSOLV (NIL) -7 NIL NIL NIL) (-1051 2540003 2540841 2541725 "REAL0Q" 2542721 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1050 2535556 2536592 2537653 "REAL0" 2538984 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1049 2535390 2535443 2535473 "REAL" 2535478 T REAL (NIL) -9 NIL 2535513 NIL) (-1048 2534801 2535107 2535201 "RDUCEAST" 2535318 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1047 2534200 2534278 2534485 "RDIV" 2534723 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1046 2533250 2533442 2533655 "RDIST" 2534022 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1045 2531835 2532134 2532506 "RDETRS" 2532958 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1044 2529629 2530101 2530639 "RDETR" 2531377 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1043 2528248 2528532 2528929 "RDEEFS" 2529345 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1042 2526751 2527063 2527488 "RDEEF" 2527936 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1041 2520239 2523705 2523735 "RCFIELD" 2525030 T RCFIELD (NIL) -9 NIL 2525761 NIL) (-1040 2518195 2518807 2519503 "RCFIELD-" 2519578 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1039 2514358 2516268 2516311 "RCAGG" 2517395 NIL RCAGG (NIL T) -9 NIL 2517860 NIL) (-1038 2513968 2514080 2514243 "RCAGG-" 2514248 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1037 2513285 2513415 2513580 "RATRET" 2513852 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1036 2512826 2512905 2513026 "RATFACT" 2513213 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1035 2512104 2512254 2512406 "RANDSRC" 2512696 T RANDSRC (NIL) -7 NIL NIL NIL) (-1034 2511832 2511882 2511955 "RADUTIL" 2512053 T RADUTIL (NIL) -7 NIL NIL NIL) (-1033 2503993 2510663 2510974 "RADIX" 2511555 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1032 2493619 2503835 2503965 "RADFF" 2503970 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1031 2493248 2493341 2493371 "RADCAT" 2493531 T RADCAT (NIL) -9 NIL NIL NIL) (-1030 2493018 2493078 2493178 "RADCAT-" 2493183 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1029 2491043 2492788 2492880 "QUEUE" 2492961 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1028 2490668 2490717 2490848 "QUATCT2" 2490994 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1027 2483053 2487091 2487133 "QUATCAT" 2487924 NIL QUATCAT (NIL T) -9 NIL 2488690 NIL) (-1026 2478955 2480243 2481626 "QUATCAT-" 2481722 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1025 2474808 2478888 2478936 "QUAT" 2478941 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1024 2472175 2473856 2473899 "QUAGG" 2474280 NIL QUAGG (NIL T) -9 NIL 2474455 NIL) (-1023 2471723 2471997 2472067 "QQUTAST" 2472127 T QQUTAST (NIL) -8 NIL NIL NIL) (-1022 2470634 2471236 2471401 "QFORM" 2471604 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1021 2470259 2470308 2470439 "QFCAT2" 2470585 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1020 2459972 2466106 2466148 "QFCAT" 2466816 NIL QFCAT (NIL T) -9 NIL 2467817 NIL) (-1019 2455342 2456778 2458353 "QFCAT-" 2458449 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1018 2454773 2454907 2455039 "QEQUAT" 2455232 T QEQUAT (NIL) -8 NIL NIL NIL) (-1017 2447791 2448972 2450158 "QCMPACK" 2453706 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1016 2447020 2447202 2447438 "QALGSET2" 2447609 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1015 2444476 2445010 2445438 "QALGSET" 2446677 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1014 2443143 2443385 2443704 "PWFFINTB" 2444249 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1013 2441305 2441503 2441859 "PUSHVAR" 2442957 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1012 2437032 2438248 2438291 "PTRANFN" 2440202 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1011 2435369 2435714 2436038 "PTPACK" 2436743 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1010 2434992 2435055 2435166 "PTFUNC2" 2435306 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1009 2429022 2433781 2433824 "PTCAT" 2434124 NIL PTCAT (NIL T) -9 NIL 2434277 NIL) (-1008 2428671 2428712 2428838 "PSQFR" 2428981 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1007 2427243 2427559 2427895 "PSEUDLIN" 2428369 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1006 2413763 2416338 2418664 "PSETPK" 2425003 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1005 2406582 2409499 2409597 "PSETCAT" 2412638 NIL PSETCAT (NIL T T T T) -9 NIL 2413452 NIL) (-1004 2404307 2405049 2405873 "PSETCAT-" 2405878 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1003 2403620 2403815 2403845 "PSCURVE" 2404117 T PSCURVE (NIL) -9 NIL 2404284 NIL) (-1002 2399343 2401110 2401177 "PSCAT" 2402029 NIL PSCAT (NIL T T T) -9 NIL 2402269 NIL) (-1001 2398337 2398619 2399022 "PSCAT-" 2399027 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1000 2396505 2397396 2397661 "PRTITION" 2398094 T PRTITION (NIL) -8 NIL NIL NIL) (-999 2395920 2396226 2396318 "PRTDAST" 2396433 T PRTDAST (NIL) -8 NIL NIL NIL) (-998 2384802 2387224 2389412 "PRS" 2393782 NIL PRS (NIL T T) -7 NIL NIL NIL) (-997 2382533 2384124 2384164 "PRQAGG" 2384347 NIL PRQAGG (NIL T) -9 NIL 2384449 NIL) (-996 2381712 2382161 2382189 "PROPLOG" 2382328 T PROPLOG (NIL) -9 NIL 2382443 NIL) (-995 2381310 2381373 2381496 "PROPFUN2" 2381635 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-994 2380607 2380746 2380918 "PROPFUN1" 2381171 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-993 2378588 2379354 2379651 "PROPFRML" 2380343 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-992 2378033 2378164 2378292 "PROPERTY" 2378480 T PROPERTY (NIL) -8 NIL NIL NIL) (-991 2371846 2376199 2377019 "PRODUCT" 2377259 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-990 2371636 2371674 2371733 "PRINT" 2371807 T PRINT (NIL) -7 NIL NIL NIL) (-989 2370952 2371093 2371245 "PRIMES" 2371516 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-988 2368999 2369418 2369884 "PRIMELT" 2370531 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-987 2368716 2368777 2368805 "PRIMCAT" 2368929 T PRIMCAT (NIL) -9 NIL NIL NIL) (-986 2367705 2367901 2368129 "PRIMARR2" 2368534 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-985 2363541 2367643 2367688 "PRIMARR" 2367693 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-984 2363178 2363240 2363351 "PREASSOC" 2363479 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-983 2360150 2362636 2362870 "PR" 2362989 NIL PR (NIL T T) -8 NIL NIL NIL) (-982 2359601 2359758 2359786 "PPCURVE" 2359991 T PPCURVE (NIL) -9 NIL 2360127 NIL) (-981 2359148 2359396 2359479 "PORTNUM" 2359538 T PORTNUM (NIL) -8 NIL NIL NIL) (-980 2356485 2356906 2357498 "POLYROOT" 2358729 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-979 2355862 2355926 2356160 "POLYLIFT" 2356421 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-978 2352083 2352586 2353215 "POLYCATQ" 2355407 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-977 2337745 2343830 2343895 "POLYCAT" 2347409 NIL POLYCAT (NIL T T T) -9 NIL 2349287 NIL) (-976 2330927 2333098 2335461 "POLYCAT-" 2335466 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-975 2330508 2330582 2330702 "POLY2UP" 2330853 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-974 2330134 2330197 2330306 "POLY2" 2330445 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-973 2323375 2329738 2329898 "POLY" 2330007 NIL POLY (NIL T) -8 NIL NIL NIL) (-972 2322036 2322299 2322575 "POLUTIL" 2323149 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-971 2320355 2320668 2320999 "POLTOPOL" 2321758 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-970 2315465 2320289 2320336 "POINT" 2320341 NIL POINT (NIL T) -8 NIL NIL NIL) (-969 2313598 2314009 2314384 "PNTHEORY" 2315110 T PNTHEORY (NIL) -7 NIL NIL NIL) (-968 2312044 2312353 2312752 "PMTOOLS" 2313296 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-967 2311631 2311715 2311832 "PMSYM" 2311960 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-966 2311133 2311208 2311383 "PMQFCAT" 2311556 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-965 2310514 2310612 2310774 "PMPREDFS" 2311034 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-964 2309857 2309979 2310135 "PMPRED" 2310391 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-963 2308511 2308729 2309107 "PMPLCAT" 2309619 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-962 2308037 2308122 2308274 "PMLSAGG" 2308426 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-961 2307504 2307586 2307768 "PMKERNEL" 2307955 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-960 2307115 2307196 2307309 "PMINS" 2307423 NIL PMINS (NIL T) -7 NIL NIL NIL) (-959 2306551 2306626 2306835 "PMFS" 2307040 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-958 2305767 2305897 2306102 "PMDOWN" 2306428 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-957 2305016 2305150 2305313 "PMASSFS" 2305654 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-956 2304159 2304341 2304522 "PMASS" 2304855 T PMASS (NIL) -7 NIL NIL NIL) (-955 2303808 2303882 2303976 "PLOTTOOL" 2304085 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-954 2299460 2300654 2301576 "PLOT3D" 2302906 T PLOT3D (NIL) -8 NIL NIL NIL) (-953 2298348 2298549 2298784 "PLOT1" 2299264 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-952 2292769 2294159 2295307 "PLOT" 2297220 T PLOT (NIL) -8 NIL NIL NIL) (-951 2267944 2272835 2277686 "PLEQN" 2288035 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-950 2267631 2267684 2267787 "PINTERPA" 2267891 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-949 2266937 2267071 2267251 "PINTERP" 2267496 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-948 2265021 2266187 2266215 "PID" 2266412 T PID (NIL) -9 NIL 2266539 NIL) (-947 2264766 2264809 2264884 "PICOERCE" 2264978 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-946 2263862 2264530 2264617 "PI" 2264657 T PI (NIL) -8 NIL NIL 2264724) (-945 2263170 2263321 2263497 "PGROEB" 2263718 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-944 2258609 2259568 2260474 "PGE" 2262284 T PGE (NIL) -7 NIL NIL NIL) (-943 2256690 2256979 2257345 "PGCD" 2258326 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-942 2256016 2256131 2256292 "PFRPAC" 2256574 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-941 2252276 2254564 2254917 "PFR" 2255695 NIL PFR (NIL T) -8 NIL NIL NIL) (-940 2250629 2250909 2251234 "PFOTOOLS" 2252023 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-939 2249144 2249401 2249752 "PFOQ" 2250386 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-938 2247627 2247857 2248213 "PFO" 2248928 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-937 2244711 2246217 2246245 "PFECAT" 2246838 T PFECAT (NIL) -9 NIL 2247215 NIL) (-936 2244159 2244324 2244531 "PFECAT-" 2244536 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-935 2242732 2243014 2243315 "PFBRU" 2243908 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-934 2240561 2240950 2241382 "PFBR" 2242383 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-933 2236509 2240450 2240519 "PF" 2240524 NIL PF (NIL NIL) -8 NIL NIL NIL) (-932 2231563 2232716 2233586 "PERMGRP" 2235672 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-931 2229475 2230587 2230628 "PERMCAT" 2231028 NIL PERMCAT (NIL T) -9 NIL 2231326 NIL) (-930 2229122 2229169 2229293 "PERMAN" 2229428 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-929 2224924 2226631 2227279 "PERM" 2228507 NIL PERM (NIL T) -8 NIL NIL NIL) (-928 2222281 2224589 2224711 "PENDTREE" 2224835 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-927 2221162 2221425 2221466 "PDSPC" 2221999 NIL PDSPC (NIL T) -9 NIL 2222244 NIL) (-926 2220217 2220483 2220845 "PDSPC-" 2220850 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-925 2218931 2219867 2219908 "PDRING" 2219913 NIL PDRING (NIL T) -9 NIL 2219941 NIL) (-924 2217674 2218436 2218490 "PDMOD" 2218495 NIL PDMOD (NIL T T) -9 NIL 2218599 NIL) (-923 2214841 2215667 2216335 "PDEPROB" 2217026 T PDEPROB (NIL) -8 NIL NIL NIL) (-922 2212350 2212890 2213445 "PDEPACK" 2214306 T PDEPACK (NIL) -7 NIL NIL NIL) (-921 2211238 2211452 2211703 "PDECOMP" 2212149 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-920 2208755 2209646 2209674 "PDECAT" 2210461 T PDECAT (NIL) -9 NIL 2211174 NIL) (-919 2208372 2208439 2208493 "PDDOM" 2208658 NIL PDDOM (NIL T T) -9 NIL 2208738 NIL) (-918 2208185 2208221 2208328 "PDDOM-" 2208333 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-917 2207930 2207969 2208059 "PCOMP" 2208146 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-916 2205970 2206731 2207028 "PBWLB" 2207659 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-915 2205596 2205659 2205768 "PATTERN2" 2205907 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-914 2203305 2203741 2204198 "PATTERN1" 2205185 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-913 2195486 2197378 2198716 "PATTERN" 2201988 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-912 2195044 2195117 2195249 "PATRES2" 2195413 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-911 2192310 2192993 2193474 "PATRES" 2194609 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-910 2190163 2190598 2191005 "PATMATCH" 2191977 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-909 2189617 2189868 2189909 "PATMAB" 2190016 NIL PATMAB (NIL T) -9 NIL 2190099 NIL) (-908 2188063 2188471 2188729 "PATLRES" 2189422 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-907 2187601 2187732 2187773 "PATAB" 2187778 NIL PATAB (NIL T) -9 NIL 2187950 NIL) (-906 2185741 2186178 2186601 "PARTPERM" 2187198 T PARTPERM (NIL) -7 NIL NIL NIL) (-905 2185350 2185425 2185527 "PARSURF" 2185672 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-904 2184976 2185039 2185148 "PARSU2" 2185287 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-903 2184734 2184780 2184847 "PARSER" 2184929 T PARSER (NIL) -7 NIL NIL NIL) (-902 2184343 2184418 2184520 "PARSCURV" 2184665 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-901 2183969 2184032 2184141 "PARSC2" 2184280 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-900 2183596 2183666 2183763 "PARPCURV" 2183905 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-899 2183222 2183285 2183394 "PARPC2" 2183533 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-898 2182211 2182595 2182777 "PARAMAST" 2183060 T PARAMAST (NIL) -8 NIL NIL NIL) (-897 2181719 2181817 2181936 "PAN2EXPR" 2182112 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-896 2180412 2180840 2181068 "PALETTE" 2181511 T PALETTE (NIL) -8 NIL NIL NIL) (-895 2178757 2179417 2179777 "PAIR" 2180098 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-894 2171706 2178014 2178209 "PADICRC" 2178611 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-893 2163979 2171050 2171235 "PADICRAT" 2171553 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-892 2160778 2162639 2162679 "PADICCT" 2163260 NIL PADICCT (NIL NIL) -9 NIL 2163542 NIL) (-891 2158796 2160715 2160760 "PADIC" 2160765 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-890 2157741 2157953 2158221 "PADEPAC" 2158583 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-889 2156941 2157086 2157292 "PADE" 2157603 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-888 2155174 2156149 2156429 "OWP" 2156745 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-887 2154619 2154880 2154977 "OVERSET" 2155097 T OVERSET (NIL) -8 NIL NIL NIL) (-886 2153539 2154224 2154396 "OVAR" 2154487 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-885 2141775 2144648 2146848 "OUTFORM" 2151359 T OUTFORM (NIL) -8 NIL NIL NIL) (-884 2141057 2141372 2141499 "OUTBFILE" 2141668 T OUTBFILE (NIL) -8 NIL NIL NIL) (-883 2140334 2140529 2140557 "OUTBCON" 2140875 T OUTBCON (NIL) -9 NIL 2141041 NIL) (-882 2139917 2140047 2140204 "OUTBCON-" 2140209 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-881 2139157 2139302 2139463 "OUT" 2139776 T OUT (NIL) -7 NIL NIL NIL) (-880 2138453 2138886 2138975 "OSI" 2139088 T OSI (NIL) -8 NIL NIL NIL) (-879 2137872 2138294 2138322 "OSGROUP" 2138327 T OSGROUP (NIL) -9 NIL 2138349 NIL) (-878 2136583 2136844 2137129 "ORTHPOL" 2137619 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-877 2133848 2136418 2136539 "OREUP" 2136544 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-876 2130965 2133539 2133666 "ORESUP" 2133790 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-875 2128465 2128993 2129554 "OREPCTO" 2130454 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-874 2121850 2124338 2124379 "OREPCAT" 2126727 NIL OREPCAT (NIL T) -9 NIL 2127831 NIL) (-873 2118844 2119793 2120844 "OREPCAT-" 2120849 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-872 2118036 2118314 2118342 "ORDTYPE" 2118651 T ORDTYPE (NIL) -9 NIL 2118814 NIL) (-871 2117337 2117553 2117808 "ORDTYPE-" 2117813 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-870 2116693 2117076 2117234 "ORDSTRCT" 2117239 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-869 2116191 2116561 2116589 "ORDSET" 2116594 T ORDSET (NIL) -9 NIL 2116616 NIL) (-868 2114842 2115813 2115841 "ORDRING" 2115846 T ORDRING (NIL) -9 NIL 2115875 NIL) (-867 2114093 2114658 2114686 "ORDMON" 2114691 T ORDMON (NIL) -9 NIL 2114712 NIL) (-866 2113237 2113402 2113597 "ORDFUNS" 2113942 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-865 2112452 2112967 2112995 "ORDFIN" 2113060 T ORDFIN (NIL) -9 NIL 2113134 NIL) (-864 2111706 2111845 2112031 "ORDCOMP2" 2112312 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-863 2108060 2110292 2110701 "ORDCOMP" 2111330 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-862 2104581 2105551 2106365 "OPTPROB" 2107266 T OPTPROB (NIL) -8 NIL NIL NIL) (-861 2101323 2102022 2102726 "OPTPACK" 2103897 T OPTPACK (NIL) -7 NIL NIL NIL) (-860 2098936 2099762 2099790 "OPTCAT" 2100609 T OPTCAT (NIL) -9 NIL 2101259 NIL) (-859 2098254 2098613 2098718 "OPSIG" 2098851 T OPSIG (NIL) -8 NIL NIL NIL) (-858 2098016 2098061 2098127 "OPQUERY" 2098208 T OPQUERY (NIL) -7 NIL NIL NIL) (-857 2097322 2097602 2097643 "OPERCAT" 2097855 NIL OPERCAT (NIL T) -9 NIL 2097952 NIL) (-856 2097065 2097133 2097250 "OPERCAT-" 2097255 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-855 2093983 2095376 2095880 "OP" 2096594 NIL OP (NIL T) -8 NIL NIL NIL) (-854 2093276 2093403 2093577 "ONECOMP2" 2093855 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-853 2089896 2092073 2092442 "ONECOMP" 2092940 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-852 2086521 2089336 2089376 "OMSAGG" 2089437 NIL OMSAGG (NIL T) -9 NIL 2089501 NIL) (-851 2085096 2085407 2085689 "OMPKG" 2086259 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2083443 2084645 2084814 "OMLO" 2084977 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2082379 2082550 2082770 "OMEXPR" 2083269 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2081464 2081800 2081960 "OMERRK" 2082239 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2080701 2081010 2081146 "OMERR" 2081348 T OMERR (NIL) -8 NIL NIL NIL) (-846 2080092 2080378 2080486 "OMENC" 2080613 T OMENC (NIL) -8 NIL NIL NIL) (-845 2073729 2075172 2076343 "OMDEV" 2078941 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2072762 2072969 2073163 "OMCONN" 2073555 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2072168 2072295 2072323 "OM" 2072622 T OM (NIL) -9 NIL NIL NIL) (-842 2070446 2071638 2071666 "OINTDOM" 2071671 T OINTDOM (NIL) -9 NIL 2071692 NIL) (-841 2067528 2069134 2069471 "OFMONOID" 2070141 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2066762 2067465 2067510 "ODVAR" 2067515 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2063908 2066507 2066662 "ODR" 2066667 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2055356 2063684 2063810 "ODPOL" 2063815 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2048771 2055228 2055333 "ODP" 2055338 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2047513 2047752 2048027 "ODETOOLS" 2048545 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2044456 2045138 2045854 "ODESYS" 2046846 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2039286 2040246 2041271 "ODERTRIC" 2043531 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2038706 2038794 2038988 "ODERED" 2039198 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2035566 2036148 2036823 "ODERAT" 2038131 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2032482 2032990 2033587 "ODEPRRIC" 2035095 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2030377 2031021 2031507 "ODEPROB" 2032016 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2026843 2027382 2028029 "ODEPRIM" 2029856 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2026086 2026194 2026454 "ODEPAL" 2026735 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2022188 2023039 2023903 "ODEPACK" 2025242 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2021231 2021356 2021578 "ODEINT" 2022077 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2015296 2016757 2018204 "ODEIFTBL" 2019804 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2010660 2011490 2012438 "ODEEF" 2014459 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2010003 2010098 2010321 "ODECONST" 2010565 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2008066 2008775 2008803 "ODECAT" 2009408 T ODECAT (NIL) -9 NIL 2009939 NIL) (-821 2007698 2007747 2007874 "OCTCT2" 2008017 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2004210 2007403 2007525 "OCT" 2007608 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2003403 2004003 2004031 "OCAMON" 2004036 T OCAMON (NIL) -9 NIL 2004057 NIL) (-818 1997681 2000446 2000486 "OC" 2001583 NIL OC (NIL T) -9 NIL 2002441 NIL) (-817 1994737 1995670 1996653 "OC-" 1996747 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 1994157 1994582 1994610 "OASGP" 1994615 T OASGP (NIL) -9 NIL 1994635 NIL) (-815 1993253 1993880 1993908 "OAMONS" 1993948 T OAMONS (NIL) -9 NIL 1993991 NIL) (-814 1992429 1992988 1993016 "OAMON" 1993074 T OAMON (NIL) -9 NIL 1993126 NIL) (-813 1992287 1992320 1992388 "OAMON-" 1992393 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-812 1991068 1991821 1991849 "OAGROUP" 1991996 T OAGROUP (NIL) -9 NIL 1992089 NIL) (-811 1990771 1990859 1990977 "OAGROUP-" 1990982 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-810 1990453 1990509 1990598 "NUMTUBE" 1990715 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-809 1983972 1985544 1987080 "NUMQUAD" 1988937 T NUMQUAD (NIL) -7 NIL NIL NIL) (-808 1979652 1980686 1981721 "NUMODE" 1982957 T NUMODE (NIL) -7 NIL NIL NIL) (-807 1976933 1977873 1977901 "NUMINT" 1978824 T NUMINT (NIL) -9 NIL 1979588 NIL) (-806 1975845 1976078 1976296 "NUMFMT" 1976735 T NUMFMT (NIL) -7 NIL NIL NIL) (-805 1962028 1965149 1967681 "NUMERIC" 1973352 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-804 1955873 1961476 1961571 "NTSCAT" 1961576 NIL NTSCAT (NIL T T T T) -9 NIL 1961615 NIL) (-803 1955053 1955232 1955425 "NTPOLFN" 1955712 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-802 1954679 1954742 1954851 "NSUP2" 1954990 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-801 1941501 1951504 1952316 "NSUP" 1953900 NIL NSUP (NIL T) -8 NIL NIL NIL) (-800 1930387 1941275 1941408 "NSMP" 1941413 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-799 1928795 1929120 1929477 "NREP" 1930075 NIL NREP (NIL T) -7 NIL NIL NIL) (-798 1927374 1927638 1927996 "NPCOEF" 1928538 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-797 1926422 1926555 1926771 "NORMRETR" 1927255 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-796 1924433 1924753 1925162 "NORMPK" 1926130 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-795 1924112 1924146 1924270 "NORMMA" 1924399 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-794 1923895 1923930 1923999 "NONE1" 1924076 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-793 1923659 1923852 1923881 "NONE" 1923886 T NONE (NIL) -8 NIL NIL NIL) (-792 1923150 1923218 1923397 "NODE1" 1923591 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-791 1921211 1922273 1922528 "NNI" 1922875 T NNI (NIL) -8 NIL NIL 1923110) (-790 1919607 1919944 1920308 "NLINSOL" 1920879 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-789 1915788 1916843 1917742 "NIPROB" 1918728 T NIPROB (NIL) -8 NIL NIL NIL) (-788 1914527 1914779 1915081 "NFINTBAS" 1915550 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-787 1913611 1914177 1914218 "NETCLT" 1914390 NIL NETCLT (NIL T) -9 NIL 1914472 NIL) (-786 1912283 1912550 1912831 "NCODIV" 1913379 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-785 1912039 1912082 1912157 "NCNTFRAC" 1912240 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-784 1910195 1910583 1911003 "NCEP" 1911664 NIL NCEP (NIL T) -7 NIL NIL NIL) (-783 1908865 1909805 1909833 "NASRING" 1909943 T NASRING (NIL) -9 NIL 1910023 NIL) (-782 1908648 1908704 1908798 "NASRING-" 1908803 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-781 1907615 1908266 1908294 "NARNG" 1908411 T NARNG (NIL) -9 NIL 1908502 NIL) (-780 1907289 1907374 1907508 "NARNG-" 1907513 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-779 1906126 1906375 1906610 "NAGSP" 1907074 T NAGSP (NIL) -7 NIL NIL NIL) (-778 1897170 1899082 1900755 "NAGS" 1904473 T NAGS (NIL) -7 NIL NIL NIL) (-777 1895694 1896026 1896357 "NAGF07" 1896859 T NAGF07 (NIL) -7 NIL NIL NIL) (-776 1890166 1891523 1892830 "NAGF04" 1894407 T NAGF04 (NIL) -7 NIL NIL NIL) (-775 1883038 1884748 1886381 "NAGF02" 1888553 T NAGF02 (NIL) -7 NIL NIL NIL) (-774 1878202 1879362 1880479 "NAGF01" 1881941 T NAGF01 (NIL) -7 NIL NIL NIL) (-773 1871782 1873396 1874981 "NAGE04" 1876637 T NAGE04 (NIL) -7 NIL NIL NIL) (-772 1862843 1865072 1867202 "NAGE02" 1869672 T NAGE02 (NIL) -7 NIL NIL NIL) (-771 1858736 1859743 1860707 "NAGE01" 1861899 T NAGE01 (NIL) -7 NIL NIL NIL) (-770 1856513 1857065 1857623 "NAGD03" 1858198 T NAGD03 (NIL) -7 NIL NIL NIL) (-769 1848209 1850191 1852145 "NAGD02" 1854579 T NAGD02 (NIL) -7 NIL NIL NIL) (-768 1841948 1843445 1844885 "NAGD01" 1846789 T NAGD01 (NIL) -7 NIL NIL NIL) (-767 1838085 1838979 1839816 "NAGC06" 1841131 T NAGC06 (NIL) -7 NIL NIL NIL) (-766 1836532 1836882 1837238 "NAGC05" 1837749 T NAGC05 (NIL) -7 NIL NIL NIL) (-765 1835896 1836027 1836171 "NAGC02" 1836408 T NAGC02 (NIL) -7 NIL NIL NIL) (-764 1834697 1835424 1835464 "NAALG" 1835543 NIL NAALG (NIL T) -9 NIL 1835604 NIL) (-763 1834526 1834561 1834651 "NAALG-" 1834656 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-762 1828398 1829584 1830771 "MULTSQFR" 1833422 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-761 1827705 1827792 1827976 "MULTFACT" 1828310 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-760 1819850 1824288 1824341 "MTSCAT" 1825411 NIL MTSCAT (NIL T T) -9 NIL 1825927 NIL) (-759 1819556 1819616 1819708 "MTHING" 1819790 NIL MTHING (NIL T) -7 NIL NIL NIL) (-758 1819342 1819381 1819441 "MSYSCMD" 1819516 T MSYSCMD (NIL) -7 NIL NIL NIL) (-757 1816198 1818903 1818944 "MSETAGG" 1818949 NIL MSETAGG (NIL T) -9 NIL 1818983 NIL) (-756 1812026 1814953 1815273 "MSET" 1815911 NIL MSET (NIL T) -8 NIL NIL NIL) (-755 1807630 1809405 1810150 "MRING" 1811326 NIL MRING (NIL T T) -8 NIL NIL NIL) (-754 1807190 1807263 1807394 "MRF2" 1807557 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-753 1806802 1806843 1806987 "MRATFAC" 1807149 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-752 1804372 1804709 1805140 "MPRFF" 1806507 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-751 1797732 1804226 1804323 "MPOLY" 1804328 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-750 1797216 1797257 1797465 "MPCPF" 1797691 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-749 1796724 1796773 1796957 "MPC3" 1797167 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-748 1795907 1796000 1796221 "MPC2" 1796639 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-747 1794184 1794545 1794935 "MONOTOOL" 1795567 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-746 1793329 1793712 1793740 "MONOID" 1793959 T MONOID (NIL) -9 NIL 1794106 NIL) (-745 1792845 1792994 1793175 "MONOID-" 1793180 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-744 1781827 1788665 1788724 "MONOGEN" 1789398 NIL MONOGEN (NIL T T) -9 NIL 1789854 NIL) (-743 1778898 1779794 1780787 "MONOGEN-" 1780906 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-742 1777615 1778163 1778191 "MONADWU" 1778583 T MONADWU (NIL) -9 NIL 1778821 NIL) (-741 1776945 1777146 1777394 "MONADWU-" 1777399 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-740 1776230 1776534 1776562 "MONAD" 1776769 T MONAD (NIL) -9 NIL 1776881 NIL) (-739 1775897 1775993 1776125 "MONAD-" 1776130 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-738 1774036 1774810 1775089 "MOEBIUS" 1775650 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-737 1773204 1773704 1773744 "MODULE" 1773749 NIL MODULE (NIL T) -9 NIL 1773788 NIL) (-736 1772742 1772868 1773058 "MODULE-" 1773063 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-735 1770316 1771150 1771477 "MODRING" 1772566 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-734 1767047 1768421 1768942 "MODOP" 1769845 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-733 1765533 1766114 1766391 "MODMONOM" 1766910 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-732 1754328 1763824 1764238 "MODMON" 1765170 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-731 1751187 1753196 1753472 "MODFIELD" 1754203 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1750098 1750468 1750658 "MMLFORM" 1751017 T MMLFORM (NIL) -8 NIL NIL NIL) (-729 1749618 1749667 1749846 "MMAP" 1750049 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-728 1747511 1748450 1748491 "MLO" 1748914 NIL MLO (NIL T) -9 NIL 1749156 NIL) (-727 1744859 1745393 1745995 "MLIFT" 1746992 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-726 1744238 1744334 1744488 "MKUCFUNC" 1744770 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-725 1743831 1743907 1744030 "MKRECORD" 1744161 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-724 1742854 1743040 1743268 "MKFUNC" 1743642 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-723 1742230 1742346 1742502 "MKFLCFN" 1742737 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-722 1741495 1741609 1741794 "MKBCFUNC" 1742123 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-721 1737494 1741049 1741185 "MINT" 1741379 T MINT (NIL) -8 NIL NIL NIL) (-720 1736276 1736549 1736826 "MHROWRED" 1737249 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-719 1731036 1734811 1735216 "MFLOAT" 1735891 T MFLOAT (NIL) -8 NIL NIL NIL) (-718 1730381 1730469 1730640 "MFINFACT" 1730948 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-717 1726680 1727559 1728438 "MESH" 1729522 T MESH (NIL) -7 NIL NIL NIL) (-716 1725034 1725382 1725735 "MDDFACT" 1726367 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-715 1721681 1724165 1724206 "MDAGG" 1724461 NIL MDAGG (NIL T) -9 NIL 1724604 NIL) (-714 1709417 1720974 1721181 "MCMPLX" 1721494 T MCMPLX (NIL) -8 NIL NIL NIL) (-713 1708536 1708700 1708901 "MCDEN" 1709266 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-712 1706384 1706696 1707076 "MCALCFN" 1708266 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-711 1705261 1705549 1705782 "MAYBE" 1706190 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-710 1702819 1703396 1703958 "MATSTOR" 1704732 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-709 1698354 1702191 1702439 "MATRIX" 1702604 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-708 1694054 1694827 1695563 "MATLIN" 1697711 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-707 1692630 1692801 1693134 "MATCAT2" 1693889 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1682077 1685684 1685761 "MATCAT" 1690796 NIL MATCAT (NIL T T T) -9 NIL 1692268 NIL) (-705 1678030 1679340 1680753 "MATCAT-" 1680758 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-704 1676106 1676466 1676850 "MAPPKG3" 1677705 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-703 1675063 1675260 1675482 "MAPPKG2" 1675930 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-702 1673520 1673846 1674173 "MAPPKG1" 1674769 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-701 1672521 1672926 1673103 "MAPPAST" 1673363 T MAPPAST (NIL) -8 NIL NIL NIL) (-700 1672126 1672190 1672313 "MAPHACK3" 1672457 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-699 1671706 1671779 1671893 "MAPHACK2" 1672058 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-698 1671132 1671247 1671389 "MAPHACK1" 1671597 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-697 1669055 1669832 1670136 "MAGMA" 1670860 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-696 1668474 1668779 1668870 "MACROAST" 1668984 T MACROAST (NIL) -8 NIL NIL NIL) (-695 1664831 1666713 1667174 "M3D" 1668046 NIL M3D (NIL T) -8 NIL NIL NIL) (-694 1658305 1663142 1663183 "LZSTAGG" 1663965 NIL LZSTAGG (NIL T) -9 NIL 1664260 NIL) (-693 1653987 1655436 1656893 "LZSTAGG-" 1656898 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-692 1650900 1651878 1652365 "LWORD" 1653532 NIL LWORD (NIL T) -8 NIL NIL NIL) (-691 1650422 1650704 1650779 "LSTAST" 1650845 T LSTAST (NIL) -8 NIL NIL NIL) (-690 1642495 1650193 1650327 "LSQM" 1650332 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-689 1641713 1641858 1642086 "LSPP" 1642350 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-688 1638513 1639212 1639925 "LSMP1" 1641032 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-687 1636318 1636642 1637091 "LSMP" 1638209 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-686 1629448 1635408 1635449 "LSAGG" 1635511 NIL LSAGG (NIL T) -9 NIL 1635589 NIL) (-685 1625957 1627067 1628280 "LSAGG-" 1628285 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-684 1623252 1625101 1625350 "LPOLY" 1625752 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-683 1622828 1622919 1623042 "LPEFRAC" 1623161 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-682 1622511 1622590 1622618 "LOGIC" 1622729 T LOGIC (NIL) -9 NIL 1622811 NIL) (-681 1622367 1622396 1622467 "LOGIC-" 1622472 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-680 1621542 1621700 1621893 "LODOOPS" 1622223 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-679 1620066 1620315 1620668 "LODOF" 1621289 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1615956 1618701 1618742 "LODOCAT" 1619180 NIL LODOCAT (NIL T) -9 NIL 1619391 NIL) (-677 1615671 1615747 1615874 "LODOCAT-" 1615879 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-676 1612671 1615512 1615630 "LODO2" 1615635 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1609792 1612608 1612653 "LODO1" 1612658 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1606901 1609708 1609774 "LODO" 1609779 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1605770 1605947 1606252 "LODEEF" 1606724 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-672 1603756 1604864 1605117 "LO" 1605602 NIL LO (NIL T T T) -8 NIL NIL NIL) (-671 1598839 1601922 1601963 "LNAGG" 1602825 NIL LNAGG (NIL T) -9 NIL 1603260 NIL) (-670 1597932 1598200 1598542 "LNAGG-" 1598547 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-669 1593912 1594857 1595496 "LMOPS" 1597347 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-668 1593211 1593689 1593730 "LMODULE" 1593735 NIL LMODULE (NIL T) -9 NIL 1593761 NIL) (-667 1590280 1592856 1592979 "LMDICT" 1593121 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-666 1589856 1590070 1590111 "LLINSET" 1590172 NIL LLINSET (NIL T) -9 NIL 1590216 NIL) (-665 1589501 1589764 1589824 "LITERAL" 1589829 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-664 1589020 1589100 1589239 "LIST3" 1589421 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-663 1587118 1587466 1587865 "LIST2MAP" 1588667 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1586107 1586303 1586531 "LIST2" 1586936 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-661 1578861 1585139 1585394 "LIST" 1585885 NIL LIST (NIL T) -8 NIL NIL NIL) (-660 1578444 1578680 1578721 "LINSET" 1578726 NIL LINSET (NIL T) -9 NIL 1578760 NIL) (-659 1577258 1577952 1578119 "LINFORM" 1578329 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-658 1575557 1576285 1576326 "LINEXP" 1576816 NIL LINEXP (NIL T) -9 NIL 1577089 NIL) (-657 1574133 1575037 1575218 "LINELT" 1575428 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-656 1572690 1572970 1573281 "LINDEP" 1573885 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-655 1571826 1572422 1572532 "LINBASIS" 1572620 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-654 1568634 1569364 1570122 "LIMITRF" 1571100 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-653 1566942 1567249 1567651 "LIMITPS" 1568336 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-652 1565770 1566345 1566385 "LIECAT" 1566525 NIL LIECAT (NIL T) -9 NIL 1566676 NIL) (-651 1565605 1565638 1565726 "LIECAT-" 1565731 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-650 1559657 1565116 1565344 "LIE" 1565426 NIL LIE (NIL T T) -8 NIL NIL NIL) (-649 1551958 1559197 1559353 "LIB" 1559521 T LIB (NIL) -8 NIL NIL NIL) (-648 1547527 1548476 1549411 "LGROBP" 1551075 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-647 1546151 1547059 1547087 "LFCAT" 1547294 T LFCAT (NIL) -9 NIL 1547433 NIL) (-646 1544089 1544423 1544773 "LF" 1545872 NIL LF (NIL T T) -7 NIL NIL NIL) (-645 1540949 1541621 1542309 "LEXTRIPK" 1543453 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-644 1537537 1538519 1539022 "LEXP" 1540529 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-643 1536953 1537258 1537350 "LETAST" 1537465 T LETAST (NIL) -8 NIL NIL NIL) (-642 1535339 1535664 1536065 "LEADCDET" 1536635 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-641 1534517 1534603 1534832 "LAZM3PK" 1535260 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-640 1529056 1532594 1533132 "LAUPOL" 1534029 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-639 1528629 1528679 1528840 "LAPLACE" 1529006 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-638 1527477 1528193 1528234 "LALG" 1528296 NIL LALG (NIL T) -9 NIL 1528355 NIL) (-637 1527173 1527250 1527386 "LALG-" 1527391 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-636 1524910 1526274 1526525 "LA" 1527006 NIL LA (NIL T T T) -8 NIL NIL NIL) (-635 1524739 1524769 1524810 "KVTFROM" 1524872 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-634 1523496 1524106 1524291 "KTVLOGIC" 1524574 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-633 1523325 1523355 1523396 "KRCFROM" 1523458 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-632 1522217 1522416 1522715 "KOVACIC" 1523125 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-631 1522046 1522076 1522117 "KONVERT" 1522179 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-630 1521875 1521905 1521946 "KOERCE" 1522008 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-629 1521359 1521452 1521584 "KERNEL2" 1521789 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-628 1519046 1519952 1520329 "KERNEL" 1521015 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-627 1512628 1517523 1517577 "KDAGG" 1517954 NIL KDAGG (NIL T T) -9 NIL 1518160 NIL) (-626 1512139 1512281 1512486 "KDAGG-" 1512491 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-625 1504955 1511800 1511955 "KAFILE" 1512017 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-624 1504559 1504844 1504907 "JVMOP" 1504912 T JVMOP (NIL) -8 NIL NIL NIL) (-623 1503295 1503799 1504048 "JVMMDACC" 1504330 T JVMMDACC (NIL) -8 NIL NIL NIL) (-622 1502231 1502685 1502890 "JVMFDACC" 1503110 T JVMFDACC (NIL) -8 NIL NIL NIL) (-621 1500812 1501307 1501607 "JVMCSTTG" 1501951 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-620 1499948 1500352 1500513 "JVMCFACC" 1500671 T JVMCFACC (NIL) -8 NIL NIL NIL) (-619 1499626 1499865 1499914 "JVMBCODE" 1499919 T JVMBCODE (NIL) -8 NIL NIL NIL) (-618 1493677 1499137 1499365 "JORDAN" 1499447 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-617 1492990 1493326 1493447 "JOINAST" 1493576 T JOINAST (NIL) -8 NIL NIL NIL) (-616 1489136 1491167 1491221 "IXAGG" 1492150 NIL IXAGG (NIL T T) -9 NIL 1492609 NIL) (-615 1487989 1488361 1488780 "IXAGG-" 1488785 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1483192 1487911 1487970 "IVECTOR" 1487975 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1481917 1482195 1482461 "ITUPLE" 1482959 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1480389 1480596 1480891 "ITRIGMNP" 1481739 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1479116 1479338 1479621 "ITFUN3" 1480165 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1478714 1478777 1478900 "ITFUN2" 1479039 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-609 1477819 1478194 1478368 "ITFORM" 1478560 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1475588 1476839 1477117 "ITAYLOR" 1477574 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1463992 1469725 1470888 "ISUPS" 1474458 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1463084 1463236 1463472 "ISUMP" 1463839 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1458048 1463029 1463070 "ISTRING" 1463075 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1457464 1457769 1457861 "ISAST" 1457976 T ISAST (NIL) -8 NIL NIL NIL) (-603 1456662 1456755 1456971 "IRURPK" 1457378 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1455574 1455799 1456039 "IRSN" 1456442 T IRSN (NIL) -7 NIL NIL NIL) (-601 1453619 1454000 1454429 "IRRF2F" 1455212 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1453360 1453404 1453480 "IRREDFFX" 1453575 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1451933 1452234 1452533 "IROOT" 1453093 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1451072 1451426 1451577 "IRFORM" 1451802 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1450154 1450285 1450499 "IR2F" 1450955 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1447743 1448262 1448828 "IR2" 1449632 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1444183 1445427 1446119 "IR" 1447083 NIL IR (NIL T) -8 NIL NIL NIL) (-594 1443968 1444008 1444068 "IPRNTPK" 1444143 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1439944 1443857 1443926 "IPF" 1443931 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1437974 1439869 1439926 "IPADIC" 1439931 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1437232 1437534 1437664 "IP4ADDR" 1437864 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1436570 1436861 1436993 "IOMODE" 1437120 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1435541 1436167 1436294 "IOBFILE" 1436463 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1434951 1435445 1435473 "IOBCON" 1435478 T IOBCON (NIL) -9 NIL 1435499 NIL) (-587 1434456 1434520 1434703 "INVLAPLA" 1434887 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1424074 1426494 1428868 "INTTR" 1432132 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1420367 1421151 1422016 "INTTOOLS" 1423259 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1419947 1420044 1420161 "INTSLPE" 1420270 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1417414 1419870 1419929 "INTRVL" 1419934 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1414992 1415528 1416103 "INTRF" 1416899 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1414385 1414500 1414642 "INTRET" 1414890 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1412358 1412771 1413241 "INTRAT" 1413993 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1409603 1410204 1410823 "INTPM" 1411843 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1406343 1406963 1407694 "INTPAF" 1408996 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1401444 1402484 1403535 "INTPACK" 1405312 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1400690 1400848 1401056 "INTHERTR" 1401286 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1400123 1400209 1400397 "INTHERAL" 1400604 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1397891 1398412 1398869 "INTHEORY" 1399686 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1389281 1390958 1392712 "INTG0" 1396261 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1375506 1378919 1382304 "INTFTBL" 1385916 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1374731 1374893 1375066 "INTFACT" 1375365 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1372134 1372608 1373163 "INTEF" 1374287 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1370331 1371226 1371254 "INTDOM" 1371555 T INTDOM (NIL) -9 NIL 1371762 NIL) (-568 1369670 1369874 1370116 "INTDOM-" 1370121 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1365538 1367959 1368013 "INTCAT" 1368812 NIL INTCAT (NIL T) -9 NIL 1369133 NIL) (-566 1364992 1365113 1365241 "INTBIT" 1365430 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1363673 1363845 1364152 "INTALG" 1364837 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1363150 1363246 1363403 "INTAF" 1363577 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1356233 1362960 1363100 "INTABL" 1363105 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1355474 1356036 1356101 "INT8" 1356135 T INT8 (NIL) -8 NIL NIL 1356180) (-561 1354714 1355276 1355341 "INT64" 1355375 T INT64 (NIL) -8 NIL NIL 1355420) (-560 1353954 1354516 1354581 "INT32" 1354615 T INT32 (NIL) -8 NIL NIL 1354660) (-559 1353194 1353756 1353821 "INT16" 1353855 T INT16 (NIL) -8 NIL NIL 1353900) (-558 1349546 1353005 1353107 "INT" 1353112 T INT (NIL) -8 NIL NIL NIL) (-557 1343657 1347094 1347122 "INS" 1348056 T INS (NIL) -9 NIL 1348721 NIL) (-556 1340814 1341734 1342675 "INS-" 1342748 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1339644 1339867 1340143 "INPSIGN" 1340589 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1338738 1338879 1339076 "INPRODPF" 1339524 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1337608 1337749 1337986 "INPRODFF" 1338618 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1336596 1336760 1337020 "INNMFACT" 1337444 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1335775 1335890 1336078 "INMODGCD" 1336495 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1334259 1334528 1334852 "INFSP" 1335520 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1333419 1333560 1333743 "INFPROD0" 1334139 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1333017 1333089 1333187 "INFORM1" 1333354 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1329584 1331082 1331597 "INFORM" 1332510 T INFORM (NIL) -8 NIL NIL NIL) (-546 1329089 1329196 1329310 "INFINITY" 1329490 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1328163 1328809 1328910 "INETCLTS" 1329008 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1326761 1327029 1327350 "INEP" 1327911 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1325791 1326658 1326723 "INDE" 1326728 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1325343 1325423 1325540 "INCRMAPS" 1325718 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1324065 1324612 1324818 "INBFILE" 1325157 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1319245 1320301 1321245 "INBFF" 1323153 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1318099 1318422 1318450 "INBCON" 1318963 T INBCON (NIL) -9 NIL 1319229 NIL) (-538 1317309 1317574 1317850 "INBCON-" 1317855 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1316728 1317033 1317124 "INAST" 1317238 T INAST (NIL) -8 NIL NIL NIL) (-536 1316095 1316407 1316513 "IMPTAST" 1316642 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1312129 1315939 1316043 "IMATRIX" 1316048 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1310821 1310960 1311276 "IMATQF" 1311985 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1309001 1309268 1309605 "IMATLIN" 1310577 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1302918 1308925 1308983 "ILIST" 1308988 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1300698 1302778 1302891 "IIARRAY2" 1302896 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1295521 1300609 1300673 "IFF" 1300678 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1294802 1295138 1295254 "IFAST" 1295425 T IFAST (NIL) -8 NIL NIL NIL) (-528 1289428 1294094 1294282 "IFARRAY" 1294659 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1288466 1289332 1289405 "IFAMON" 1289410 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1288038 1288115 1288169 "IEVALAB" 1288376 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1287701 1287781 1287941 "IEVALAB-" 1287946 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1286734 1287590 1287665 "IDPOAMS" 1287670 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1285836 1286623 1286698 "IDPOAM" 1286703 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1285217 1285751 1285813 "IDPO" 1285818 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1283697 1284224 1284276 "IDPC" 1284788 NIL IDPC (NIL T T) -9 NIL 1285069 NIL) (-520 1283029 1283589 1283662 "IDPAM" 1283667 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1282244 1282921 1282994 "IDPAG" 1282999 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1281788 1282050 1282140 "IDENT" 1282174 T IDENT (NIL) -8 NIL NIL NIL) (-517 1278007 1278891 1279786 "IDECOMP" 1280945 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1270642 1271930 1272977 "IDEAL" 1277043 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1269784 1269914 1270114 "ICDEN" 1270526 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1268759 1269264 1269411 "ICARD" 1269657 T ICARD (NIL) -8 NIL NIL NIL) (-513 1266789 1267132 1267537 "IBPTOOLS" 1268436 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1262018 1266409 1266522 "IBITS" 1266708 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1258693 1259317 1260012 "IBATOOL" 1261435 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1256454 1256934 1257467 "IBACHIN" 1258228 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1254158 1256300 1256403 "IARRAY2" 1256408 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1249985 1254084 1254141 "IARRAY1" 1254146 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1243011 1248397 1248878 "IAN" 1249524 T IAN (NIL) -8 NIL NIL NIL) (-506 1242516 1242579 1242752 "IALGFACT" 1242948 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1242008 1242157 1242185 "HYPCAT" 1242392 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1241510 1241663 1241849 "HYPCAT-" 1241854 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1241057 1241305 1241388 "HOSTNAME" 1241447 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1240890 1240939 1240980 "HOMOTOP" 1240985 NIL HOMOTOP (NIL T) -9 NIL 1241018 NIL) (-501 1237434 1238822 1238863 "HOAGG" 1239844 NIL HOAGG (NIL T) -9 NIL 1240573 NIL) (-500 1235950 1236427 1236953 "HOAGG-" 1236958 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1229023 1235543 1235693 "HEXADEC" 1235820 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1227735 1227993 1228256 "HEUGCD" 1228800 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1226667 1227572 1227702 "HELLFDIV" 1227707 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1224791 1226444 1226532 "HEAP" 1226611 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1223988 1224343 1224477 "HEADAST" 1224677 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1217447 1223903 1223965 "HDP" 1223970 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1210492 1217082 1217234 "HDMP" 1217348 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1209798 1209956 1210120 "HB" 1210348 T HB (NIL) -7 NIL NIL NIL) (-491 1202924 1209644 1209748 "HASHTBL" 1209753 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1202340 1202645 1202737 "HASAST" 1202852 T HASAST (NIL) -8 NIL NIL NIL) (-489 1199757 1201962 1202144 "HACKPI" 1202178 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1195070 1199610 1199723 "GTSET" 1199728 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1188225 1194948 1195046 "GSTBL" 1195051 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1179990 1187390 1187646 "GSERIES" 1188025 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1179021 1179534 1179562 "GROUP" 1179765 T GROUP (NIL) -9 NIL 1179899 NIL) (-484 1178345 1178546 1178797 "GROUP-" 1178802 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1176694 1177033 1177420 "GROEBSOL" 1178022 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1175522 1175882 1175933 "GRMOD" 1176462 NIL GRMOD (NIL T T) -9 NIL 1176630 NIL) (-481 1175278 1175326 1175454 "GRMOD-" 1175459 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1170418 1171632 1172632 "GRIMAGE" 1174298 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1168812 1169145 1169469 "GRDEF" 1170114 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1168244 1168372 1168513 "GRAY" 1168691 T GRAY (NIL) -7 NIL NIL NIL) (-477 1167321 1167823 1167874 "GRALG" 1168027 NIL GRALG (NIL T T) -9 NIL 1168120 NIL) (-476 1166958 1167055 1167218 "GRALG-" 1167223 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1163553 1166541 1166720 "GPOLSET" 1166864 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1162901 1162964 1163222 "GOSPER" 1163490 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1158471 1159339 1159865 "GMODPOL" 1162600 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1157458 1157660 1157898 "GHENSEL" 1158283 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1151530 1152457 1153477 "GENUPS" 1156542 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1151221 1151278 1151367 "GENUFACT" 1151473 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1150621 1150710 1150875 "GENPGCD" 1151139 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1150089 1150130 1150343 "GENMFACT" 1150580 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1148626 1148912 1149219 "GENEEZ" 1149832 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1141830 1148237 1148399 "GDMP" 1148549 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1130590 1135601 1136707 "GCNAALG" 1140813 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1128717 1129765 1129793 "GCDDOM" 1130048 T GCDDOM (NIL) -9 NIL 1130205 NIL) (-463 1128157 1128314 1128529 "GCDDOM-" 1128534 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1116629 1119103 1121495 "GBINTERN" 1125848 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1114430 1114758 1115179 "GBF" 1116304 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1113187 1113376 1113643 "GBEUCLID" 1114246 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1111837 1112044 1112348 "GB" 1112966 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-458 1111168 1111311 1111460 "GAUSSFAC" 1111708 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1109489 1109837 1110151 "GALUTIL" 1110887 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1107749 1108071 1108395 "GALPOLYU" 1109216 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1105048 1105404 1105811 "GALFACTU" 1107446 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1096662 1098353 1099961 "GALFACT" 1103480 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1093948 1094708 1094736 "FVFUN" 1095892 T FVFUN (NIL) -9 NIL 1096612 NIL) (-452 1093178 1093396 1093424 "FVC" 1093715 T FVC (NIL) -9 NIL 1093898 NIL) (-451 1092779 1093003 1093071 "FUNDESC" 1093130 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1092352 1092576 1092657 "FUNCTION" 1092731 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1091029 1091653 1091856 "FTEM" 1092169 T FTEM (NIL) -8 NIL NIL NIL) (-448 1088671 1089360 1089823 "FT" 1090586 T FT (NIL) -8 NIL NIL NIL) (-447 1086940 1087251 1087648 "FSUPFACT" 1088362 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1085259 1085626 1085958 "FST" 1086628 T FST (NIL) -8 NIL NIL NIL) (-445 1084440 1084564 1084752 "FSRED" 1085141 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1083129 1083395 1083742 "FSPRMELT" 1084155 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1080339 1080873 1081359 "FSPECF" 1082692 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1079861 1079921 1080091 "FSINT" 1080280 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 1077997 1078854 1079157 "FSERIES" 1079640 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 1077021 1077155 1077379 "FSCINT" 1077877 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 1076045 1076206 1076433 "FSAGG2" 1076874 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-438 1072020 1074989 1075030 "FSAGG" 1075400 NIL FSAGG (NIL T) -9 NIL 1075659 NIL) (-437 1069620 1070383 1071179 "FSAGG-" 1071274 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 1067280 1067578 1068126 "FS2UPS" 1069338 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 1066146 1066329 1066631 "FS2EXPXP" 1067105 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-434 1065774 1065823 1065952 "FS2" 1066097 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 1046041 1055548 1055589 "FS" 1059473 NIL FS (NIL T) -9 NIL 1061762 NIL) (-432 1034183 1037731 1041761 "FS-" 1042061 NIL FS- (NIL T T) -8 NIL NIL NIL) (-431 1033597 1033724 1033876 "FRUTIL" 1034063 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 1028140 1031286 1031326 "FRNAALG" 1032646 NIL FRNAALG (NIL T) -9 NIL 1033244 NIL) (-429 1023672 1024923 1026181 "FRNAALG-" 1026931 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 1023304 1023353 1023480 "FRNAAF2" 1023623 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 1021591 1022153 1022449 "FRMOD" 1023116 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 1020776 1020869 1021160 "FRIDEAL2" 1021498 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 1018381 1019151 1019469 "FRIDEAL" 1020567 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 1017479 1017928 1017969 "FRETRCT" 1017974 NIL FRETRCT (NIL T) -9 NIL 1018150 NIL) (-423 1016558 1016836 1017180 "FRETRCT-" 1017185 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 1013379 1014842 1014901 "FRAMALG" 1015783 NIL FRAMALG (NIL T T) -9 NIL 1016075 NIL) (-421 1011417 1011968 1012598 "FRAMALG-" 1012821 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 1011047 1011110 1011217 "FRAC2" 1011354 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 1004534 1010692 1010883 "FRAC" 1010888 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 1004164 1004227 1004334 "FR2" 1004471 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 995196 999740 1001071 "FR" 1002865 NIL FR (NIL T) -8 NIL NIL NIL) (-416 989119 992575 992603 "FPS" 993722 T FPS (NIL) -9 NIL 994279 NIL) (-415 988544 988677 988841 "FPS-" 988987 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 985512 987501 987529 "FPC" 987754 T FPC (NIL) -9 NIL 987896 NIL) (-413 985293 985345 985442 "FPC-" 985447 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 984051 984781 984822 "FPATMAB" 984827 NIL FPATMAB (NIL T) -9 NIL 984979 NIL) (-411 982194 982793 983140 "FPARFRAC" 983767 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 977525 978125 978807 "FORTRAN" 981626 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 975099 975763 975791 "FORTFN" 976851 T FORTFN (NIL) -9 NIL 977475 NIL) (-408 974851 974913 974941 "FORTCAT" 975000 T FORTCAT (NIL) -9 NIL 975062 NIL) (-407 972537 973067 973606 "FORT" 974332 T FORT (NIL) -7 NIL NIL NIL) (-406 972054 972112 972285 "FORDER" 972479 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 971114 971314 971507 "FOP" 971881 T FOP (NIL) -7 NIL NIL NIL) (-404 969527 970394 970568 "FNLA" 970996 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 968146 968657 968685 "FNCAT" 969145 T FNCAT (NIL) -9 NIL 969405 NIL) (-402 967589 968105 968133 "FNAME" 968138 T FNAME (NIL) -8 NIL NIL NIL) (-401 965915 967088 967116 "FMTC" 967121 T FMTC (NIL) -9 NIL 967157 NIL) (-400 964471 965851 965897 "FMONOID" 965902 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 961060 962426 962467 "FMONCAT" 963684 NIL FMONCAT (NIL T) -9 NIL 964289 NIL) (-398 958382 959130 959158 "FMFUN" 960302 T FMFUN (NIL) -9 NIL 961010 NIL) (-397 955255 956307 956361 "FMCAT" 957556 NIL FMCAT (NIL T T) -9 NIL 958051 NIL) (-396 954488 954705 954733 "FMC" 955023 T FMC (NIL) -9 NIL 955205 NIL) (-395 953156 954254 954354 "FM1" 954433 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 952174 952898 953047 "FM" 953052 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 949912 950364 950858 "FLOATRP" 951725 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 947314 947850 948428 "FLOATCP" 949379 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 940132 945057 945671 "FLOAT" 946720 T FLOAT (NIL) -8 NIL NIL NIL) (-390 938650 939724 939765 "FLINEXP" 939770 NIL FLINEXP (NIL T) -9 NIL 939863 NIL) (-389 937780 938039 938367 "FLINEXP-" 938372 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 936838 937000 937224 "FLASORT" 937632 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 933756 934808 934860 "FLALG" 936087 NIL FLALG (NIL T T) -9 NIL 936554 NIL) (-386 932780 932941 933168 "FLAGG2" 933609 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 926149 930189 930230 "FLAGG" 931492 NIL FLAGG (NIL T) -9 NIL 932144 NIL) (-384 924803 925214 925704 "FLAGG-" 925709 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 921441 922648 922707 "FINRALG" 923835 NIL FINRALG (NIL T T) -9 NIL 924343 NIL) (-382 920565 920830 921169 "FINRALG-" 921174 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 919871 920170 920198 "FINITE" 920394 T FINITE (NIL) -9 NIL 920501 NIL) (-380 911822 914401 914441 "FINAALG" 918108 NIL FINAALG (NIL T) -9 NIL 919561 NIL) (-379 906938 908204 909348 "FINAALG-" 910727 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 905498 905920 905974 "FILECAT" 906658 NIL FILECAT (NIL T T) -9 NIL 906874 NIL) (-377 904776 905253 905356 "FILE" 905428 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 902181 904006 904034 "FIELD" 904074 T FIELD (NIL) -9 NIL 904154 NIL) (-375 900723 901186 901697 "FIELD-" 901702 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 898406 899358 899705 "FGROUP" 900409 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 897478 897660 897880 "FGLMICPK" 898238 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 892735 897403 897460 "FFX" 897465 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 892330 892397 892532 "FFSLPE" 892668 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 891828 891870 892079 "FFPOLY2" 892288 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 887704 888600 889396 "FFPOLY" 891064 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 882975 887623 887686 "FFP" 887691 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 877508 882318 882508 "FFNBX" 882829 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 871843 876643 876901 "FFNBP" 877362 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 865883 871127 871338 "FFNB" 871676 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 864703 864913 865228 "FFINTBAS" 865680 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 860298 862950 862978 "FFIELDC" 863598 T FFIELDC (NIL) -9 NIL 863974 NIL) (-362 858918 859359 859842 "FFIELDC-" 859847 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 858475 858533 858657 "FFHOM" 858860 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 856134 856657 857174 "FFF" 857990 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 851171 855876 855977 "FFCGX" 856077 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 846212 850903 851010 "FFCGP" 851114 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 840814 845939 846047 "FFCG" 846148 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 840219 840268 840503 "FFCAT2" 840765 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 818910 829951 830037 "FFCAT" 835202 NIL FFCAT (NIL T T T) -9 NIL 836653 NIL) (-354 813921 815155 816469 "FFCAT-" 817699 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 808744 813832 813896 "FF" 813901 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 797399 801716 802936 "FEXPR" 807596 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 796327 796796 796837 "FEVALAB" 796921 NIL FEVALAB (NIL T) -9 NIL 797182 NIL) (-350 795444 795696 796034 "FEVALAB-" 796039 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 792306 793191 793306 "FDIVCAT" 794874 NIL FDIVCAT (NIL T T T T) -9 NIL 795311 NIL) (-348 792062 792095 792265 "FDIVCAT-" 792270 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 791276 791369 791646 "FDIV2" 791969 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 789686 790659 790862 "FDIV" 791175 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 788594 788981 789183 "FCTRDATA" 789504 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 787250 787539 787828 "FCPAK1" 788325 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 786253 786750 786891 "FCOMP" 787141 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 769567 773403 776941 "FC" 782735 T FC (NIL) -8 NIL NIL NIL) (-341 761278 765888 765928 "FAXF" 767730 NIL FAXF (NIL T) -9 NIL 768422 NIL) (-340 758419 759226 760044 "FAXF-" 760509 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 753102 757795 757971 "FARRAY" 758276 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 747674 750049 750102 "FAMR" 751125 NIL FAMR (NIL T T) -9 NIL 751585 NIL) (-337 746498 746866 747301 "FAMR-" 747306 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 745525 746420 746473 "FAMONOID" 746478 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 743155 744007 744060 "FAMONC" 745001 NIL FAMONC (NIL T T) -9 NIL 745387 NIL) (-334 741629 742909 743046 "FAGROUP" 743051 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 739382 739743 740146 "FACUTIL" 741310 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 738469 738666 738888 "FACTFUNC" 739192 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 730212 737772 737971 "EXPUPXS" 738325 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 727665 728235 728821 "EXPRTUBE" 729646 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 723876 724528 725258 "EXPRODE" 727004 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 718310 719017 719823 "EXPR2UPS" 723174 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 717936 717999 718108 "EXPR2" 718247 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 702305 716585 717014 "EXPR" 717540 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 692664 701456 701747 "EXPEXPAN" 702141 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 692084 692388 692479 "EXITAST" 692593 T EXITAST (NIL) -8 NIL NIL NIL) (-323 691848 692041 692070 "EXIT" 692075 T EXIT (NIL) -8 NIL NIL NIL) (-322 691469 691537 691650 "EVALCYC" 691780 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 690986 691128 691169 "EVALAB" 691339 NIL EVALAB (NIL T) -9 NIL 691443 NIL) (-320 690443 690589 690810 "EVALAB-" 690815 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 687558 689099 689127 "EUCDOM" 689682 T EUCDOM (NIL) -9 NIL 690032 NIL) (-318 685918 686419 687002 "EUCDOM-" 687007 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 685544 685607 685716 "ESTOOLS2" 685855 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 685289 685337 685417 "ESTOOLS1" 685496 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 672606 675587 678337 "ESTOOLS" 682559 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 672345 672383 672465 "ESCONT1" 672568 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 668653 669480 670260 "ESCONT" 671585 T ESCONT (NIL) -7 NIL NIL NIL) (-312 668322 668378 668478 "ES2" 668597 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 667946 668010 668119 "ES1" 668258 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 661647 663577 663605 "ES" 666373 T ES (NIL) -9 NIL 667783 NIL) (-309 656324 657881 659698 "ES-" 659862 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 655516 655669 655845 "ERROR" 656168 T ERROR (NIL) -7 NIL NIL NIL) (-307 648648 655375 655466 "EQTBL" 655471 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 648274 648337 648446 "EQ2" 648585 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 640533 643588 645037 "EQ" 646858 NIL -4033 (NIL T) -8 NIL NIL NIL) (-304 635775 636871 637964 "EP" 639472 NIL EP (NIL T) -7 NIL NIL NIL) (-303 634315 634666 634972 "ENV" 635489 T ENV (NIL) -8 NIL NIL NIL) (-302 633275 633949 633977 "ENTIRER" 633982 T ENTIRER (NIL) -9 NIL 634028 NIL) (-301 629740 631501 631862 "EMR" 633083 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 628844 629055 629109 "ELTAGG" 629489 NIL ELTAGG (NIL T T) -9 NIL 629700 NIL) (-299 628551 628625 628766 "ELTAGG-" 628771 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 628309 628344 628398 "ELTAB" 628482 NIL ELTAB (NIL T T) -9 NIL 628534 NIL) (-297 627411 627581 627780 "ELFUTS" 628160 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 627135 627209 627237 "ELEMFUN" 627342 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 626999 627026 627094 "ELEMFUN-" 627099 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 621524 625041 625082 "ELAGG" 626022 NIL ELAGG (NIL T) -9 NIL 626485 NIL) (-293 619701 620243 620906 "ELAGG-" 620911 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 618983 619150 619306 "ELABOR" 619565 T ELABOR (NIL) -8 NIL NIL NIL) (-291 617589 617923 618217 "ELABEXPR" 618709 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 610228 612226 613055 "EFUPXS" 616864 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 603481 605477 606288 "EFULS" 609503 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 600918 601324 601796 "EFSTRUC" 603113 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 590356 592275 593823 "EF" 599433 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 589334 589841 589990 "EAB" 590227 T EAB (NIL) -8 NIL NIL NIL) (-285 588456 589293 589321 "E04UCFA" 589326 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 587578 588415 588443 "E04NAFA" 588448 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 586700 587537 587565 "E04MBFA" 587570 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 585822 586659 586687 "E04JAFA" 586692 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 584946 585781 585809 "E04GCFA" 585814 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 584070 584905 584933 "E04FDFA" 584938 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 583192 584029 584057 "E04DGFA" 584062 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 577269 578717 580081 "E04AGNT" 581848 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 575889 576570 576610 "DVARCAT" 576951 NIL DVARCAT (NIL T) -9 NIL 577114 NIL) (-276 575039 575305 575619 "DVARCAT-" 575624 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 567043 574838 574967 "DSMP" 574972 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 565394 566185 566226 "DSEXT" 566589 NIL DSEXT (NIL T) -9 NIL 566883 NIL) (-273 563583 564107 564773 "DSEXT-" 564778 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 563242 563307 563405 "DROPT1" 563518 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 558261 559483 560620 "DROPT0" 562125 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 552844 554206 555274 "DROPT" 557213 T DROPT (NIL) -8 NIL NIL NIL) (-269 551153 551514 551900 "DRAWPT" 552478 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 550780 550839 550957 "DRAWHACK" 551094 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 549481 549780 550071 "DRAWCX" 550509 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 548990 549065 549216 "DRAWCURV" 549407 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 539308 541420 543535 "DRAWCFUN" 546895 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 533799 534818 535897 "DRAW" 538282 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 530381 532464 532505 "DQAGG" 533134 NIL DQAGG (NIL T) -9 NIL 533408 NIL) (-262 516995 524592 524675 "DPOLCAT" 526527 NIL DPOLCAT (NIL T T T T) -9 NIL 527072 NIL) (-261 511565 513214 515155 "DPOLCAT-" 515160 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 504494 511426 511524 "DPMO" 511529 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 497320 504274 504441 "DPMM" 504446 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 496842 497104 497193 "DOMTMPLT" 497251 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 496191 496644 496724 "DOMCTOR" 496782 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 495343 495671 495822 "DOMAIN" 496060 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 488388 494978 495130 "DMP" 495244 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 486165 487455 487496 "DMEXT" 487501 NIL DMEXT (NIL T) -9 NIL 487677 NIL) (-253 485759 485821 485965 "DLP" 486103 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 478884 485086 485276 "DLIST" 485601 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 475534 477709 477750 "DLAGG" 478300 NIL DLAGG (NIL T) -9 NIL 478530 NIL) (-250 474046 474860 474888 "DIVRING" 474980 T DIVRING (NIL) -9 NIL 475063 NIL) (-249 473229 473473 473773 "DIVRING-" 473778 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 471271 471688 472094 "DISPLAY" 472843 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 470101 470322 470587 "DIRPROD2" 471064 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 463580 470015 470078 "DIRPROD" 470083 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 451864 458291 458344 "DIRPCAT" 458602 NIL DIRPCAT (NIL NIL T) -9 NIL 459477 NIL) (-244 449064 449832 450713 "DIRPCAT-" 451050 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 448345 448511 448697 "DIOSP" 448898 T DIOSP (NIL) -7 NIL NIL NIL) (-242 444870 447229 447270 "DIOPS" 447704 NIL DIOPS (NIL T) -9 NIL 447933 NIL) (-241 444389 444533 444724 "DIOPS-" 444729 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 443296 444068 444096 "DIFRING" 444101 T DIFRING (NIL) -9 NIL 444123 NIL) (-239 442944 443042 443070 "DIFFSPC" 443189 T DIFFSPC (NIL) -9 NIL 443264 NIL) (-238 442565 442667 442819 "DIFFSPC-" 442824 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 441501 442099 442140 "DIFFMOD" 442145 NIL DIFFMOD (NIL T) -9 NIL 442243 NIL) (-236 441197 441254 441295 "DIFFDOM" 441416 NIL DIFFDOM (NIL T) -9 NIL 441484 NIL) (-235 441044 441074 441158 "DIFFDOM-" 441163 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 438784 440248 440289 "DIFEXT" 440294 NIL DIFEXT (NIL T) -9 NIL 440447 NIL) (-233 435929 438288 438329 "DIAGG" 438334 NIL DIAGG (NIL T) -9 NIL 438354 NIL) (-232 435277 435470 435722 "DIAGG-" 435727 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 430240 434236 434513 "DHMATRIX" 435046 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 425708 426761 427771 "DFSFUN" 429250 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 419972 424552 424880 "DFLOAT" 425400 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 418211 418516 418905 "DFINTTLS" 419680 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 415030 416232 416632 "DERHAM" 417877 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 412680 414805 414894 "DEQUEUE" 414974 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 411922 412067 412250 "DEGRED" 412542 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 408508 409232 410033 "DEFINTRF" 411195 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 406157 406616 407180 "DEFINTEF" 408055 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 405441 405777 405892 "DEFAST" 406062 T DEFAST (NIL) -8 NIL NIL NIL) (-221 398514 405034 405184 "DECIMAL" 405311 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 395972 396484 396990 "DDFACT" 398058 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 395562 395611 395762 "DBLRESP" 395923 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 394763 395332 395423 "DBASIS" 395511 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 392547 392993 393354 "DBASE" 394529 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 391735 392027 392173 "DATAARY" 392446 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 390793 391694 391722 "D03FAFA" 391727 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 389852 390752 390780 "D03EEFA" 390785 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 387778 388268 388757 "D03AGNT" 389383 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 387019 387737 387765 "D02EJFA" 387770 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 386260 386978 387006 "D02CJFA" 387011 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 385501 386219 386247 "D02BHFA" 386252 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 384742 385460 385488 "D02BBFA" 385493 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 377873 379528 381134 "D02AGNT" 383156 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 375623 376164 376710 "D01WGTS" 377347 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 374630 375582 375610 "D01TRNS" 375615 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 373638 374589 374617 "D01GBFA" 374622 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 372646 373597 373625 "D01FCFA" 373630 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 371654 372605 372633 "D01ASFA" 372638 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 370662 371613 371641 "D01AQFA" 371646 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 369670 370621 370649 "D01APFA" 370654 T D01APFA (NIL) -8 NIL NIL NIL) (-200 368678 369629 369657 "D01ANFA" 369662 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 367686 368637 368665 "D01AMFA" 368670 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 366694 367645 367673 "D01ALFA" 367678 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 365702 366653 366681 "D01AKFA" 366686 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 364710 365661 365689 "D01AJFA" 365694 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 357933 359558 361119 "D01AGNT" 363169 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 357252 357398 357550 "CYCLOTOM" 357801 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 353907 354700 355427 "CYCLES" 356545 T CYCLES (NIL) -7 NIL NIL NIL) (-192 353207 353353 353524 "CVMP" 353768 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 350994 351306 351675 "CTRIGMNP" 352935 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 350467 350725 350826 "CTORKIND" 350913 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 349672 350060 350088 "CTORCAT" 350270 T CTORCAT (NIL) -9 NIL 350383 NIL) (-188 349246 349381 349540 "CTORCAT-" 349545 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 348660 348920 349028 "CTORCALL" 349170 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 348018 348454 348527 "CTOR" 348607 T CTOR (NIL) -8 NIL NIL NIL) (-185 347374 347491 347644 "CSTTOOLS" 347915 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 343071 343830 344588 "CRFP" 346686 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 342486 342792 342884 "CRCEAST" 342999 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 341509 341718 341946 "CRAPACK" 342290 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 340889 340994 341198 "CPMATCH" 341385 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 340608 340642 340748 "CPIMA" 340855 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 336866 337628 338347 "COORDSYS" 339943 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 336254 336399 336541 "CONTOUR" 336744 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 331727 334257 334749 "CONTFRAC" 335794 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 331601 331628 331656 "CONDUIT" 331693 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 330555 331229 331257 "COMRING" 331262 T COMRING (NIL) -9 NIL 331314 NIL) (-174 329537 329913 330097 "COMPPROP" 330391 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 329192 329233 329361 "COMPLPAT" 329496 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 328822 328885 328992 "COMPLEX2" 329129 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 317566 328759 328804 "COMPLEX" 328809 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 316887 317026 317186 "COMPILER" 317426 T COMPILER (NIL) -8 NIL NIL NIL) (-169 316599 316640 316738 "COMPFACT" 316846 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298002 310303 310343 "COMPCAT" 311347 NIL COMPCAT (NIL T) -9 NIL 312695 NIL) (-167 286911 290455 294075 "COMPCAT-" 294431 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 286634 286668 286771 "COMMUPC" 286877 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 286422 286462 286521 "COMMONOP" 286595 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 285944 286226 286301 "COMMAAST" 286367 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 285451 285695 285782 "COMM" 285877 T COMM (NIL) -8 NIL NIL NIL) (-162 284646 284894 284922 "COMBOPC" 285260 T COMBOPC (NIL) -9 NIL 285435 NIL) (-161 283500 283752 283994 "COMBINAT" 284436 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 279843 280531 281158 "COMBF" 282922 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 278505 278959 279194 "COLOR" 279628 T COLOR (NIL) -8 NIL NIL NIL) (-158 277921 278226 278318 "COLONAST" 278433 T COLONAST (NIL) -8 NIL NIL NIL) (-157 277555 277608 277733 "CMPLXRT" 277868 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 276943 277255 277354 "CLLCTAST" 277476 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 272403 273473 274553 "CLIP" 275883 T CLIP (NIL) -7 NIL NIL NIL) (-154 270576 271504 271744 "CLIF" 272230 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 266669 268694 268735 "CLAGG" 269664 NIL CLAGG (NIL T) -9 NIL 270200 NIL) (-152 265013 265548 266131 "CLAGG-" 266136 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 264551 264642 264782 "CINTSLPE" 264922 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262016 262523 263071 "CHVAR" 264079 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261056 261730 261758 "CHARZ" 261763 T CHARZ (NIL) -9 NIL 261778 NIL) (-148 260804 260850 260928 "CHARPOL" 261010 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 259722 260428 260456 "CHARNZ" 260517 T CHARNZ (NIL) -9 NIL 260566 NIL) (-146 256666 257776 258305 "CHAR" 259213 T CHAR (NIL) -8 NIL NIL NIL) (-145 256374 256453 256481 "CFCAT" 256592 T CFCAT (NIL) -9 NIL NIL NIL) (-144 255597 255726 255909 "CDEN" 256258 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 251308 254750 255030 "CCLASS" 255337 T CCLASS (NIL) -8 NIL NIL NIL) (-142 250529 250716 250893 "CATEGORY" 251151 T -10 (NIL) -8 NIL NIL NIL) (-141 250024 250448 250496 "CATCTOR" 250501 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 249415 249727 249825 "CATAST" 249946 T CATAST (NIL) -8 NIL NIL NIL) (-139 248831 249136 249228 "CASEAST" 249343 T CASEAST (NIL) -8 NIL NIL NIL) (-138 247927 248087 248308 "CARTEN2" 248678 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 242824 244084 244828 "CARTEN" 247239 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 240954 241974 242231 "CARD" 242587 T CARD (NIL) -8 NIL NIL NIL) (-135 240476 240758 240833 "CAPSLAST" 240899 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 239918 240174 240202 "CACHSET" 240334 T CACHSET (NIL) -9 NIL 240412 NIL) (-133 239308 239696 239724 "CABMON" 239774 T CABMON (NIL) -9 NIL 239830 NIL) (-132 238745 239012 239122 "BYTEORD" 239218 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 233786 238250 238422 "BYTEBUF" 238593 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 232617 233329 233464 "BYTE" 233627 T BYTE (NIL) -8 NIL NIL 233742) (-129 229995 232309 232416 "BTREE" 232543 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 227313 229643 229765 "BTOURN" 229905 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 224533 226755 226796 "BTCAT" 226864 NIL BTCAT (NIL T) -9 NIL 226941 NIL) (-126 224182 224280 224429 "BTCAT-" 224434 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 219185 223428 223456 "BTAGG" 223570 T BTAGG (NIL) -9 NIL 223680 NIL) (-124 218639 218800 219006 "BTAGG-" 219011 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 215491 217917 218132 "BSTREE" 218456 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 214599 214755 214939 "BRILL" 215347 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 211106 213297 213338 "BRAGG" 213987 NIL BRAGG (NIL T) -9 NIL 214245 NIL) (-120 209542 210043 210597 "BRAGG-" 210602 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 201815 208886 209071 "BPADICRT" 209389 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 199833 201752 201797 "BPADIC" 201802 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 199525 199561 199675 "BOUNDZRO" 199797 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197252 197710 198185 "BOP1" 199083 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 192282 193712 194610 "BOP" 196374 T BOP (NIL) -8 NIL NIL NIL) (-114 191042 191940 192064 "BOOLEAN" 192178 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 190635 190792 190820 "BOOLE" 190931 T BOOLE (NIL) -9 NIL 191012 NIL) (-112 190503 190530 190596 "BOOLE-" 190601 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 189672 190172 190226 "BMODULE" 190231 NIL BMODULE (NIL T T) -9 NIL 190296 NIL) (-110 185107 189470 189543 "BITS" 189619 T BITS (NIL) -8 NIL NIL NIL) (-109 184504 184647 184787 "BINDING" 184987 T BINDING (NIL) -8 NIL NIL NIL) (-108 177580 184099 184248 "BINARY" 184375 T BINARY (NIL) -8 NIL NIL NIL) (-107 175298 176807 176848 "BGAGG" 177108 NIL BGAGG (NIL T) -9 NIL 177245 NIL) (-106 175123 175161 175252 "BGAGG-" 175257 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 174146 174507 174712 "BFUNCT" 174938 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 172810 173011 173299 "BEZOUT" 173970 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 169124 171662 171992 "BBTREE" 172513 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 168707 168803 168831 "BASTYPE" 169008 T BASTYPE (NIL) -9 NIL 169107 NIL) (-101 168365 168464 168599 "BASTYPE-" 168604 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 167787 167875 168027 "BALFACT" 168276 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 166523 167202 167388 "AUTOMOR" 167632 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 166249 166254 166280 "ATTREG" 166285 T ATTREG (NIL) -9 NIL NIL NIL) (-97 164411 164946 165298 "ATTRBUT" 165915 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 163965 164239 164305 "ATTRAST" 164363 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 163465 163614 163640 "ATRIG" 163841 T ATRIG (NIL) -9 NIL NIL NIL) (-94 163262 163315 163402 "ATRIG-" 163407 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 162845 163079 163105 "ASTCAT" 163110 T ASTCAT (NIL) -9 NIL 163140 NIL) (-92 162554 162631 162750 "ASTCAT-" 162755 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 160642 162330 162418 "ASTACK" 162497 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 159131 159444 159809 "ASSOCEQ" 160324 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 158077 158790 158914 "ASP9" 159038 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 156859 157682 157824 "ASP80" 157966 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 156587 156807 156846 "ASP8" 156851 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 155455 156264 156382 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\ No newline at end of file
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T) ((-633 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-630 (-877)) . T) ((-175) -3957 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-631 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1041))) ((-631 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1041))) ((-631 (-547)) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-547)))) ((-631 (-905 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-905 (-391))))) ((-631 (-905 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-631 (-905 (-558))))) ((-236 $) -3957 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -3957 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-239) -3957 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-419 (-558)))) ((-298 #1# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-558) (-1133)) ((-302) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-412 |#2|) |has| |#1| (-376)) ((-464) |has| |#1| (-376)) ((-505) |has| |#1| (-38 (-419 (-558)))) ((-526 (-1198) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-526 (-1198) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-569) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-666 #2#) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 |#2|) |has| |#1| (-376)) ((-666 $) . T) ((-668 #2#) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-668 #4=(-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-660 #2#) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-660 |#1|) |has| |#1| (-175)) ((-660 |#2|) |has| |#1| (-376)) ((-660 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-658 #4#) -12 (|has| |#1| (-376)) (|has| |#2| (-658 (-558)))) ((-658 |#2|) |has| |#1| (-376)) ((-737 #2#) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-737 |#1|) |has| |#1| (-175)) ((-737 |#2|) |has| |#1| (-376)) ((-737 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376))) ((-746) . T) ((-812) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-819) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-860) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-861) -3957 (-12 (|has| |#1| (-376)) (|has| |#2| (-861))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-864) -3957 (-12 (|has| |#1| (-376)) (|has| |#2| (-861))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-911 $ #5=(-1198)) -3957 (-12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-919 (-1198)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-917 (-1198))))) ((-917 (-1198)) -3957 (-12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-917 (-1198))))) ((-919 #5#) -3957 (-12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-558) |#1|)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-919 (-1198)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-917 (-1198))))) ((-901 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-901 (-391)))) ((-901 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-901 (-558)))) ((-899 |#2|) |has| |#1| (-376)) ((-929) -12 (|has| |#1| (-376)) (|has| |#2| (-929))) ((-994 |#1| #1# (-1103)) . T) ((-940) |has| |#1| (-376)) ((-1012 |#2|) |has| |#1| (-376)) ((-1023) |has| |#1| (-38 (-419 (-558)))) ((-1041) -12 (|has| |#1| (-376)) (|has| |#2| (-1041))) ((-1059 (-419 (-558))) -12 (|has| |#1| (-376)) (|has| |#2| (-1059 (-558)))) ((-1059 (-558)) -12 (|has| |#1| (-376)) (|has| |#2| (-1059 (-558)))) ((-1059 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-1059 (-1198)))) ((-1059 |#2|) . T) ((-1072 #2#) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1072 |#1|) . T) ((-1072 |#2|) |has| |#1| (-376)) ((-1072 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1077 #2#) -3957 (|has| |#1| (-376)) (|has| |#1| (-38 (-419 (-558))))) ((-1077 |#1|) . T) ((-1077 |#2|) |has| |#1| (-376)) ((-1077 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1173) -12 (|has| |#1| (-376)) (|has| |#2| (-1173))) ((-1224) |has| |#1| (-38 (-419 (-558)))) ((-1227) |has| |#1| (-38 (-419 (-558)))) ((-1238) . T) ((-1243) |has| |#1| (-376)) ((-1250 |#1|) . T) ((-1267 |#1| #1#) . T)) 
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+NIL 
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+(((-21) . T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #1=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-569)) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #1#) |has| |#1| (-38 (-419 (-558)))) ((-633 (-558)) . T) ((-633 |#1|) |has| |#1| (-175)) ((-633 $) |has| |#1| (-569)) ((-630 (-877)) . T) ((-175) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-240) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-239) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-298 |#2| |#1|) . T) ((-298 $ $) |has| |#2| (-1133)) ((-302) |has| |#1| (-569)) ((-569) |has| |#1| (-569)) ((-666 #1#) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #1#) |has| |#1| (-38 (-419 (-558)))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #1#) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) |has| |#1| (-569)) ((-737 #1#) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) |has| |#1| (-569)) ((-746) . T) ((-911 $ #2=(-1198)) -12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ((-917 #2#) -12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ((-919 #2#) -12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ((-994 |#1| |#2| (-1103)) . T) ((-1072 #1#) |has| |#1| (-38 (-419 (-558)))) ((-1072 |#1|) . T) ((-1072 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1077 #1#) |has| |#1| (-38 (-419 (-558)))) ((-1077 |#1|) . T) ((-1077 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1238) . T)) 
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+(((-21) . T) ((-23) . T) ((-47 |#1| #1=(-791)) . T) ((-25) . T) ((-38 #2=(-419 (-558))) |has| |#1| (-38 (-419 (-558)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-569)) ((-35) |has| |#1| (-38 (-419 (-558)))) ((-95) |has| |#1| (-38 (-419 (-558)))) ((-102) . T) ((-111 #2# #2#) |has| |#1| (-38 (-419 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-633 #2#) |has| |#1| (-38 (-419 (-558)))) ((-633 (-558)) . T) ((-633 |#1|) |has| |#1| (-175)) ((-633 $) |has| |#1| (-569)) ((-630 (-877)) . T) ((-175) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-791) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-791) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-791) |#1|))) ((-296) |has| |#1| (-38 (-419 (-558)))) ((-298 #1# |#1|) . T) ((-298 $ $) |has| (-791) (-1133)) ((-302) |has| |#1| (-569)) ((-505) |has| |#1| (-38 (-419 (-558)))) ((-569) |has| |#1| (-569)) ((-666 #2#) |has| |#1| (-38 (-419 (-558)))) ((-666 (-558)) . T) ((-666 |#1|) . T) ((-666 $) . T) ((-668 #2#) |has| |#1| (-38 (-419 (-558)))) ((-668 |#1|) . T) ((-668 $) . T) ((-660 #2#) |has| |#1| (-38 (-419 (-558)))) ((-660 |#1|) |has| |#1| (-175)) ((-660 $) |has| |#1| (-569)) ((-737 #2#) |has| |#1| (-38 (-419 (-558)))) ((-737 |#1|) |has| |#1| (-175)) ((-737 $) |has| |#1| (-569)) ((-746) . T) ((-911 $ #3=(-1198)) -12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-791) |#1|)))) ((-917 #3#) -12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-791) |#1|)))) ((-919 #3#) -12 (|has| |#1| (-917 (-1198))) (|has| |#1| (-15 * (|#1| (-791) |#1|)))) ((-994 |#1| #1# (-1103)) . T) ((-1023) |has| |#1| (-38 (-419 (-558)))) ((-1072 #2#) |has| |#1| (-38 (-419 (-558)))) ((-1072 |#1|) . T) ((-1072 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1077 #2#) |has| |#1| (-38 (-419 (-558)))) ((-1077 |#1|) . T) ((-1077 $) -3957 (|has| |#1| (-569)) (|has| |#1| (-175))) ((-1070) . T) ((-1078) . T) ((-1133) . T) ((-1122) . T) ((-1224) |has| |#1| (-38 (-419 (-558)))) ((-1227) |has| |#1| (-38 (-419 (-558)))) ((-1238) . T) ((-1267 |#1| #1#) . T)) 
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+((-4260 (*1 *2 *3) (-12 (-5 *3 (-419 *5)) (-4 *5 (-1264 *4)) (-4 *4 (-569)) (-4 *4 (-1070)) (-4 *2 (-1281 *4)) (-5 *1 (-1283 *4 *5 *6 *2)) (-4 *6 (-678 *5)))) (-4259 (*1 *2 *3) (-12 (-4 *4 (-1070)) (-4 *5 (-1264 *4)) (-5 *2 (-1 *6 (-661 *6))) (-5 *1 (-1283 *4 *5 *3 *6)) (-4 *3 (-678 *5)) (-4 *6 (-1281 *4)))) (-4258 (*1 *2 *3 *4) (-12 (-5 *4 (-791)) (-4 *5 (-1070)) (-4 *2 (-1264 *5)) (-5 *1 (-1283 *5 *2 *6 *3)) (-4 *6 (-678 *2)) (-4 *3 (-1281 *5)))) (-4257 (*1 *2 *3) (-12 (-4 *4 (-1070)) (-4 *3 (-1264 *4)) (-4 *2 (-1281 *4)) (-5 *1 (-1283 *4 *3 *5 *2)) (-4 *5 (-678 *3))))) 
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+NIL 
+(((-1284) (-142)) (T -1284)) 
+NIL 
+(-13 (-10 -7 (-6 -2501))) 
+((-2967 (((-114) $ $) NIL T ELT)) (-4261 (((-1198)) 12 T ELT)) (-3660 (((-1180) $) 18 T ELT)) (-3661 (((-1141) $) NIL T ELT)) (-4376 (((-877) $) 11 T ELT) (((-1198) $) 8 T ELT)) (-1378 (((-114) $ $) NIL T ELT)) (-3454 (((-114) $ $) 15 T ELT))) 
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+NIL 
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+NIL 
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+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
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XPOLY (NIL T) -8 NIL NIL NIL) (-1309 3402632 3405201 3405589 "XPBWPOLY" 3406342 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1308 3397524 3399103 3399158 "XFALG" 3401330 NIL XFALG (NIL T T) -9 NIL 3402119 NIL) (-1307 3392802 3395500 3395542 "XF" 3396163 NIL XF (NIL T) -9 NIL 3396563 NIL) (-1306 3392399 3392511 3392680 "XF-" 3392685 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1305 3391514 3391636 3391841 "XEXPPKG" 3392291 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1304 3389255 3391364 3391460 "XDPOLY" 3391465 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1303 3387910 3388648 3388691 "XALG" 3388696 NIL XALG (NIL T) -9 NIL 3388807 NIL) (-1302 3380961 3385887 3386381 "WUTSET" 3387502 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1301 3379063 3380013 3380336 "WP" 3380772 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1300 3378611 3378885 3378955 "WHILEAST" 3379015 T WHILEAST (NIL) -8 NIL NIL NIL) (-1299 3378023 3378328 3378422 "WHEREAST" 3378539 T WHEREAST (NIL) -8 NIL NIL NIL) (-1298 3376897 3377107 3377402 "WFFINTBS" 3377820 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1297 3374765 3375228 3375690 "WEIER" 3376469 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1296 3373689 3374247 3374289 "VSPACE" 3374425 NIL VSPACE (NIL T) -9 NIL 3374499 NIL) (-1295 3373521 3373554 3373645 "VSPACE-" 3373650 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1294 3373318 3373372 3373440 "VOID" 3373475 T VOID (NIL) -8 NIL NIL NIL) (-1293 3369586 3370381 3371118 "VIEWDEF" 3372603 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1292 3358530 3361134 3363307 "VIEW3D" 3367435 T VIEW3D (NIL) -8 NIL NIL NIL) (-1291 3350547 3352441 3354020 "VIEW2D" 3356973 T VIEW2D (NIL) -8 NIL NIL NIL) (-1290 3348647 3349042 3349448 "VIEW" 3350163 T VIEW (NIL) -7 NIL NIL NIL) (-1289 3347200 3347483 3347801 "VECTOR2" 3348377 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1288 3342220 3346970 3347062 "VECTOR" 3347143 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1287 3335279 3339924 3339967 "VECTCAT" 3340962 NIL VECTCAT (NIL T) -9 NIL 3341549 NIL) (-1286 3334221 3334547 3334937 "VECTCAT-" 3334942 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1285 3333627 3333872 3333992 "VARIABLE" 3334136 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1284 3333560 3333565 3333595 "UTYPE" 3333600 T UTYPE (NIL) -9 NIL NIL NIL) (-1283 3332368 3332544 3332806 "UTSODETL" 3333386 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1282 3329760 3330268 3330792 "UTSODE" 3331909 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1281 3319771 3325694 3325737 "UTSCAT" 3326849 NIL UTSCAT (NIL T) -9 NIL 3327607 NIL) (-1280 3316897 3317841 3318830 "UTSCAT-" 3318835 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1279 3316518 3316567 3316700 "UTS2" 3316848 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1278 3307835 3314279 3314759 "UTS" 3316096 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3301814 3304645 3304688 "URAGG" 3306758 NIL URAGG (NIL T) -9 NIL 3307481 NIL) (-1276 3298849 3299816 3300839 "URAGG-" 3300844 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1275 3294232 3297484 3297949 "UPXSSING" 3298513 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1274 3286663 3294136 3294208 "UPXSCONS" 3294213 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1273 3275424 3282866 3282928 "UPXSCCA" 3283502 NIL UPXSCCA (NIL T T) -9 NIL 3283735 NIL) (-1272 3275044 3275147 3275321 "UPXSCCA-" 3275326 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1271 3263705 3270872 3270915 "UPXSCAT" 3271563 NIL UPXSCAT (NIL T) -9 NIL 3272172 NIL) (-1270 3263129 3263214 3263393 "UPXS2" 3263620 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1269 3254625 3262511 3262775 "UPXS" 3262923 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1268 3253264 3253534 3253884 "UPSQFREE" 3254369 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1267 3246097 3249532 3249587 "UPSCAT" 3250667 NIL UPSCAT (NIL T T) -9 NIL 3251432 NIL) (-1266 3245253 3245508 3245835 "UPSCAT-" 3245840 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1265 3244874 3244923 3245056 "UPOLYC2" 3245204 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1264 3229050 3238001 3238044 "UPOLYC" 3240145 NIL UPOLYC (NIL T) -9 NIL 3241366 NIL) (-1263 3219955 3222842 3225970 "UPOLYC-" 3225975 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1262 3219276 3219401 3219565 "UPMP" 3219844 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1261 3218823 3218910 3219049 "UPDIVP" 3219189 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1260 3217361 3217640 3217956 "UPDECOMP" 3218572 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1259 3216574 3216704 3216890 "UPCDEN" 3217245 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1258 3216087 3216162 3216311 "UP2" 3216499 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1257 3206718 3215770 3215899 "UP" 3216006 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1256 3205923 3206060 3206265 "UNISEG2" 3206561 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1255 3204276 3205127 3205404 "UNISEG" 3205681 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1254 3203318 3203516 3203742 "UNIFACT" 3204092 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1253 3190065 3203222 3203294 "ULSCONS" 3203299 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1252 3169899 3183146 3183208 "ULSCCAT" 3183846 NIL ULSCCAT (NIL T T) -9 NIL 3184135 NIL) (-1251 3168931 3169218 3169594 "ULSCCAT-" 3169599 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1250 3157389 3164478 3164521 "ULSCAT" 3165384 NIL ULSCAT (NIL T) -9 NIL 3166115 NIL) (-1249 3156813 3156898 3157077 "ULS2" 3157304 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1248 3138660 3156125 3156367 "ULS" 3156629 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1247 3137579 3138279 3138393 "UINT8" 3138504 T UINT8 (NIL) -8 NIL NIL 3138596) (-1246 3136497 3137197 3137311 "UINT64" 3137422 T UINT64 (NIL) -8 NIL NIL 3137514) (-1245 3135415 3136115 3136229 "UINT32" 3136340 T UINT32 (NIL) -8 NIL NIL 3136432) (-1244 3134333 3135033 3135147 "UINT16" 3135258 T UINT16 (NIL) -8 NIL NIL 3135350) (-1243 3132412 3133579 3133609 "UFD" 3133821 T UFD (NIL) -9 NIL 3133935 NIL) (-1242 3132194 3132252 3132347 "UFD-" 3132352 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1241 3131252 3131459 3131675 "UDVO" 3132000 T UDVO (NIL) -7 NIL NIL NIL) (-1240 3129018 3129477 3129948 "UDPO" 3130816 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1239 3128730 3128973 3129004 "TYPEAST" 3129009 T TYPEAST (NIL) -8 NIL NIL NIL) (-1238 3128663 3128668 3128698 "TYPE" 3128703 T TYPE (NIL) -9 NIL NIL NIL) (-1237 3127616 3127836 3128076 "TWOFACT" 3128457 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1236 3126591 3127025 3127260 "TUPLE" 3127416 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1235 3124228 3124801 3125340 "TUBETOOL" 3126074 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1234 3123041 3123282 3123523 "TUBE" 3124021 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1233 3111292 3115800 3115897 "TSETCAT" 3121166 NIL TSETCAT (NIL T T T T) -9 NIL 3122697 NIL) (-1232 3105760 3107624 3109515 "TSETCAT-" 3109520 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1231 3099946 3104732 3105015 "TS" 3105512 NIL TS (NIL T) -8 NIL NIL NIL) (-1230 3094419 3095432 3096361 "TRMANIP" 3099082 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1229 3093848 3093923 3094086 "TRIMAT" 3094351 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1228 3091660 3091951 3092308 "TRIGMNIP" 3093597 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1227 3091144 3091293 3091323 "TRIGCAT" 3091536 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1226 3090789 3090892 3091033 "TRIGCAT-" 3091038 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1225 3087515 3089647 3089928 "TREE" 3090543 NIL TREE (NIL T) -8 NIL NIL NIL) (-1224 3086621 3087317 3087347 "TRANFUN" 3087382 T TRANFUN (NIL) -9 NIL 3087448 NIL) (-1223 3085840 3086091 3086371 "TRANFUN-" 3086376 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1222 3085638 3085676 3085737 "TOPSP" 3085801 T TOPSP (NIL) -7 NIL NIL NIL) (-1221 3084968 3085101 3085255 "TOOLSIGN" 3085519 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1220 3083482 3084145 3084384 "TEXTFILE" 3084751 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1219 3083257 3083294 3083366 "TEX1" 3083445 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1218 3081061 3081710 3082139 "TEX" 3082850 T TEX (NIL) -8 NIL NIL NIL) (-1217 3080697 3080772 3080862 "TEMUTL" 3080993 T TEMUTL (NIL) -7 NIL NIL NIL) (-1216 3078791 3079131 3079456 "TBCMPPK" 3080420 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1215 3070227 3076877 3076933 "TBAGG" 3077333 NIL TBAGG (NIL T T) -9 NIL 3077544 NIL) (-1214 3065111 3066785 3068539 "TBAGG-" 3068544 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1213 3064477 3064602 3064747 "TANEXP" 3065000 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1212 3063928 3064252 3064342 "TALGOP" 3064422 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1211 3063322 3063439 3063577 "TABLEAU" 3063825 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1210 3056452 3063179 3063272 "TABLE" 3063277 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1209 3050982 3052280 3053528 "TABLBUMP" 3055238 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1208 3050192 3050351 3050532 "SYSTEM" 3050823 T SYSTEM (NIL) -8 NIL NIL NIL) (-1207 3046597 3047350 3048133 "SYSSOLP" 3049443 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1206 3046359 3046552 3046583 "SYSPTR" 3046588 T SYSPTR (NIL) -8 NIL NIL NIL) (-1205 3045198 3045890 3046016 "SYSNNI" 3046202 NIL SYSNNI (NIL NIL) -8 NIL NIL 3046294) (-1204 3044405 3044960 3045039 "SYSINT" 3045099 NIL SYSINT (NIL NIL) -8 NIL NIL 3045144) (-1203 3040515 3041683 3042393 "SYNTAX" 3043717 T SYNTAX (NIL) -8 NIL NIL NIL) (-1202 3037595 3038275 3038907 "SYMTAB" 3039905 T SYMTAB (NIL) -8 NIL NIL NIL) (-1201 3032718 3033764 3034741 "SYMS" 3036640 T SYMS (NIL) -8 NIL NIL NIL) (-1200 3029650 3032179 3032409 "SYMPOLY" 3032526 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1199 3029155 3029242 3029365 "SYMFUNC" 3029562 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1198 3025098 3026481 3027287 "SYMBOL" 3028371 T SYMBOL (NIL) -8 NIL NIL NIL) (-1197 3018571 3020326 3022046 "SWITCH" 3023400 T SWITCH (NIL) -8 NIL NIL NIL) (-1196 3011332 3017527 3017821 "SUTS" 3018335 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1195 3002828 3010714 3010978 "SUPXS" 3011126 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 3001975 3002114 3002331 "SUPFRACF" 3002696 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1193 3001590 3001655 3001768 "SUP2" 3001910 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1192 2992169 3001208 3001334 "SUP" 3001499 NIL SUP (NIL T) -8 NIL NIL NIL) (-1191 2990593 2990891 2991247 "SUMRF" 2991868 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1190 2989916 2989994 2990186 "SUMFS" 2990514 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1189 2971798 2989228 2989470 "SULS" 2989732 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1188 2971346 2971620 2971690 "SUCHTAST" 2971750 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1187 2970587 2970871 2971011 "SUCH" 2971254 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1186 2964226 2965493 2966452 "SUBSPACE" 2969675 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1185 2963646 2963746 2963910 "SUBRESP" 2964114 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1184 2957657 2958939 2960086 "STTFNC" 2962546 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1183 2950851 2952322 2953633 "STTF" 2956393 NIL STTF (NIL T) -7 NIL NIL NIL) (-1182 2941967 2944033 2945827 "STTAYLOR" 2949092 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1181 2934837 2941831 2941914 "STRTBL" 2941919 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1180 2929490 2934560 2934652 "STRING" 2934767 T STRING (NIL) -8 NIL NIL NIL) (-1179 2928994 2929077 2929221 "STREAM3" 2929407 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1178 2927958 2928159 2928394 "STREAM2" 2928807 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1177 2927640 2927698 2927791 "STREAM1" 2927900 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1176 2919756 2925259 2925870 "STREAM" 2927064 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1175 2918748 2918953 2919184 "STINPROD" 2919572 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1174 2917863 2918237 2918385 "STEPAST" 2918622 T STEPAST (NIL) -8 NIL NIL NIL) (-1173 2917359 2917604 2917634 "STEP" 2917728 T STEP (NIL) -9 NIL 2917799 NIL) (-1172 2910531 2917258 2917335 "STBL" 2917340 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1171 2904714 2909325 2909368 "STAGG" 2909800 NIL STAGG (NIL T) -9 NIL 2909979 NIL) (-1170 2902272 2903022 2903892 "STAGG-" 2903897 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1169 2900358 2902042 2902134 "STACK" 2902215 NIL STACK (NIL T) -8 NIL NIL NIL) (-1168 2899675 2900188 2900218 "SRING" 2900223 T SRING (NIL) -9 NIL 2900243 NIL) (-1167 2891824 2897816 2898272 "SREGSET" 2899305 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1166 2884171 2885618 2887131 "SRDCMPK" 2890430 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1165 2876585 2881530 2881560 "SRAGG" 2882863 T SRAGG (NIL) -9 NIL 2883471 NIL) (-1164 2875536 2875857 2876236 "SRAGG-" 2876241 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1163 2869238 2874483 2874904 "SQMATRIX" 2875162 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1162 2862765 2865956 2866683 "SPLTREE" 2868583 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1161 2858590 2859421 2860067 "SPLNODE" 2862191 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1160 2857565 2857870 2857900 "SPFCAT" 2858344 T SPFCAT (NIL) -9 NIL NIL NIL) (-1159 2856260 2856512 2856776 "SPECOUT" 2857323 T SPECOUT (NIL) -7 NIL NIL NIL) (-1158 2846912 2849228 2849258 "SPADXPT" 2853934 T SPADXPT (NIL) -9 NIL 2856098 NIL) (-1157 2846667 2846713 2846782 "SPADPRSR" 2846865 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1156 2844272 2846622 2846653 "SPADAST" 2846658 T SPADAST (NIL) -8 NIL NIL NIL) (-1155 2835873 2837976 2838019 "SPACEC" 2842392 NIL SPACEC (NIL T) -9 NIL 2844208 NIL) (-1154 2833673 2835805 2835854 "SPACE3" 2835859 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1153 2832405 2832596 2832887 "SORTPAK" 2833478 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1152 2830467 2830800 2831212 "SOLVETRA" 2832069 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1151 2829505 2829739 2830000 "SOLVESER" 2830240 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1150 2824737 2825697 2826692 "SOLVERAD" 2828557 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1149 2820462 2821161 2821890 "SOLVEFOR" 2824104 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1148 2814208 2819811 2819908 "SNTSCAT" 2819913 NIL SNTSCAT (NIL T T T T) -9 NIL 2819983 NIL) (-1147 2807759 2812531 2812922 "SMTS" 2813898 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1146 2801507 2807647 2807724 "SMP" 2807729 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1145 2799636 2799967 2800365 "SMITH" 2801204 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1144 2791273 2796209 2796312 "SMATCAT" 2797666 NIL SMATCAT (NIL NIL T T T) -9 NIL 2798216 NIL) (-1143 2788066 2789050 2790221 "SMATCAT-" 2790226 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1142 2785646 2787274 2787317 "SKAGG" 2787578 NIL SKAGG (NIL T) -9 NIL 2787713 NIL) (-1141 2781310 2785143 2785313 "SINT" 2785465 T SINT (NIL) -8 NIL NIL 2785613) (-1140 2781076 2781120 2781186 "SIMPAN" 2781266 T SIMPAN (NIL) -7 NIL NIL NIL) (-1139 2779917 2780149 2780417 "SIGNRF" 2780842 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1138 2778753 2778915 2779192 "SIGNEF" 2779753 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1137 2777993 2778336 2778460 "SIGAST" 2778651 T SIGAST (NIL) -8 NIL NIL NIL) (-1136 2777218 2777528 2777668 "SIG" 2777875 T SIG (NIL) -8 NIL NIL NIL) (-1135 2774870 2775362 2775868 "SHP" 2776759 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1134 2768315 2774771 2774847 "SHDP" 2774852 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1133 2767826 2768066 2768096 "SGROUP" 2768189 T SGROUP (NIL) -9 NIL 2768251 NIL) (-1132 2767678 2767710 2767783 "SGROUP-" 2767788 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1131 2764397 2765167 2765890 "SGCF" 2766977 T SGCF (NIL) -7 NIL NIL NIL) (-1130 2758241 2763844 2763941 "SFRTCAT" 2763946 NIL SFRTCAT (NIL T T T T) -9 NIL 2763985 NIL) (-1129 2751560 2752680 2753816 "SFRGCD" 2757224 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1128 2744578 2745759 2746945 "SFQCMPK" 2750493 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1127 2744180 2744287 2744398 "SFORT" 2744519 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1126 2743106 2744020 2744141 "SEXOF" 2744146 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1125 2738695 2739602 2739697 "SEXCAT" 2742319 NIL SEXCAT (NIL T T T T T) -9 NIL 2742879 NIL) (-1124 2737610 2738576 2738644 "SEX" 2738649 T SEX (NIL) -8 NIL NIL NIL) (-1123 2735738 2736327 2736630 "SETMN" 2737353 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1122 2735268 2735456 2735486 "SETCAT" 2735603 T SETCAT (NIL) -9 NIL 2735688 NIL) (-1121 2735036 2735100 2735199 "SETCAT-" 2735204 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1120 2731250 2733497 2733540 "SETAGG" 2734410 NIL SETAGG (NIL T) -9 NIL 2734750 NIL) (-1119 2730672 2730824 2731061 "SETAGG-" 2731066 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1118 2727595 2730606 2730654 "SET" 2730659 NIL SET (NIL T) -8 NIL NIL NIL) (-1117 2726978 2727291 2727392 "SEQAST" 2727516 T SEQAST (NIL) -8 NIL NIL NIL) (-1116 2726105 2726471 2726532 "SEGXCAT" 2726818 NIL SEGXCAT (NIL T T) -9 NIL 2726938 NIL) (-1115 2725030 2725298 2725341 "SEGCAT" 2725863 NIL SEGCAT (NIL T) -9 NIL 2726084 NIL) (-1114 2724645 2724710 2724823 "SEGBIND2" 2724965 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1113 2723535 2724008 2724216 "SEGBIND" 2724472 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1112 2723054 2723336 2723413 "SEGAST" 2723480 T SEGAST (NIL) -8 NIL NIL NIL) (-1111 2722263 2722399 2722603 "SEG2" 2722898 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1110 2721179 2721929 2722111 "SEG" 2722116 NIL SEG (NIL T) -8 NIL NIL NIL) (-1109 2720412 2721114 2721161 "SDVAR" 2721166 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1108 2711806 2720182 2720312 "SDPOL" 2720317 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1107 2710375 2710665 2710984 "SCPKG" 2711521 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1106 2709497 2709711 2709903 "SCOPE" 2710205 T SCOPE (NIL) -8 NIL NIL NIL) (-1105 2708693 2708851 2709030 "SCACHE" 2709352 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1104 2708277 2708511 2708541 "SASTCAT" 2708546 T SASTCAT (NIL) -9 NIL 2708559 NIL) (-1103 2707680 2708112 2708188 "SAOS" 2708223 T SAOS (NIL) -8 NIL NIL NIL) (-1102 2707239 2707280 2707453 "SAERFFC" 2707639 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1101 2706826 2706867 2707026 "SAEFACT" 2707198 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1100 2699883 2706723 2706803 "SAE" 2706808 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1099 2698186 2698518 2698919 "RURPK" 2699549 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1098 2696763 2697129 2697434 "RULESET" 2698020 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1097 2696333 2696557 2696640 "RULECOLD" 2696715 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1096 2693448 2694086 2694544 "RULE" 2696014 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1095 2693232 2693266 2693337 "RTVALUE" 2693399 T RTVALUE (NIL) -8 NIL NIL NIL) (-1094 2692643 2692949 2693043 "RSTRCAST" 2693160 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1093 2687413 2688286 2689206 "RSETGCD" 2691842 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1092 2676119 2681722 2681819 "RSETCAT" 2685938 NIL RSETCAT (NIL T T T T) -9 NIL 2687035 NIL) (-1091 2673938 2674585 2675409 "RSETCAT-" 2675414 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1090 2666246 2667700 2669220 "RSDCMPK" 2672537 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1089 2664115 2664678 2664752 "RRCC" 2665838 NIL RRCC (NIL T T) -9 NIL 2666182 NIL) (-1088 2663436 2663640 2663919 "RRCC-" 2663924 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1087 2662819 2663132 2663233 "RPTAST" 2663357 T RPTAST (NIL) -8 NIL NIL NIL) (-1086 2635231 2645931 2645998 "RPOLCAT" 2656664 NIL RPOLCAT (NIL T T T) -9 NIL 2659824 NIL) (-1085 2626237 2629093 2632203 "RPOLCAT-" 2632208 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1084 2616806 2624448 2624930 "ROUTINE" 2625777 T ROUTINE (NIL) -8 NIL NIL NIL) (-1083 2612871 2616432 2616572 "ROMAN" 2616688 T ROMAN (NIL) -8 NIL NIL NIL) (-1082 2610985 2611731 2611991 "ROIRC" 2612676 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1081 2606762 2609527 2609557 "RNS" 2609826 T RNS (NIL) -9 NIL 2610082 NIL) (-1080 2605169 2605654 2606188 "RNS-" 2606263 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1079 2604130 2604534 2604736 "RNGBIND" 2605020 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1078 2603423 2603927 2603957 "RNG" 2603962 T RNG (NIL) -9 NIL 2603983 NIL) (-1077 2602718 2603196 2603239 "RMODULE" 2603244 NIL RMODULE (NIL T) -9 NIL 2603271 NIL) (-1076 2601542 2601648 2601984 "RMCAT2" 2602619 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1075 2598158 2600888 2601185 "RMATRIX" 2601304 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1074 2590768 2593245 2593360 "RMATCAT" 2596719 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2597701 NIL) (-1073 2590107 2590290 2590597 "RMATCAT-" 2590602 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1072 2589680 2589894 2589937 "RLINSET" 2589999 NIL RLINSET (NIL T) -9 NIL 2590043 NIL) (-1071 2589241 2589322 2589450 "RINTERP" 2589599 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1070 2588165 2588839 2588869 "RING" 2588925 T RING (NIL) -9 NIL 2589017 NIL) (-1069 2587945 2588001 2588098 "RING-" 2588103 NIL RING- (NIL T) -8 NIL NIL NIL) (-1068 2586756 2587023 2587281 "RIDIST" 2587709 T RIDIST (NIL) -7 NIL NIL NIL) (-1067 2577522 2586224 2586430 "RGCHAIN" 2586604 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1066 2576780 2577264 2577305 "RGBCSPC" 2577363 NIL RGBCSPC (NIL T) -9 NIL 2577415 NIL) (-1065 2575846 2576305 2576346 "RGBCMDL" 2576578 NIL RGBCMDL (NIL T) -9 NIL 2576692 NIL) (-1064 2575486 2575555 2575658 "RFFACTOR" 2575777 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1063 2575205 2575246 2575343 "RFFACT" 2575445 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1062 2573256 2573686 2574068 "RFDIST" 2574845 T RFDIST (NIL) -7 NIL NIL NIL) (-1061 2570196 2570864 2571534 "RF" 2572620 NIL RF (NIL T) -7 NIL NIL NIL) (-1060 2569643 2569741 2569904 "RETSOL" 2570098 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1059 2569261 2569359 2569402 "RETRACT" 2569535 NIL RETRACT (NIL T) -9 NIL 2569622 NIL) (-1058 2569104 2569135 2569222 "RETRACT-" 2569227 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1057 2568652 2568926 2568996 "RETAST" 2569056 T RETAST (NIL) -8 NIL NIL NIL) (-1056 2561118 2568305 2568432 "RESULT" 2568547 T RESULT (NIL) -8 NIL NIL NIL) (-1055 2559553 2560387 2560586 "RESRING" 2561021 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1054 2559177 2559238 2559336 "RESLATC" 2559490 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1053 2558876 2558917 2559024 "REPSQ" 2559136 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1052 2558567 2558608 2558719 "REPDB" 2558835 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1051 2552399 2553856 2555079 "REP2" 2557379 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1050 2548702 2549457 2550265 "REP1" 2551626 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1049 2546082 2546704 2547306 "REP" 2548122 T REP (NIL) -7 NIL NIL NIL) (-1048 2538231 2544223 2544679 "REGSET" 2545712 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1047 2536940 2537379 2537629 "REF" 2538016 NIL REF (NIL T) -8 NIL NIL NIL) (-1046 2536305 2536420 2536587 "REDORDER" 2536824 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1045 2531707 2535518 2535745 "RECLOS" 2536133 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1044 2530741 2530940 2531155 "REALSOLV" 2531514 T REALSOLV (NIL) -7 NIL NIL NIL) (-1043 2527188 2528026 2528910 "REAL0Q" 2529906 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1042 2522741 2523777 2524838 "REAL0" 2526169 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1041 2522575 2522628 2522658 "REAL" 2522663 T REAL (NIL) -9 NIL 2522698 NIL) (-1040 2521986 2522292 2522386 "RDUCEAST" 2522503 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1039 2521385 2521463 2521670 "RDIV" 2521908 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1038 2520435 2520627 2520840 "RDIST" 2521207 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1037 2519020 2519319 2519691 "RDETRS" 2520143 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1036 2516814 2517286 2517824 "RDETR" 2518562 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1035 2515433 2515717 2516114 "RDEEFS" 2516530 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1034 2513936 2514248 2514673 "RDEEF" 2515121 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1033 2507424 2510890 2510920 "RCFIELD" 2512215 T RCFIELD (NIL) -9 NIL 2512946 NIL) (-1032 2505380 2505992 2506688 "RCFIELD-" 2506763 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1031 2501543 2503453 2503496 "RCAGG" 2504580 NIL RCAGG (NIL T) -9 NIL 2505045 NIL) (-1030 2501153 2501265 2501428 "RCAGG-" 2501433 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1029 2500470 2500600 2500765 "RATRET" 2501037 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1028 2500011 2500090 2500211 "RATFACT" 2500398 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1027 2499289 2499439 2499591 "RANDSRC" 2499881 T RANDSRC (NIL) -7 NIL NIL NIL) (-1026 2499017 2499067 2499140 "RADUTIL" 2499238 T RADUTIL (NIL) -7 NIL NIL NIL) (-1025 2491178 2497848 2498159 "RADIX" 2498740 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1024 2480804 2491020 2491150 "RADFF" 2491155 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1023 2480433 2480526 2480556 "RADCAT" 2480716 T RADCAT (NIL) -9 NIL NIL NIL) (-1022 2480203 2480263 2480363 "RADCAT-" 2480368 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1021 2478228 2479973 2480065 "QUEUE" 2480146 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1020 2477853 2477902 2478033 "QUATCT2" 2478179 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1019 2470238 2474276 2474318 "QUATCAT" 2475109 NIL QUATCAT (NIL T) -9 NIL 2475875 NIL) (-1018 2466140 2467428 2468811 "QUATCAT-" 2468907 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1017 2461993 2466073 2466121 "QUAT" 2466126 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1016 2459360 2461041 2461084 "QUAGG" 2461465 NIL QUAGG (NIL T) -9 NIL 2461640 NIL) (-1015 2458908 2459182 2459252 "QQUTAST" 2459312 T QQUTAST (NIL) -8 NIL NIL NIL) (-1014 2457819 2458421 2458586 "QFORM" 2458789 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1013 2457444 2457493 2457624 "QFCAT2" 2457770 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1012 2447157 2453291 2453333 "QFCAT" 2454001 NIL QFCAT (NIL T) -9 NIL 2455002 NIL) (-1011 2442527 2443963 2445538 "QFCAT-" 2445634 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1010 2441958 2442092 2442224 "QEQUAT" 2442417 T QEQUAT (NIL) -8 NIL NIL NIL) (-1009 2434976 2436157 2437343 "QCMPACK" 2440891 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1008 2434205 2434387 2434623 "QALGSET2" 2434794 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1007 2431661 2432195 2432623 "QALGSET" 2433862 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1006 2430328 2430570 2430889 "PWFFINTB" 2431434 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1005 2428490 2428688 2429044 "PUSHVAR" 2430142 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1004 2424217 2425433 2425476 "PTRANFN" 2427387 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1003 2422554 2422899 2423223 "PTPACK" 2423928 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1002 2422177 2422240 2422351 "PTFUNC2" 2422491 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1001 2416207 2420966 2421009 "PTCAT" 2421309 NIL PTCAT (NIL T) -9 NIL 2421462 NIL) (-1000 2415856 2415897 2416023 "PSQFR" 2416166 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-999 2414433 2414749 2415083 "PSEUDLIN" 2415554 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-998 2400992 2403567 2405891 "PSETPK" 2412193 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-997 2393833 2396750 2396846 "PSETCAT" 2399867 NIL PSETCAT (NIL T T T T) -9 NIL 2400681 NIL) (-996 2391561 2392303 2393124 "PSETCAT-" 2393129 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-995 2390880 2391075 2391103 "PSCURVE" 2391371 T PSCURVE (NIL) -9 NIL 2391538 NIL) (-994 2386613 2388380 2388445 "PSCAT" 2389289 NIL PSCAT (NIL T T T) -9 NIL 2389529 NIL) (-993 2385610 2385892 2386292 "PSCAT-" 2386297 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-992 2383788 2384679 2384942 "PRTITION" 2385367 T PRTITION (NIL) -8 NIL NIL NIL) (-991 2383203 2383509 2383601 "PRTDAST" 2383716 T PRTDAST (NIL) -8 NIL NIL NIL) (-990 2372085 2374507 2376695 "PRS" 2381065 NIL PRS (NIL T T) -7 NIL NIL NIL) (-989 2369816 2371407 2371447 "PRQAGG" 2371630 NIL PRQAGG (NIL T) -9 NIL 2371732 NIL) (-988 2368995 2369444 2369472 "PROPLOG" 2369611 T PROPLOG (NIL) -9 NIL 2369726 NIL) (-987 2368593 2368656 2368779 "PROPFUN2" 2368918 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-986 2367890 2368029 2368201 "PROPFUN1" 2368454 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-985 2365871 2366637 2366934 "PROPFRML" 2367626 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-984 2365316 2365447 2365575 "PROPERTY" 2365763 T PROPERTY (NIL) -8 NIL NIL NIL) (-983 2359129 2363482 2364302 "PRODUCT" 2364542 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-982 2358919 2358957 2359016 "PRINT" 2359090 T PRINT (NIL) -7 NIL NIL NIL) (-981 2358235 2358376 2358528 "PRIMES" 2358799 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-980 2356282 2356701 2357167 "PRIMELT" 2357814 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-979 2355999 2356060 2356088 "PRIMCAT" 2356212 T PRIMCAT (NIL) -9 NIL NIL NIL) (-978 2354988 2355184 2355412 "PRIMARR2" 2355817 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-977 2350824 2354926 2354971 "PRIMARR" 2354976 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-976 2350461 2350523 2350634 "PREASSOC" 2350762 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-975 2347433 2349919 2350153 "PR" 2350272 NIL PR (NIL T T) -8 NIL NIL NIL) (-974 2346884 2347041 2347069 "PPCURVE" 2347274 T PPCURVE (NIL) -9 NIL 2347410 NIL) (-973 2346431 2346679 2346762 "PORTNUM" 2346821 T PORTNUM (NIL) -8 NIL NIL NIL) (-972 2343768 2344189 2344781 "POLYROOT" 2346012 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-971 2343145 2343209 2343443 "POLYLIFT" 2343704 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-970 2339366 2339869 2340498 "POLYCATQ" 2342690 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-969 2325028 2331113 2331178 "POLYCAT" 2334692 NIL POLYCAT (NIL T T T) -9 NIL 2336570 NIL) (-968 2318210 2320381 2322744 "POLYCAT-" 2322749 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2317791 2317865 2317985 "POLY2UP" 2318136 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-966 2317417 2317480 2317589 "POLY2" 2317728 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-965 2310658 2317021 2317181 "POLY" 2317290 NIL POLY (NIL T) -8 NIL NIL NIL) (-964 2309319 2309582 2309858 "POLUTIL" 2310432 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-963 2307638 2307951 2308282 "POLTOPOL" 2309041 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-962 2302748 2307572 2307619 "POINT" 2307624 NIL POINT (NIL T) -8 NIL NIL NIL) (-961 2300881 2301292 2301667 "PNTHEORY" 2302393 T PNTHEORY (NIL) -7 NIL NIL NIL) (-960 2299327 2299636 2300035 "PMTOOLS" 2300579 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-959 2298914 2298998 2299115 "PMSYM" 2299243 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-958 2298416 2298491 2298666 "PMQFCAT" 2298839 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-957 2297797 2297895 2298057 "PMPREDFS" 2298317 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-956 2297140 2297262 2297418 "PMPRED" 2297674 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-955 2295794 2296012 2296390 "PMPLCAT" 2296902 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-954 2295320 2295405 2295557 "PMLSAGG" 2295709 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-953 2294787 2294869 2295051 "PMKERNEL" 2295238 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-952 2294398 2294479 2294592 "PMINS" 2294706 NIL PMINS (NIL T) -7 NIL NIL NIL) (-951 2293834 2293909 2294118 "PMFS" 2294323 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-950 2293050 2293180 2293385 "PMDOWN" 2293711 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-949 2292299 2292433 2292596 "PMASSFS" 2292937 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-948 2291442 2291624 2291805 "PMASS" 2292138 T PMASS (NIL) -7 NIL NIL NIL) (-947 2291091 2291165 2291259 "PLOTTOOL" 2291368 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-946 2286745 2287939 2288860 "PLOT3D" 2290190 T PLOT3D (NIL) -8 NIL NIL NIL) (-945 2285633 2285834 2286069 "PLOT1" 2286549 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-944 2280054 2281444 2282592 "PLOT" 2284505 T PLOT (NIL) -8 NIL NIL NIL) (-943 2255229 2260120 2264971 "PLEQN" 2275320 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-942 2254916 2254969 2255072 "PINTERPA" 2255176 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-941 2254222 2254356 2254536 "PINTERP" 2254781 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-940 2252306 2253472 2253500 "PID" 2253697 T PID (NIL) -9 NIL 2253824 NIL) (-939 2252051 2252094 2252169 "PICOERCE" 2252263 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-938 2251147 2251815 2251902 "PI" 2251942 T PI (NIL) -8 NIL NIL 2252009) (-937 2250455 2250606 2250782 "PGROEB" 2251003 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-936 2245898 2246856 2247761 "PGE" 2249570 T PGE (NIL) -7 NIL NIL NIL) (-935 2243979 2244268 2244634 "PGCD" 2245615 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-934 2243305 2243420 2243581 "PFRPAC" 2243863 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-933 2239565 2241853 2242206 "PFR" 2242984 NIL PFR (NIL T) -8 NIL NIL NIL) (-932 2237918 2238198 2238523 "PFOTOOLS" 2239312 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-931 2236433 2236690 2237041 "PFOQ" 2237675 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-930 2234916 2235146 2235502 "PFO" 2236217 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-929 2232000 2233506 2233534 "PFECAT" 2234127 T PFECAT (NIL) -9 NIL 2234504 NIL) (-928 2231448 2231613 2231820 "PFECAT-" 2231825 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-927 2230021 2230303 2230604 "PFBRU" 2231197 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-926 2227850 2228239 2228671 "PFBR" 2229672 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-925 2223798 2227739 2227808 "PF" 2227813 NIL PF (NIL NIL) -8 NIL NIL NIL) (-924 2218852 2220005 2220875 "PERMGRP" 2222961 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-923 2216764 2217876 2217917 "PERMCAT" 2218317 NIL PERMCAT (NIL T) -9 NIL 2218615 NIL) (-922 2216411 2216458 2216582 "PERMAN" 2216717 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-921 2212217 2213923 2214570 "PERM" 2215797 NIL PERM (NIL T) -8 NIL NIL NIL) (-920 2209574 2211882 2212004 "PENDTREE" 2212128 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-919 2208455 2208718 2208759 "PDSPC" 2209292 NIL PDSPC (NIL T) -9 NIL 2209537 NIL) (-918 2207510 2207776 2208138 "PDSPC-" 2208143 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-917 2206224 2207160 2207201 "PDRING" 2207206 NIL PDRING (NIL T) -9 NIL 2207234 NIL) (-916 2204967 2205729 2205783 "PDMOD" 2205788 NIL PDMOD (NIL T T) -9 NIL 2205892 NIL) (-915 2202134 2202960 2203628 "PDEPROB" 2204319 T PDEPROB (NIL) -8 NIL NIL NIL) (-914 2199643 2200183 2200738 "PDEPACK" 2201599 T PDEPACK (NIL) -7 NIL NIL NIL) (-913 2198531 2198745 2198996 "PDECOMP" 2199442 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-912 2196048 2196939 2196967 "PDECAT" 2197754 T PDECAT (NIL) -9 NIL 2198467 NIL) (-911 2195665 2195732 2195786 "PDDOM" 2195951 NIL PDDOM (NIL T T) -9 NIL 2196031 NIL) (-910 2195478 2195514 2195621 "PDDOM-" 2195626 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-909 2195223 2195262 2195352 "PCOMP" 2195439 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-908 2193263 2194024 2194321 "PBWLB" 2194952 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-907 2192889 2192952 2193061 "PATTERN2" 2193200 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-906 2190598 2191034 2191491 "PATTERN1" 2192478 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-905 2182779 2184671 2186009 "PATTERN" 2189281 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-904 2182337 2182410 2182542 "PATRES2" 2182706 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-903 2179603 2180286 2180767 "PATRES" 2181902 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-902 2177456 2177891 2178298 "PATMATCH" 2179270 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-901 2176910 2177161 2177202 "PATMAB" 2177309 NIL PATMAB (NIL T) -9 NIL 2177392 NIL) (-900 2175356 2175764 2176022 "PATLRES" 2176715 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-899 2174894 2175025 2175066 "PATAB" 2175071 NIL PATAB (NIL T) -9 NIL 2175243 NIL) (-898 2173034 2173471 2173894 "PARTPERM" 2174491 T PARTPERM (NIL) -7 NIL NIL NIL) (-897 2172643 2172718 2172820 "PARSURF" 2172965 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-896 2172269 2172332 2172441 "PARSU2" 2172580 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-895 2172027 2172073 2172140 "PARSER" 2172222 T PARSER (NIL) -7 NIL NIL NIL) (-894 2171636 2171711 2171813 "PARSCURV" 2171958 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-893 2171262 2171325 2171434 "PARSC2" 2171573 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-892 2170889 2170959 2171056 "PARPCURV" 2171198 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-891 2170515 2170578 2170687 "PARPC2" 2170826 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-890 2169504 2169888 2170070 "PARAMAST" 2170353 T PARAMAST (NIL) -8 NIL NIL NIL) (-889 2169012 2169110 2169229 "PAN2EXPR" 2169405 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-888 2167705 2168133 2168361 "PALETTE" 2168804 T PALETTE (NIL) -8 NIL NIL NIL) (-887 2166050 2166710 2167070 "PAIR" 2167391 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-886 2158999 2165307 2165502 "PADICRC" 2165904 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-885 2151272 2158343 2158528 "PADICRAT" 2158846 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-884 2148071 2149932 2149972 "PADICCT" 2150553 NIL PADICCT (NIL NIL) -9 NIL 2150835 NIL) (-883 2146089 2148008 2148053 "PADIC" 2148058 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-882 2145034 2145246 2145514 "PADEPAC" 2145876 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-881 2144234 2144379 2144585 "PADE" 2144896 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-880 2142467 2143442 2143722 "OWP" 2144038 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-879 2141912 2142173 2142270 "OVERSET" 2142390 T OVERSET (NIL) -8 NIL NIL NIL) (-878 2140832 2141517 2141689 "OVAR" 2141780 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-877 2129068 2131941 2134141 "OUTFORM" 2138652 T OUTFORM (NIL) -8 NIL NIL NIL) (-876 2128350 2128665 2128792 "OUTBFILE" 2128961 T OUTBFILE (NIL) -8 NIL NIL NIL) (-875 2127627 2127822 2127850 "OUTBCON" 2128168 T OUTBCON (NIL) -9 NIL 2128334 NIL) (-874 2127210 2127340 2127497 "OUTBCON-" 2127502 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-873 2126450 2126595 2126756 "OUT" 2127069 T OUT (NIL) -7 NIL NIL NIL) (-872 2125746 2126179 2126268 "OSI" 2126381 T OSI (NIL) -8 NIL NIL NIL) (-871 2125165 2125587 2125615 "OSGROUP" 2125620 T OSGROUP (NIL) -9 NIL 2125642 NIL) (-870 2123876 2124137 2124422 "ORTHPOL" 2124912 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-869 2121141 2123711 2123832 "OREUP" 2123837 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-868 2118258 2120832 2120959 "ORESUP" 2121083 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-867 2115758 2116286 2116847 "OREPCTO" 2117747 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-866 2109143 2111631 2111672 "OREPCAT" 2114020 NIL OREPCAT (NIL T) -9 NIL 2115124 NIL) (-865 2106137 2107086 2108137 "OREPCAT-" 2108142 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-864 2105329 2105607 2105635 "ORDTYPE" 2105944 T ORDTYPE (NIL) -9 NIL 2106107 NIL) (-863 2104630 2104846 2105101 "ORDTYPE-" 2105106 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-862 2103986 2104369 2104527 "ORDSTRCT" 2104532 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-861 2103484 2103854 2103882 "ORDSET" 2103887 T ORDSET (NIL) -9 NIL 2103909 NIL) (-860 2102135 2103106 2103134 "ORDRING" 2103139 T ORDRING (NIL) -9 NIL 2103168 NIL) (-859 2101386 2101951 2101979 "ORDMON" 2101984 T ORDMON (NIL) -9 NIL 2102005 NIL) (-858 2100530 2100695 2100890 "ORDFUNS" 2101235 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-857 2099745 2100260 2100288 "ORDFIN" 2100353 T ORDFIN (NIL) -9 NIL 2100427 NIL) (-856 2098999 2099138 2099324 "ORDCOMP2" 2099605 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-855 2095353 2097585 2097994 "ORDCOMP" 2098623 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 2091874 2092844 2093658 "OPTPROB" 2094559 T OPTPROB (NIL) -8 NIL NIL NIL) (-853 2088616 2089315 2090019 "OPTPACK" 2091190 T OPTPACK (NIL) -7 NIL NIL NIL) (-852 2086229 2087055 2087083 "OPTCAT" 2087902 T OPTCAT (NIL) -9 NIL 2088552 NIL) (-851 2085547 2085906 2086011 "OPSIG" 2086144 T OPSIG (NIL) -8 NIL NIL NIL) (-850 2085309 2085354 2085420 "OPQUERY" 2085501 T OPQUERY (NIL) -7 NIL NIL NIL) (-849 2084615 2084895 2084936 "OPERCAT" 2085148 NIL OPERCAT (NIL T) -9 NIL 2085245 NIL) (-848 2084358 2084426 2084543 "OPERCAT-" 2084548 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-847 2081276 2082669 2083173 "OP" 2083887 NIL OP (NIL T) -8 NIL NIL NIL) (-846 2080569 2080696 2080870 "ONECOMP2" 2081148 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-845 2077189 2079366 2079735 "ONECOMP" 2080233 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 2073814 2076629 2076669 "OMSAGG" 2076730 NIL OMSAGG (NIL T) -9 NIL 2076794 NIL) (-843 2072161 2073363 2073532 "OMLO" 2073695 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-842 2070439 2071631 2071659 "OINTDOM" 2071664 T OINTDOM (NIL) -9 NIL 2071685 NIL) (-841 2067521 2069127 2069464 "OFMONOID" 2070134 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2066755 2067458 2067503 "ODVAR" 2067508 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2063901 2066500 2066655 "ODR" 2066660 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2055349 2063677 2063803 "ODPOL" 2063808 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2048764 2055221 2055326 "ODP" 2055331 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2047506 2047745 2048020 "ODETOOLS" 2048538 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2044449 2045131 2045847 "ODESYS" 2046839 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2039279 2040239 2041264 "ODERTRIC" 2043524 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2038699 2038787 2038981 "ODERED" 2039191 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2035559 2036141 2036816 "ODERAT" 2038124 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2032475 2032983 2033580 "ODEPRRIC" 2035088 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2030370 2031014 2031500 "ODEPROB" 2032009 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2026836 2027375 2028022 "ODEPRIM" 2029849 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2026079 2026187 2026447 "ODEPAL" 2026728 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2022181 2023032 2023896 "ODEPACK" 2025235 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2021224 2021349 2021571 "ODEINT" 2022070 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2015289 2016750 2018197 "ODEIFTBL" 2019797 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2010653 2011483 2012431 "ODEEF" 2014452 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2009996 2010091 2010314 "ODECONST" 2010558 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2008059 2008768 2008796 "ODECAT" 2009401 T ODECAT (NIL) -9 NIL 2009932 NIL) (-821 2007691 2007740 2007867 "OCTCT2" 2008010 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2004203 2007396 2007518 "OCT" 2007601 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2003396 2003996 2004024 "OCAMON" 2004029 T OCAMON (NIL) -9 NIL 2004050 NIL) (-818 1997674 2000439 2000479 "OC" 2001576 NIL OC (NIL T) -9 NIL 2002434 NIL) (-817 1994730 1995663 1996646 "OC-" 1996740 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 1994150 1994575 1994603 "OASGP" 1994608 T OASGP (NIL) -9 NIL 1994628 NIL) (-815 1993246 1993873 1993901 "OAMONS" 1993941 T OAMONS (NIL) -9 NIL 1993984 NIL) (-814 1992422 1992981 1993009 "OAMON" 1993067 T OAMON (NIL) -9 NIL 1993119 NIL) (-813 1992280 1992313 1992381 "OAMON-" 1992386 NIL OAMON- (NIL T) -8 NIL NIL NIL) (-812 1991061 1991814 1991842 "OAGROUP" 1991989 T OAGROUP (NIL) -9 NIL 1992082 NIL) (-811 1990764 1990852 1990970 "OAGROUP-" 1990975 NIL OAGROUP- (NIL T) -8 NIL NIL NIL) (-810 1990448 1990504 1990592 "NUMTUBE" 1990708 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-809 1983967 1985539 1987075 "NUMQUAD" 1988932 T NUMQUAD (NIL) -7 NIL NIL NIL) (-808 1979647 1980681 1981716 "NUMODE" 1982952 T NUMODE (NIL) -7 NIL NIL NIL) (-807 1976928 1977868 1977896 "NUMINT" 1978819 T NUMINT (NIL) -9 NIL 1979583 NIL) (-806 1975840 1976073 1976291 "NUMFMT" 1976730 T NUMFMT (NIL) -7 NIL NIL NIL) (-805 1962023 1965144 1967676 "NUMERIC" 1973347 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-804 1955869 1961472 1961567 "NTSCAT" 1961572 NIL NTSCAT (NIL T T T T) -9 NIL 1961611 NIL) (-803 1955049 1955228 1955421 "NTPOLFN" 1955708 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-802 1954675 1954738 1954847 "NSUP2" 1954986 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-801 1941497 1951500 1952312 "NSUP" 1953896 NIL NSUP (NIL T) -8 NIL NIL NIL) (-800 1930383 1941271 1941404 "NSMP" 1941409 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-799 1928791 1929116 1929473 "NREP" 1930071 NIL NREP (NIL T) -7 NIL NIL NIL) (-798 1927370 1927634 1927992 "NPCOEF" 1928534 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-797 1926418 1926551 1926767 "NORMRETR" 1927251 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-796 1924429 1924749 1925158 "NORMPK" 1926126 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-795 1924108 1924142 1924266 "NORMMA" 1924395 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-794 1923891 1923926 1923995 "NONE1" 1924072 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-793 1923655 1923848 1923877 "NONE" 1923882 T NONE (NIL) -8 NIL NIL NIL) (-792 1923146 1923214 1923393 "NODE1" 1923587 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-791 1921207 1922269 1922524 "NNI" 1922871 T NNI (NIL) -8 NIL NIL 1923106) (-790 1919603 1919940 1920304 "NLINSOL" 1920875 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-789 1915784 1916839 1917738 "NIPROB" 1918724 T NIPROB (NIL) -8 NIL NIL NIL) (-788 1914523 1914775 1915077 "NFINTBAS" 1915546 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-787 1913607 1914173 1914214 "NETCLT" 1914386 NIL NETCLT (NIL T) -9 NIL 1914468 NIL) (-786 1912279 1912546 1912827 "NCODIV" 1913375 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-785 1912035 1912078 1912153 "NCNTFRAC" 1912236 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-784 1910191 1910579 1910999 "NCEP" 1911660 NIL NCEP (NIL T) -7 NIL NIL NIL) (-783 1908861 1909801 1909829 "NASRING" 1909939 T NASRING (NIL) -9 NIL 1910019 NIL) (-782 1908644 1908700 1908794 "NASRING-" 1908799 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-781 1907611 1908262 1908290 "NARNG" 1908407 T NARNG (NIL) -9 NIL 1908498 NIL) (-780 1907285 1907370 1907504 "NARNG-" 1907509 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-779 1906122 1906371 1906606 "NAGSP" 1907070 T NAGSP (NIL) -7 NIL NIL NIL) (-778 1897166 1899078 1900751 "NAGS" 1904469 T NAGS (NIL) -7 NIL NIL NIL) (-777 1895690 1896022 1896353 "NAGF07" 1896855 T NAGF07 (NIL) -7 NIL NIL NIL) (-776 1890162 1891519 1892826 "NAGF04" 1894403 T NAGF04 (NIL) -7 NIL NIL NIL) (-775 1883034 1884744 1886377 "NAGF02" 1888549 T NAGF02 (NIL) -7 NIL NIL NIL) (-774 1878198 1879358 1880475 "NAGF01" 1881937 T NAGF01 (NIL) -7 NIL NIL NIL) (-773 1871778 1873392 1874977 "NAGE04" 1876633 T NAGE04 (NIL) -7 NIL NIL NIL) (-772 1862839 1865068 1867198 "NAGE02" 1869668 T NAGE02 (NIL) -7 NIL NIL NIL) (-771 1858732 1859739 1860703 "NAGE01" 1861895 T NAGE01 (NIL) -7 NIL NIL NIL) (-770 1856509 1857061 1857619 "NAGD03" 1858194 T NAGD03 (NIL) -7 NIL NIL NIL) (-769 1848205 1850187 1852141 "NAGD02" 1854575 T NAGD02 (NIL) -7 NIL NIL NIL) (-768 1841944 1843441 1844881 "NAGD01" 1846785 T NAGD01 (NIL) -7 NIL NIL NIL) (-767 1838081 1838975 1839812 "NAGC06" 1841127 T NAGC06 (NIL) -7 NIL NIL NIL) (-766 1836528 1836878 1837234 "NAGC05" 1837745 T NAGC05 (NIL) -7 NIL NIL NIL) (-765 1835892 1836023 1836167 "NAGC02" 1836404 T NAGC02 (NIL) -7 NIL NIL NIL) (-764 1834693 1835420 1835460 "NAALG" 1835539 NIL NAALG (NIL T) -9 NIL 1835600 NIL) (-763 1834522 1834557 1834647 "NAALG-" 1834652 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-762 1828394 1829580 1830767 "MULTSQFR" 1833418 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-761 1827701 1827788 1827972 "MULTFACT" 1828306 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-760 1819848 1824286 1824339 "MTSCAT" 1825409 NIL MTSCAT (NIL T T) -9 NIL 1825924 NIL) (-759 1819554 1819614 1819706 "MTHING" 1819788 NIL MTHING (NIL T) -7 NIL NIL NIL) (-758 1819340 1819379 1819439 "MSYSCMD" 1819514 T MSYSCMD (NIL) -7 NIL NIL NIL) (-757 1816196 1818901 1818942 "MSETAGG" 1818947 NIL MSETAGG (NIL T) -9 NIL 1818981 NIL) (-756 1812024 1814951 1815271 "MSET" 1815909 NIL MSET (NIL T) -8 NIL NIL NIL) (-755 1807628 1809403 1810148 "MRING" 1811324 NIL MRING (NIL T T) -8 NIL NIL NIL) (-754 1807188 1807261 1807392 "MRF2" 1807555 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-753 1806800 1806841 1806985 "MRATFAC" 1807147 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-752 1804370 1804707 1805138 "MPRFF" 1806505 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-751 1797730 1804224 1804321 "MPOLY" 1804326 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-750 1797214 1797255 1797463 "MPCPF" 1797689 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-749 1796722 1796771 1796955 "MPC3" 1797165 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-748 1795905 1795998 1796219 "MPC2" 1796637 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-747 1794182 1794543 1794933 "MONOTOOL" 1795565 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-746 1793327 1793710 1793738 "MONOID" 1793957 T MONOID (NIL) -9 NIL 1794104 NIL) (-745 1792843 1792992 1793173 "MONOID-" 1793178 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-744 1781825 1788663 1788722 "MONOGEN" 1789396 NIL MONOGEN (NIL T T) -9 NIL 1789852 NIL) (-743 1778896 1779792 1780785 "MONOGEN-" 1780904 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-742 1777613 1778161 1778189 "MONADWU" 1778581 T MONADWU (NIL) -9 NIL 1778819 NIL) (-741 1776943 1777144 1777392 "MONADWU-" 1777397 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-740 1776228 1776532 1776560 "MONAD" 1776767 T MONAD (NIL) -9 NIL 1776879 NIL) (-739 1775895 1775991 1776123 "MONAD-" 1776128 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-738 1774034 1774808 1775087 "MOEBIUS" 1775648 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-737 1773202 1773702 1773742 "MODULE" 1773747 NIL MODULE (NIL T) -9 NIL 1773786 NIL) (-736 1772740 1772866 1773056 "MODULE-" 1773061 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-735 1770314 1771148 1771475 "MODRING" 1772564 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-734 1767045 1768419 1768940 "MODOP" 1769843 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-733 1765531 1766112 1766389 "MODMONOM" 1766908 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-732 1754326 1763822 1764236 "MODMON" 1765168 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-731 1751185 1753194 1753470 "MODFIELD" 1754201 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1750096 1750466 1750656 "MMLFORM" 1751015 T MMLFORM (NIL) -8 NIL NIL NIL) (-729 1749616 1749665 1749844 "MMAP" 1750047 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-728 1747509 1748448 1748489 "MLO" 1748912 NIL MLO (NIL T) -9 NIL 1749154 NIL) (-727 1744857 1745391 1745993 "MLIFT" 1746990 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-726 1744236 1744332 1744486 "MKUCFUNC" 1744768 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-725 1743829 1743905 1744028 "MKRECORD" 1744159 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-724 1742852 1743038 1743266 "MKFUNC" 1743640 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-723 1742228 1742344 1742500 "MKFLCFN" 1742735 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-722 1741493 1741607 1741792 "MKBCFUNC" 1742121 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-721 1737492 1741047 1741183 "MINT" 1741377 T MINT (NIL) -8 NIL NIL NIL) (-720 1736274 1736547 1736824 "MHROWRED" 1737247 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-719 1731034 1734809 1735214 "MFLOAT" 1735889 T MFLOAT (NIL) -8 NIL NIL NIL) (-718 1730379 1730467 1730638 "MFINFACT" 1730946 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-717 1726678 1727557 1728436 "MESH" 1729520 T MESH (NIL) -7 NIL NIL NIL) (-716 1725032 1725380 1725733 "MDDFACT" 1726365 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-715 1721679 1724163 1724204 "MDAGG" 1724459 NIL MDAGG (NIL T) -9 NIL 1724602 NIL) (-714 1709415 1720972 1721179 "MCMPLX" 1721492 T MCMPLX (NIL) -8 NIL NIL NIL) (-713 1708534 1708698 1708899 "MCDEN" 1709264 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-712 1706382 1706694 1707074 "MCALCFN" 1708264 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-711 1705259 1705547 1705780 "MAYBE" 1706188 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-710 1702817 1703394 1703956 "MATSTOR" 1704730 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-709 1698352 1702189 1702437 "MATRIX" 1702602 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-708 1694052 1694825 1695561 "MATLIN" 1697709 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-707 1692628 1692799 1693132 "MATCAT2" 1693887 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-706 1682075 1685682 1685759 "MATCAT" 1690794 NIL MATCAT (NIL T T T) -9 NIL 1692266 NIL) (-705 1678028 1679338 1680751 "MATCAT-" 1680756 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-704 1676104 1676464 1676848 "MAPPKG3" 1677703 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-703 1675061 1675258 1675480 "MAPPKG2" 1675928 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-702 1673518 1673844 1674171 "MAPPKG1" 1674767 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-701 1672519 1672924 1673101 "MAPPAST" 1673361 T MAPPAST (NIL) -8 NIL NIL NIL) (-700 1672124 1672188 1672311 "MAPHACK3" 1672455 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-699 1671704 1671777 1671891 "MAPHACK2" 1672056 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-698 1671130 1671245 1671387 "MAPHACK1" 1671595 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-697 1669053 1669830 1670134 "MAGMA" 1670858 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-696 1668472 1668777 1668868 "MACROAST" 1668982 T MACROAST (NIL) -8 NIL NIL NIL) (-695 1664829 1666711 1667172 "M3D" 1668044 NIL M3D (NIL T) -8 NIL NIL NIL) (-694 1658303 1663140 1663181 "LZSTAGG" 1663963 NIL LZSTAGG (NIL T) -9 NIL 1664258 NIL) (-693 1653985 1655434 1656891 "LZSTAGG-" 1656896 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-692 1650898 1651876 1652363 "LWORD" 1653530 NIL LWORD (NIL T) -8 NIL NIL NIL) (-691 1650420 1650702 1650777 "LSTAST" 1650843 T LSTAST (NIL) -8 NIL NIL NIL) (-690 1642493 1650191 1650325 "LSQM" 1650330 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-689 1641711 1641856 1642084 "LSPP" 1642348 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-688 1638511 1639210 1639923 "LSMP1" 1641030 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-687 1636316 1636640 1637089 "LSMP" 1638207 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-686 1629446 1635406 1635447 "LSAGG" 1635509 NIL LSAGG (NIL T) -9 NIL 1635587 NIL) (-685 1625955 1627065 1628278 "LSAGG-" 1628283 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-684 1623250 1625099 1625348 "LPOLY" 1625750 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-683 1622826 1622917 1623040 "LPEFRAC" 1623159 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-682 1622509 1622588 1622616 "LOGIC" 1622727 T LOGIC (NIL) -9 NIL 1622809 NIL) (-681 1622365 1622394 1622465 "LOGIC-" 1622470 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-680 1621540 1621698 1621891 "LODOOPS" 1622221 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-679 1620064 1620313 1620666 "LODOF" 1621287 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-678 1615954 1618699 1618740 "LODOCAT" 1619178 NIL LODOCAT (NIL T) -9 NIL 1619389 NIL) (-677 1615669 1615745 1615872 "LODOCAT-" 1615877 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-676 1612669 1615510 1615628 "LODO2" 1615633 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-675 1609790 1612606 1612651 "LODO1" 1612656 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-674 1606899 1609706 1609772 "LODO" 1609777 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1605768 1605945 1606250 "LODEEF" 1606722 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-672 1603754 1604862 1605115 "LO" 1605600 NIL LO (NIL T T T) -8 NIL NIL NIL) (-671 1598837 1601920 1601961 "LNAGG" 1602823 NIL LNAGG (NIL T) -9 NIL 1603258 NIL) (-670 1597930 1598198 1598540 "LNAGG-" 1598545 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-669 1593910 1594855 1595494 "LMOPS" 1597345 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-668 1593209 1593687 1593728 "LMODULE" 1593733 NIL LMODULE (NIL T) -9 NIL 1593759 NIL) (-667 1590278 1592854 1592977 "LMDICT" 1593119 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-666 1589854 1590068 1590109 "LLINSET" 1590170 NIL LLINSET (NIL T) -9 NIL 1590214 NIL) (-665 1589499 1589762 1589822 "LITERAL" 1589827 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-664 1589018 1589098 1589237 "LIST3" 1589419 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-663 1587116 1587464 1587863 "LIST2MAP" 1588665 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-662 1586105 1586301 1586529 "LIST2" 1586934 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-661 1578859 1585137 1585392 "LIST" 1585883 NIL LIST (NIL T) -8 NIL NIL NIL) (-660 1578442 1578678 1578719 "LINSET" 1578724 NIL LINSET (NIL T) -9 NIL 1578758 NIL) (-659 1577256 1577950 1578117 "LINFORM" 1578327 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-658 1575555 1576283 1576324 "LINEXP" 1576814 NIL LINEXP (NIL T) -9 NIL 1577087 NIL) (-657 1574131 1575035 1575216 "LINELT" 1575426 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-656 1572688 1572968 1573279 "LINDEP" 1573883 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-655 1571824 1572420 1572530 "LINBASIS" 1572618 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-654 1568632 1569362 1570120 "LIMITRF" 1571098 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-653 1566940 1567247 1567649 "LIMITPS" 1568334 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-652 1565768 1566343 1566383 "LIECAT" 1566523 NIL LIECAT (NIL T) -9 NIL 1566674 NIL) (-651 1565603 1565636 1565724 "LIECAT-" 1565729 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-650 1559655 1565114 1565342 "LIE" 1565424 NIL LIE (NIL T T) -8 NIL NIL NIL) (-649 1551956 1559195 1559351 "LIB" 1559519 T LIB (NIL) -8 NIL NIL NIL) (-648 1547525 1548474 1549409 "LGROBP" 1551073 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-647 1546149 1547057 1547085 "LFCAT" 1547292 T LFCAT (NIL) -9 NIL 1547431 NIL) (-646 1544087 1544421 1544771 "LF" 1545870 NIL LF (NIL T T) -7 NIL NIL NIL) (-645 1540947 1541619 1542307 "LEXTRIPK" 1543451 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-644 1537535 1538517 1539020 "LEXP" 1540527 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-643 1536951 1537256 1537348 "LETAST" 1537463 T LETAST (NIL) -8 NIL NIL NIL) (-642 1535337 1535662 1536063 "LEADCDET" 1536633 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-641 1534515 1534601 1534830 "LAZM3PK" 1535258 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-640 1529054 1532592 1533130 "LAUPOL" 1534027 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-639 1528627 1528677 1528838 "LAPLACE" 1529004 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-638 1527475 1528191 1528232 "LALG" 1528294 NIL LALG (NIL T) -9 NIL 1528353 NIL) (-637 1527171 1527248 1527384 "LALG-" 1527389 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-636 1524908 1526272 1526523 "LA" 1527004 NIL LA (NIL T T T) -8 NIL NIL NIL) (-635 1524737 1524767 1524808 "KVTFROM" 1524870 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-634 1523494 1524104 1524289 "KTVLOGIC" 1524572 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-633 1523323 1523353 1523394 "KRCFROM" 1523456 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-632 1522215 1522414 1522713 "KOVACIC" 1523123 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-631 1522044 1522074 1522115 "KONVERT" 1522177 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-630 1521873 1521903 1521944 "KOERCE" 1522006 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-629 1521357 1521450 1521582 "KERNEL2" 1521787 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-628 1519044 1519950 1520327 "KERNEL" 1521013 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-627 1512626 1517521 1517575 "KDAGG" 1517952 NIL KDAGG (NIL T T) -9 NIL 1518158 NIL) (-626 1512137 1512279 1512484 "KDAGG-" 1512489 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-625 1504953 1511798 1511953 "KAFILE" 1512015 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-624 1504557 1504842 1504905 "JVMOP" 1504910 T JVMOP (NIL) -8 NIL NIL NIL) (-623 1503293 1503797 1504046 "JVMMDACC" 1504328 T JVMMDACC (NIL) -8 NIL NIL NIL) (-622 1502229 1502683 1502888 "JVMFDACC" 1503108 T JVMFDACC (NIL) -8 NIL NIL NIL) (-621 1500810 1501305 1501605 "JVMCSTTG" 1501949 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-620 1499946 1500350 1500511 "JVMCFACC" 1500669 T JVMCFACC (NIL) -8 NIL NIL NIL) (-619 1499624 1499863 1499912 "JVMBCODE" 1499917 T JVMBCODE (NIL) -8 NIL NIL NIL) (-618 1493675 1499135 1499363 "JORDAN" 1499445 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-617 1492988 1493324 1493445 "JOINAST" 1493574 T JOINAST (NIL) -8 NIL NIL NIL) (-616 1489134 1491165 1491219 "IXAGG" 1492148 NIL IXAGG (NIL T T) -9 NIL 1492607 NIL) (-615 1487987 1488359 1488778 "IXAGG-" 1488783 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1483190 1487909 1487968 "IVECTOR" 1487973 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1481915 1482193 1482459 "ITUPLE" 1482957 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1480387 1480594 1480889 "ITRIGMNP" 1481737 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1479114 1479336 1479619 "ITFUN3" 1480163 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1478712 1478775 1478898 "ITFUN2" 1479037 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-609 1477817 1478192 1478366 "ITFORM" 1478558 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1475586 1476837 1477115 "ITAYLOR" 1477572 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1463990 1469723 1470886 "ISUPS" 1474456 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1463082 1463234 1463470 "ISUMP" 1463837 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1458046 1463027 1463068 "ISTRING" 1463073 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1457462 1457767 1457859 "ISAST" 1457974 T ISAST (NIL) -8 NIL NIL NIL) (-603 1456660 1456753 1456969 "IRURPK" 1457376 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1455572 1455797 1456037 "IRSN" 1456440 T IRSN (NIL) -7 NIL NIL NIL) (-601 1453617 1453998 1454427 "IRRF2F" 1455210 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1453358 1453402 1453478 "IRREDFFX" 1453573 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1451931 1452232 1452531 "IROOT" 1453091 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1451070 1451424 1451575 "IRFORM" 1451800 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1450152 1450283 1450497 "IR2F" 1450953 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-596 1447741 1448260 1448826 "IR2" 1449630 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1444181 1445425 1446117 "IR" 1447081 NIL IR (NIL T) -8 NIL NIL NIL) (-594 1443966 1444006 1444066 "IPRNTPK" 1444141 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1439942 1443855 1443924 "IPF" 1443929 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1437972 1439867 1439924 "IPADIC" 1439929 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1437230 1437532 1437662 "IP4ADDR" 1437862 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1436568 1436859 1436991 "IOMODE" 1437118 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1435539 1436165 1436292 "IOBFILE" 1436461 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1434949 1435443 1435471 "IOBCON" 1435476 T IOBCON (NIL) -9 NIL 1435497 NIL) (-587 1434454 1434518 1434701 "INVLAPLA" 1434885 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1424072 1426492 1428866 "INTTR" 1432130 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1420365 1421149 1422014 "INTTOOLS" 1423257 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1419945 1420042 1420159 "INTSLPE" 1420268 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1417412 1419868 1419927 "INTRVL" 1419932 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1414990 1415526 1416101 "INTRF" 1416897 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1414383 1414498 1414640 "INTRET" 1414888 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1412356 1412769 1413239 "INTRAT" 1413991 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1409601 1410202 1410821 "INTPM" 1411841 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1406341 1406961 1407692 "INTPAF" 1408994 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1401442 1402482 1403533 "INTPACK" 1405310 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1400688 1400846 1401054 "INTHERTR" 1401284 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1400121 1400207 1400395 "INTHERAL" 1400602 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1397889 1398410 1398867 "INTHEORY" 1399684 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1389279 1390956 1392710 "INTG0" 1396259 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1375504 1378917 1382302 "INTFTBL" 1385914 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1374729 1374891 1375064 "INTFACT" 1375363 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1372132 1372606 1373161 "INTEF" 1374285 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1370329 1371224 1371252 "INTDOM" 1371553 T INTDOM (NIL) -9 NIL 1371760 NIL) (-568 1369668 1369872 1370114 "INTDOM-" 1370119 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1365536 1367957 1368011 "INTCAT" 1368810 NIL INTCAT (NIL T) -9 NIL 1369131 NIL) (-566 1364990 1365111 1365239 "INTBIT" 1365428 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1363671 1363843 1364150 "INTALG" 1364835 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1363148 1363244 1363401 "INTAF" 1363575 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1356231 1362958 1363098 "INTABL" 1363103 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1355472 1356034 1356099 "INT8" 1356133 T INT8 (NIL) -8 NIL NIL 1356178) (-561 1354712 1355274 1355339 "INT64" 1355373 T INT64 (NIL) -8 NIL NIL 1355418) (-560 1353952 1354514 1354579 "INT32" 1354613 T INT32 (NIL) -8 NIL NIL 1354658) (-559 1353192 1353754 1353819 "INT16" 1353853 T INT16 (NIL) -8 NIL NIL 1353898) (-558 1349544 1353003 1353105 "INT" 1353110 T INT (NIL) -8 NIL NIL NIL) (-557 1343655 1347092 1347120 "INS" 1348054 T INS (NIL) -9 NIL 1348719 NIL) (-556 1340812 1341732 1342673 "INS-" 1342746 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1339642 1339865 1340141 "INPSIGN" 1340587 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1338736 1338877 1339074 "INPRODPF" 1339522 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1337606 1337747 1337984 "INPRODFF" 1338616 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1336594 1336758 1337018 "INNMFACT" 1337442 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1335773 1335888 1336076 "INMODGCD" 1336493 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1334257 1334526 1334850 "INFSP" 1335518 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1333417 1333558 1333741 "INFPROD0" 1334137 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1333015 1333087 1333185 "INFORM1" 1333352 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1329582 1331080 1331595 "INFORM" 1332508 T INFORM (NIL) -8 NIL NIL NIL) (-546 1329087 1329194 1329308 "INFINITY" 1329488 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1328161 1328807 1328908 "INETCLTS" 1329006 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1326759 1327027 1327348 "INEP" 1327909 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1325789 1326656 1326721 "INDE" 1326726 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1325341 1325421 1325538 "INCRMAPS" 1325716 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1324063 1324610 1324816 "INBFILE" 1325155 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1319243 1320299 1321243 "INBFF" 1323151 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1318097 1318420 1318448 "INBCON" 1318961 T INBCON (NIL) -9 NIL 1319227 NIL) (-538 1317307 1317572 1317848 "INBCON-" 1317853 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1316726 1317031 1317122 "INAST" 1317236 T INAST (NIL) -8 NIL NIL NIL) (-536 1316093 1316405 1316511 "IMPTAST" 1316640 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1312127 1315937 1316041 "IMATRIX" 1316046 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1310819 1310958 1311274 "IMATQF" 1311983 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1308999 1309266 1309603 "IMATLIN" 1310575 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1302916 1308923 1308981 "ILIST" 1308986 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1300696 1302776 1302889 "IIARRAY2" 1302894 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1295519 1300607 1300671 "IFF" 1300676 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1294800 1295136 1295252 "IFAST" 1295423 T IFAST (NIL) -8 NIL NIL NIL) (-528 1289426 1294092 1294280 "IFARRAY" 1294657 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1288464 1289330 1289403 "IFAMON" 1289408 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1288036 1288113 1288167 "IEVALAB" 1288374 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1287699 1287779 1287939 "IEVALAB-" 1287944 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1286732 1287588 1287663 "IDPOAMS" 1287668 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1285834 1286621 1286696 "IDPOAM" 1286701 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1285215 1285749 1285811 "IDPO" 1285816 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1283695 1284222 1284274 "IDPC" 1284786 NIL IDPC (NIL T T) -9 NIL 1285067 NIL) (-520 1283027 1283587 1283660 "IDPAM" 1283665 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1282242 1282919 1282992 "IDPAG" 1282997 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1281786 1282048 1282138 "IDENT" 1282172 T IDENT (NIL) -8 NIL NIL NIL) (-517 1278005 1278889 1279784 "IDECOMP" 1280943 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1270640 1271928 1272975 "IDEAL" 1277041 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1269782 1269912 1270112 "ICDEN" 1270524 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1268757 1269262 1269409 "ICARD" 1269655 T ICARD (NIL) -8 NIL NIL NIL) (-513 1266787 1267130 1267535 "IBPTOOLS" 1268434 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1262016 1266407 1266520 "IBITS" 1266706 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1258691 1259315 1260010 "IBATOOL" 1261433 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1256452 1256932 1257465 "IBACHIN" 1258226 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1254156 1256298 1256401 "IARRAY2" 1256406 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1249983 1254082 1254139 "IARRAY1" 1254144 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1243009 1248395 1248876 "IAN" 1249522 T IAN (NIL) -8 NIL NIL NIL) (-506 1242514 1242577 1242750 "IALGFACT" 1242946 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1242006 1242155 1242183 "HYPCAT" 1242390 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1241508 1241661 1241847 "HYPCAT-" 1241852 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1241055 1241303 1241386 "HOSTNAME" 1241445 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1240888 1240937 1240978 "HOMOTOP" 1240983 NIL HOMOTOP (NIL T) -9 NIL 1241016 NIL) (-501 1237432 1238820 1238861 "HOAGG" 1239842 NIL HOAGG (NIL T) -9 NIL 1240571 NIL) (-500 1235948 1236425 1236951 "HOAGG-" 1236956 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1229021 1235541 1235691 "HEXADEC" 1235818 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1227733 1227991 1228254 "HEUGCD" 1228798 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1226665 1227570 1227700 "HELLFDIV" 1227705 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1224789 1226442 1226530 "HEAP" 1226609 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1223986 1224341 1224475 "HEADAST" 1224675 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1217445 1223901 1223963 "HDP" 1223968 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1210490 1217080 1217232 "HDMP" 1217346 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1209796 1209954 1210118 "HB" 1210346 T HB (NIL) -7 NIL NIL NIL) (-491 1202922 1209642 1209746 "HASHTBL" 1209751 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1202338 1202643 1202735 "HASAST" 1202850 T HASAST (NIL) -8 NIL NIL NIL) (-489 1199755 1201960 1202142 "HACKPI" 1202176 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1195068 1199608 1199721 "GTSET" 1199726 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1188223 1194946 1195044 "GSTBL" 1195049 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1179988 1187388 1187644 "GSERIES" 1188023 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1179019 1179532 1179560 "GROUP" 1179763 T GROUP (NIL) -9 NIL 1179897 NIL) (-484 1178343 1178544 1178795 "GROUP-" 1178800 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1176692 1177031 1177418 "GROEBSOL" 1178020 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1175520 1175880 1175931 "GRMOD" 1176460 NIL GRMOD (NIL T T) -9 NIL 1176628 NIL) (-481 1175276 1175324 1175452 "GRMOD-" 1175457 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1170416 1171630 1172630 "GRIMAGE" 1174296 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1168810 1169143 1169467 "GRDEF" 1170112 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1168242 1168370 1168511 "GRAY" 1168689 T GRAY (NIL) -7 NIL NIL NIL) (-477 1167319 1167821 1167872 "GRALG" 1168025 NIL GRALG (NIL T T) -9 NIL 1168118 NIL) (-476 1166956 1167053 1167216 "GRALG-" 1167221 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1163553 1166541 1166719 "GPOLSET" 1166863 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1162901 1162964 1163222 "GOSPER" 1163490 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1158471 1159339 1159865 "GMODPOL" 1162600 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1157458 1157660 1157898 "GHENSEL" 1158283 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1151530 1152457 1153477 "GENUPS" 1156542 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1151221 1151278 1151367 "GENUFACT" 1151473 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1150621 1150710 1150875 "GENPGCD" 1151139 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1150089 1150130 1150343 "GENMFACT" 1150580 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1148626 1148912 1149219 "GENEEZ" 1149832 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1141830 1148237 1148399 "GDMP" 1148549 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1130590 1135601 1136707 "GCNAALG" 1140813 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1128717 1129765 1129793 "GCDDOM" 1130048 T GCDDOM (NIL) -9 NIL 1130205 NIL) (-463 1128157 1128314 1128529 "GCDDOM-" 1128534 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1116629 1119103 1121495 "GBINTERN" 1125848 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1114430 1114758 1115179 "GBF" 1116304 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1113187 1113376 1113643 "GBEUCLID" 1114246 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1111837 1112044 1112348 "GB" 1112966 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-458 1111168 1111311 1111460 "GAUSSFAC" 1111708 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1109489 1109837 1110151 "GALUTIL" 1110887 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1107749 1108071 1108395 "GALPOLYU" 1109216 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1105048 1105404 1105811 "GALFACTU" 1107446 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1096662 1098353 1099961 "GALFACT" 1103480 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1093948 1094708 1094736 "FVFUN" 1095892 T FVFUN (NIL) -9 NIL 1096612 NIL) (-452 1093178 1093396 1093424 "FVC" 1093715 T FVC (NIL) -9 NIL 1093898 NIL) (-451 1092779 1093003 1093071 "FUNDESC" 1093130 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1092352 1092576 1092657 "FUNCTION" 1092731 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1091029 1091653 1091856 "FTEM" 1092169 T FTEM (NIL) -8 NIL NIL NIL) (-448 1088671 1089360 1089823 "FT" 1090586 T FT (NIL) -8 NIL NIL NIL) (-447 1086940 1087251 1087648 "FSUPFACT" 1088362 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1085259 1085626 1085958 "FST" 1086628 T FST (NIL) -8 NIL NIL NIL) (-445 1084440 1084564 1084752 "FSRED" 1085141 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1083129 1083395 1083742 "FSPRMELT" 1084155 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1080339 1080873 1081359 "FSPECF" 1082692 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1079861 1079921 1080091 "FSINT" 1080280 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-441 1077997 1078854 1079157 "FSERIES" 1079640 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-440 1077021 1077155 1077379 "FSCINT" 1077877 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-439 1076045 1076206 1076433 "FSAGG2" 1076874 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-438 1072020 1074989 1075030 "FSAGG" 1075400 NIL FSAGG (NIL T) -9 NIL 1075659 NIL) (-437 1069620 1070383 1071179 "FSAGG-" 1071274 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 1067280 1067578 1068126 "FS2UPS" 1069338 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-435 1066146 1066329 1066631 "FS2EXPXP" 1067105 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-434 1065774 1065823 1065952 "FS2" 1066097 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 1046041 1055548 1055589 "FS" 1059473 NIL FS (NIL T) -9 NIL 1061762 NIL) (-432 1034183 1037731 1041761 "FS-" 1042061 NIL FS- (NIL T T) -8 NIL NIL NIL) (-431 1033597 1033724 1033876 "FRUTIL" 1034063 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 1028140 1031286 1031326 "FRNAALG" 1032646 NIL FRNAALG (NIL T) -9 NIL 1033244 NIL) (-429 1023672 1024923 1026181 "FRNAALG-" 1026931 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 1023304 1023353 1023480 "FRNAAF2" 1023623 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 1021591 1022153 1022449 "FRMOD" 1023116 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 1020776 1020869 1021160 "FRIDEAL2" 1021498 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-425 1018381 1019151 1019469 "FRIDEAL" 1020567 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 1017479 1017928 1017969 "FRETRCT" 1017974 NIL FRETRCT (NIL T) -9 NIL 1018150 NIL) (-423 1016558 1016836 1017180 "FRETRCT-" 1017185 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 1013379 1014842 1014901 "FRAMALG" 1015783 NIL FRAMALG (NIL T T) -9 NIL 1016075 NIL) (-421 1011417 1011968 1012598 "FRAMALG-" 1012821 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 1011047 1011110 1011217 "FRAC2" 1011354 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-419 1004534 1010692 1010883 "FRAC" 1010888 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 1004164 1004227 1004334 "FR2" 1004471 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 995196 999740 1001071 "FR" 1002865 NIL FR (NIL T) -8 NIL NIL NIL) (-416 989119 992575 992603 "FPS" 993722 T FPS (NIL) -9 NIL 994279 NIL) (-415 988544 988677 988841 "FPS-" 988987 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 985512 987501 987529 "FPC" 987754 T FPC (NIL) -9 NIL 987896 NIL) (-413 985293 985345 985442 "FPC-" 985447 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 984051 984781 984822 "FPATMAB" 984827 NIL FPATMAB (NIL T) -9 NIL 984979 NIL) (-411 982194 982793 983140 "FPARFRAC" 983767 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 977525 978125 978807 "FORTRAN" 981626 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 975099 975763 975791 "FORTFN" 976851 T FORTFN (NIL) -9 NIL 977475 NIL) (-408 974851 974913 974941 "FORTCAT" 975000 T FORTCAT (NIL) -9 NIL 975062 NIL) (-407 972537 973067 973606 "FORT" 974332 T FORT (NIL) -7 NIL NIL NIL) (-406 972054 972112 972285 "FORDER" 972479 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 971114 971314 971507 "FOP" 971881 T FOP (NIL) -7 NIL NIL NIL) (-404 969527 970394 970568 "FNLA" 970996 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 968146 968657 968685 "FNCAT" 969145 T FNCAT (NIL) -9 NIL 969405 NIL) (-402 967589 968105 968133 "FNAME" 968138 T FNAME (NIL) -8 NIL NIL NIL) (-401 965915 967088 967116 "FMTC" 967121 T FMTC (NIL) -9 NIL 967157 NIL) (-400 964471 965851 965897 "FMONOID" 965902 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 961060 962426 962467 "FMONCAT" 963684 NIL FMONCAT (NIL T) -9 NIL 964289 NIL) (-398 958382 959130 959158 "FMFUN" 960302 T FMFUN (NIL) -9 NIL 961010 NIL) (-397 955255 956307 956361 "FMCAT" 957556 NIL FMCAT (NIL T T) -9 NIL 958051 NIL) (-396 954488 954705 954733 "FMC" 955023 T FMC (NIL) -9 NIL 955205 NIL) (-395 953156 954254 954354 "FM1" 954433 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 952174 952898 953047 "FM" 953052 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 949912 950364 950858 "FLOATRP" 951725 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 947314 947850 948428 "FLOATCP" 949379 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 940132 945057 945671 "FLOAT" 946720 T FLOAT (NIL) -8 NIL NIL NIL) (-390 938650 939724 939765 "FLINEXP" 939770 NIL FLINEXP (NIL T) -9 NIL 939863 NIL) (-389 937780 938039 938367 "FLINEXP-" 938372 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 936838 937000 937224 "FLASORT" 937632 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 933756 934808 934860 "FLALG" 936087 NIL FLALG (NIL T T) -9 NIL 936554 NIL) (-386 932780 932941 933168 "FLAGG2" 933609 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 926149 930189 930230 "FLAGG" 931492 NIL FLAGG (NIL T) -9 NIL 932144 NIL) (-384 924803 925214 925704 "FLAGG-" 925709 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 921441 922648 922707 "FINRALG" 923835 NIL FINRALG (NIL T T) -9 NIL 924343 NIL) (-382 920565 920830 921169 "FINRALG-" 921174 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 919871 920170 920198 "FINITE" 920394 T FINITE (NIL) -9 NIL 920501 NIL) (-380 911822 914401 914441 "FINAALG" 918108 NIL FINAALG (NIL T) -9 NIL 919561 NIL) (-379 906938 908204 909348 "FINAALG-" 910727 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 905498 905920 905974 "FILECAT" 906658 NIL FILECAT (NIL T T) -9 NIL 906874 NIL) (-377 904776 905253 905356 "FILE" 905428 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 902181 904006 904034 "FIELD" 904074 T FIELD (NIL) -9 NIL 904154 NIL) (-375 900723 901186 901697 "FIELD-" 901702 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 898406 899358 899705 "FGROUP" 900409 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 897478 897660 897880 "FGLMICPK" 898238 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 892735 897403 897460 "FFX" 897465 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 892330 892397 892532 "FFSLPE" 892668 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 891828 891870 892079 "FFPOLY2" 892288 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 887704 888600 889396 "FFPOLY" 891064 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 882975 887623 887686 "FFP" 887691 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 877508 882318 882508 "FFNBX" 882829 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 871843 876643 876901 "FFNBP" 877362 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 865883 871127 871338 "FFNB" 871676 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 864703 864913 865228 "FFINTBAS" 865680 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 860298 862950 862978 "FFIELDC" 863598 T FFIELDC (NIL) -9 NIL 863974 NIL) (-362 858918 859359 859842 "FFIELDC-" 859847 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 858475 858533 858657 "FFHOM" 858860 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 856134 856657 857174 "FFF" 857990 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 851171 855876 855977 "FFCGX" 856077 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 846212 850903 851010 "FFCGP" 851114 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 840814 845939 846047 "FFCG" 846148 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 840219 840268 840503 "FFCAT2" 840765 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 818910 829951 830037 "FFCAT" 835202 NIL FFCAT (NIL T T T) -9 NIL 836653 NIL) (-354 813921 815155 816469 "FFCAT-" 817699 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 808744 813832 813896 "FF" 813901 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 797399 801716 802936 "FEXPR" 807596 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 796327 796796 796837 "FEVALAB" 796921 NIL FEVALAB (NIL T) -9 NIL 797182 NIL) (-350 795444 795696 796034 "FEVALAB-" 796039 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 792306 793191 793306 "FDIVCAT" 794874 NIL FDIVCAT (NIL T T T T) -9 NIL 795311 NIL) (-348 792062 792095 792265 "FDIVCAT-" 792270 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 791276 791369 791646 "FDIV2" 791969 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 789686 790659 790862 "FDIV" 791175 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 788594 788981 789183 "FCTRDATA" 789504 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 787250 787539 787828 "FCPAK1" 788325 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 786253 786750 786891 "FCOMP" 787141 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 769567 773403 776941 "FC" 782735 T FC (NIL) -8 NIL NIL NIL) (-341 761278 765888 765928 "FAXF" 767730 NIL FAXF (NIL T) -9 NIL 768422 NIL) (-340 758419 759226 760044 "FAXF-" 760509 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 753102 757795 757971 "FARRAY" 758276 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 747674 750049 750102 "FAMR" 751125 NIL FAMR (NIL T T) -9 NIL 751585 NIL) (-337 746498 746866 747301 "FAMR-" 747306 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 745525 746420 746473 "FAMONOID" 746478 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 743155 744007 744060 "FAMONC" 745001 NIL FAMONC (NIL T T) -9 NIL 745387 NIL) (-334 741629 742909 743046 "FAGROUP" 743051 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 739382 739743 740146 "FACUTIL" 741310 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 738469 738666 738888 "FACTFUNC" 739192 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 730212 737772 737971 "EXPUPXS" 738325 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 727665 728235 728821 "EXPRTUBE" 729646 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 723876 724528 725258 "EXPRODE" 727004 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 718310 719017 719823 "EXPR2UPS" 723174 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 717936 717999 718108 "EXPR2" 718247 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 702305 716585 717014 "EXPR" 717540 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 692664 701456 701747 "EXPEXPAN" 702141 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 692084 692388 692479 "EXITAST" 692593 T EXITAST (NIL) -8 NIL NIL NIL) (-323 691848 692041 692070 "EXIT" 692075 T EXIT (NIL) -8 NIL NIL NIL) (-322 691469 691537 691650 "EVALCYC" 691780 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 690986 691128 691169 "EVALAB" 691339 NIL EVALAB (NIL T) -9 NIL 691443 NIL) (-320 690443 690589 690810 "EVALAB-" 690815 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 687558 689099 689127 "EUCDOM" 689682 T EUCDOM (NIL) -9 NIL 690032 NIL) (-318 685918 686419 687002 "EUCDOM-" 687007 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 685544 685607 685716 "ESTOOLS2" 685855 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 685289 685337 685417 "ESTOOLS1" 685496 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 672606 675587 678337 "ESTOOLS" 682559 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 672345 672383 672465 "ESCONT1" 672568 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 668653 669480 670260 "ESCONT" 671585 T ESCONT (NIL) -7 NIL NIL NIL) (-312 668322 668378 668478 "ES2" 668597 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 667946 668010 668119 "ES1" 668258 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 661647 663577 663605 "ES" 666373 T ES (NIL) -9 NIL 667783 NIL) (-309 656324 657881 659698 "ES-" 659862 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 655516 655669 655845 "ERROR" 656168 T ERROR (NIL) -7 NIL NIL NIL) (-307 648648 655375 655466 "EQTBL" 655471 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 648274 648337 648446 "EQ2" 648585 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 640533 643588 645037 "EQ" 646858 NIL -3956 (NIL T) -8 NIL NIL NIL) (-304 635775 636871 637964 "EP" 639472 NIL EP (NIL T) -7 NIL NIL NIL) (-303 634315 634666 634972 "ENV" 635489 T ENV (NIL) -8 NIL NIL NIL) (-302 633275 633949 633977 "ENTIRER" 633982 T ENTIRER (NIL) -9 NIL 634028 NIL) (-301 629740 631501 631862 "EMR" 633083 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 628844 629055 629109 "ELTAGG" 629489 NIL ELTAGG (NIL T T) -9 NIL 629700 NIL) (-299 628551 628625 628766 "ELTAGG-" 628771 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 628309 628344 628398 "ELTAB" 628482 NIL ELTAB (NIL T T) -9 NIL 628534 NIL) (-297 627411 627581 627780 "ELFUTS" 628160 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 627135 627209 627237 "ELEMFUN" 627342 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 626999 627026 627094 "ELEMFUN-" 627099 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 621524 625041 625082 "ELAGG" 626022 NIL ELAGG (NIL T) -9 NIL 626485 NIL) (-293 619701 620243 620906 "ELAGG-" 620911 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 618983 619150 619306 "ELABOR" 619565 T ELABOR (NIL) -8 NIL NIL NIL) (-291 617589 617923 618217 "ELABEXPR" 618709 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 610228 612226 613055 "EFUPXS" 616864 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 603481 605477 606288 "EFULS" 609503 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 600918 601324 601796 "EFSTRUC" 603113 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 590356 592275 593823 "EF" 599433 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 589334 589841 589990 "EAB" 590227 T EAB (NIL) -8 NIL NIL NIL) (-285 588456 589293 589321 "E04UCFA" 589326 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 587578 588415 588443 "E04NAFA" 588448 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 586700 587537 587565 "E04MBFA" 587570 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 585822 586659 586687 "E04JAFA" 586692 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 584946 585781 585809 "E04GCFA" 585814 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 584070 584905 584933 "E04FDFA" 584938 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 583192 584029 584057 "E04DGFA" 584062 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 577269 578717 580081 "E04AGNT" 581848 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 575889 576570 576610 "DVARCAT" 576951 NIL DVARCAT (NIL T) -9 NIL 577114 NIL) (-276 575039 575305 575619 "DVARCAT-" 575624 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 567043 574838 574967 "DSMP" 574972 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 565394 566185 566226 "DSEXT" 566589 NIL DSEXT (NIL T) -9 NIL 566883 NIL) (-273 563583 564107 564773 "DSEXT-" 564778 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 563242 563307 563405 "DROPT1" 563518 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 558261 559483 560620 "DROPT0" 562125 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 552844 554206 555274 "DROPT" 557213 T DROPT (NIL) -8 NIL NIL NIL) (-269 551153 551514 551900 "DRAWPT" 552478 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 550780 550839 550957 "DRAWHACK" 551094 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 549481 549780 550071 "DRAWCX" 550509 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 548990 549065 549216 "DRAWCURV" 549407 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 539308 541420 543535 "DRAWCFUN" 546895 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 533799 534818 535897 "DRAW" 538282 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 530381 532464 532505 "DQAGG" 533134 NIL DQAGG (NIL T) -9 NIL 533408 NIL) (-262 516995 524592 524675 "DPOLCAT" 526527 NIL DPOLCAT (NIL T T T T) -9 NIL 527072 NIL) (-261 511565 513214 515155 "DPOLCAT-" 515160 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 504494 511426 511524 "DPMO" 511529 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 497320 504274 504441 "DPMM" 504446 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 496842 497104 497193 "DOMTMPLT" 497251 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 496191 496644 496724 "DOMCTOR" 496782 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 495343 495671 495822 "DOMAIN" 496060 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 488388 494978 495130 "DMP" 495244 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 486165 487455 487496 "DMEXT" 487501 NIL DMEXT (NIL T) -9 NIL 487677 NIL) (-253 485759 485821 485965 "DLP" 486103 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 478884 485086 485276 "DLIST" 485601 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 475534 477709 477750 "DLAGG" 478300 NIL DLAGG (NIL T) -9 NIL 478530 NIL) (-250 474046 474860 474888 "DIVRING" 474980 T DIVRING (NIL) -9 NIL 475063 NIL) (-249 473229 473473 473773 "DIVRING-" 473778 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 471271 471688 472094 "DISPLAY" 472843 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 470101 470322 470587 "DIRPROD2" 471064 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 463580 470015 470078 "DIRPROD" 470083 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 451864 458291 458344 "DIRPCAT" 458602 NIL DIRPCAT (NIL NIL T) -9 NIL 459477 NIL) (-244 449064 449832 450713 "DIRPCAT-" 451050 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 448345 448511 448697 "DIOSP" 448898 T DIOSP (NIL) -7 NIL NIL NIL) (-242 444870 447229 447270 "DIOPS" 447704 NIL DIOPS (NIL T) -9 NIL 447933 NIL) (-241 444389 444533 444724 "DIOPS-" 444729 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 443296 444068 444096 "DIFRING" 444101 T DIFRING (NIL) -9 NIL 444123 NIL) (-239 442944 443042 443070 "DIFFSPC" 443189 T DIFFSPC (NIL) -9 NIL 443264 NIL) (-238 442565 442667 442819 "DIFFSPC-" 442824 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 441501 442099 442140 "DIFFMOD" 442145 NIL DIFFMOD (NIL T) -9 NIL 442243 NIL) (-236 441197 441254 441295 "DIFFDOM" 441416 NIL DIFFDOM (NIL T) -9 NIL 441484 NIL) (-235 441044 441074 441158 "DIFFDOM-" 441163 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 438784 440248 440289 "DIFEXT" 440294 NIL DIFEXT (NIL T) -9 NIL 440447 NIL) (-233 435929 438288 438329 "DIAGG" 438334 NIL DIAGG (NIL T) -9 NIL 438354 NIL) (-232 435277 435470 435722 "DIAGG-" 435727 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 430240 434236 434513 "DHMATRIX" 435046 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 425708 426761 427771 "DFSFUN" 429250 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 419972 424552 424880 "DFLOAT" 425400 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 418211 418516 418905 "DFINTTLS" 419680 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 415030 416232 416632 "DERHAM" 417877 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 412680 414805 414894 "DEQUEUE" 414974 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 411922 412067 412250 "DEGRED" 412542 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 408508 409232 410033 "DEFINTRF" 411195 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 406157 406616 407180 "DEFINTEF" 408055 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 405441 405777 405892 "DEFAST" 406062 T DEFAST (NIL) -8 NIL NIL NIL) (-221 398514 405034 405184 "DECIMAL" 405311 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 395972 396484 396990 "DDFACT" 398058 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 395562 395611 395762 "DBLRESP" 395923 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 394763 395332 395423 "DBASIS" 395511 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 392547 392993 393354 "DBASE" 394529 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 391735 392027 392173 "DATAARY" 392446 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 390793 391694 391722 "D03FAFA" 391727 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 389852 390752 390780 "D03EEFA" 390785 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 387778 388268 388757 "D03AGNT" 389383 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 387019 387737 387765 "D02EJFA" 387770 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 386260 386978 387006 "D02CJFA" 387011 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 385501 386219 386247 "D02BHFA" 386252 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 384742 385460 385488 "D02BBFA" 385493 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 377873 379528 381134 "D02AGNT" 383156 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 375623 376164 376710 "D01WGTS" 377347 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 374630 375582 375610 "D01TRNS" 375615 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 373638 374589 374617 "D01GBFA" 374622 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 372646 373597 373625 "D01FCFA" 373630 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 371654 372605 372633 "D01ASFA" 372638 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 370662 371613 371641 "D01AQFA" 371646 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 369670 370621 370649 "D01APFA" 370654 T D01APFA (NIL) -8 NIL NIL NIL) (-200 368678 369629 369657 "D01ANFA" 369662 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 367686 368637 368665 "D01AMFA" 368670 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 366694 367645 367673 "D01ALFA" 367678 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 365702 366653 366681 "D01AKFA" 366686 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 364710 365661 365689 "D01AJFA" 365694 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 357933 359558 361119 "D01AGNT" 363169 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 357252 357398 357550 "CYCLOTOM" 357801 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 353907 354700 355427 "CYCLES" 356545 T CYCLES (NIL) -7 NIL NIL NIL) (-192 353207 353353 353524 "CVMP" 353768 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 350994 351306 351675 "CTRIGMNP" 352935 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 350467 350725 350826 "CTORKIND" 350913 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 349672 350060 350088 "CTORCAT" 350270 T CTORCAT (NIL) -9 NIL 350383 NIL) (-188 349246 349381 349540 "CTORCAT-" 349545 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 348660 348920 349028 "CTORCALL" 349170 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 348018 348454 348527 "CTOR" 348607 T CTOR (NIL) -8 NIL NIL NIL) (-185 347374 347491 347644 "CSTTOOLS" 347915 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 343071 343830 344588 "CRFP" 346686 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 342486 342792 342884 "CRCEAST" 342999 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 341509 341718 341946 "CRAPACK" 342290 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 340889 340994 341198 "CPMATCH" 341385 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 340608 340642 340748 "CPIMA" 340855 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 336866 337628 338347 "COORDSYS" 339943 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 336254 336399 336541 "CONTOUR" 336744 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 331727 334257 334749 "CONTFRAC" 335794 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 331601 331628 331656 "CONDUIT" 331693 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 330555 331229 331257 "COMRING" 331262 T COMRING (NIL) -9 NIL 331314 NIL) (-174 329537 329913 330097 "COMPPROP" 330391 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 329192 329233 329361 "COMPLPAT" 329496 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 328822 328885 328992 "COMPLEX2" 329129 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 317566 328759 328804 "COMPLEX" 328809 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 316887 317026 317186 "COMPILER" 317426 T COMPILER (NIL) -8 NIL NIL NIL) (-169 316599 316640 316738 "COMPFACT" 316846 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 298002 310303 310343 "COMPCAT" 311347 NIL COMPCAT (NIL T) -9 NIL 312695 NIL) (-167 286911 290455 294075 "COMPCAT-" 294431 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 286634 286668 286771 "COMMUPC" 286877 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 286422 286462 286521 "COMMONOP" 286595 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 285944 286226 286301 "COMMAAST" 286367 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 285451 285695 285782 "COMM" 285877 T COMM (NIL) -8 NIL NIL NIL) (-162 284646 284894 284922 "COMBOPC" 285260 T COMBOPC (NIL) -9 NIL 285435 NIL) (-161 283500 283752 283994 "COMBINAT" 284436 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 279843 280531 281158 "COMBF" 282922 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 278505 278959 279194 "COLOR" 279628 T COLOR (NIL) -8 NIL NIL NIL) (-158 277921 278226 278318 "COLONAST" 278433 T COLONAST (NIL) -8 NIL NIL NIL) (-157 277555 277608 277733 "CMPLXRT" 277868 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 276943 277255 277354 "CLLCTAST" 277476 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 272403 273473 274553 "CLIP" 275883 T CLIP (NIL) -7 NIL NIL NIL) (-154 270576 271504 271744 "CLIF" 272230 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 266669 268694 268735 "CLAGG" 269664 NIL CLAGG (NIL T) -9 NIL 270200 NIL) (-152 265013 265548 266131 "CLAGG-" 266136 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 264551 264642 264782 "CINTSLPE" 264922 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 262016 262523 263071 "CHVAR" 264079 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 261056 261730 261758 "CHARZ" 261763 T CHARZ (NIL) -9 NIL 261778 NIL) (-148 260804 260850 260928 "CHARPOL" 261010 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 259722 260428 260456 "CHARNZ" 260517 T CHARNZ (NIL) -9 NIL 260566 NIL) (-146 256666 257776 258305 "CHAR" 259213 T CHAR (NIL) -8 NIL NIL NIL) (-145 256374 256453 256481 "CFCAT" 256592 T CFCAT (NIL) -9 NIL NIL NIL) (-144 255597 255726 255909 "CDEN" 256258 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 251308 254750 255030 "CCLASS" 255337 T CCLASS (NIL) -8 NIL NIL NIL) (-142 250529 250716 250893 "CATEGORY" 251151 T -10 (NIL) -8 NIL NIL NIL) (-141 250024 250448 250496 "CATCTOR" 250501 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 249415 249727 249825 "CATAST" 249946 T CATAST (NIL) -8 NIL NIL NIL) (-139 248831 249136 249228 "CASEAST" 249343 T CASEAST (NIL) -8 NIL NIL NIL) (-138 247927 248087 248308 "CARTEN2" 248678 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 242824 244084 244828 "CARTEN" 247239 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 240954 241974 242231 "CARD" 242587 T CARD (NIL) -8 NIL NIL NIL) (-135 240476 240758 240833 "CAPSLAST" 240899 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 239918 240174 240202 "CACHSET" 240334 T CACHSET (NIL) -9 NIL 240412 NIL) (-133 239308 239696 239724 "CABMON" 239774 T CABMON (NIL) -9 NIL 239830 NIL) (-132 238745 239012 239122 "BYTEORD" 239218 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 233786 238250 238422 "BYTEBUF" 238593 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 232617 233329 233464 "BYTE" 233627 T BYTE (NIL) -8 NIL NIL 233742) (-129 229995 232309 232416 "BTREE" 232543 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 227313 229643 229765 "BTOURN" 229905 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 224533 226755 226796 "BTCAT" 226864 NIL BTCAT (NIL T) -9 NIL 226941 NIL) (-126 224182 224280 224429 "BTCAT-" 224434 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 219185 223428 223456 "BTAGG" 223570 T BTAGG (NIL) -9 NIL 223680 NIL) (-124 218639 218800 219006 "BTAGG-" 219011 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 215491 217917 218132 "BSTREE" 218456 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 214599 214755 214939 "BRILL" 215347 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 211106 213297 213338 "BRAGG" 213987 NIL BRAGG (NIL T) -9 NIL 214245 NIL) (-120 209542 210043 210597 "BRAGG-" 210602 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 201815 208886 209071 "BPADICRT" 209389 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 199833 201752 201797 "BPADIC" 201802 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 199525 199561 199675 "BOUNDZRO" 199797 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 197252 197710 198185 "BOP1" 199083 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 192282 193712 194610 "BOP" 196374 T BOP (NIL) -8 NIL NIL NIL) (-114 191042 191940 192064 "BOOLEAN" 192178 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 190635 190792 190820 "BOOLE" 190931 T BOOLE (NIL) -9 NIL 191012 NIL) (-112 190503 190530 190596 "BOOLE-" 190601 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 189672 190172 190226 "BMODULE" 190231 NIL BMODULE (NIL T T) -9 NIL 190296 NIL) (-110 185107 189470 189543 "BITS" 189619 T BITS (NIL) -8 NIL NIL NIL) (-109 184504 184647 184787 "BINDING" 184987 T BINDING (NIL) -8 NIL NIL NIL) (-108 177580 184099 184248 "BINARY" 184375 T BINARY (NIL) -8 NIL NIL NIL) (-107 175298 176807 176848 "BGAGG" 177108 NIL BGAGG (NIL T) -9 NIL 177245 NIL) (-106 175123 175161 175252 "BGAGG-" 175257 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 174146 174507 174712 "BFUNCT" 174938 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 172810 173011 173299 "BEZOUT" 173970 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 169124 171662 171992 "BBTREE" 172513 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 168707 168803 168831 "BASTYPE" 169008 T BASTYPE (NIL) -9 NIL 169107 NIL) (-101 168365 168464 168599 "BASTYPE-" 168604 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 167787 167875 168027 "BALFACT" 168276 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 166523 167202 167388 "AUTOMOR" 167632 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 166249 166254 166280 "ATTREG" 166285 T ATTREG (NIL) -9 NIL NIL NIL) (-97 164411 164946 165298 "ATTRBUT" 165915 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 163965 164239 164305 "ATTRAST" 164363 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 163465 163614 163640 "ATRIG" 163841 T ATRIG (NIL) -9 NIL NIL NIL) (-94 163262 163315 163402 "ATRIG-" 163407 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 162845 163079 163105 "ASTCAT" 163110 T ASTCAT (NIL) -9 NIL 163140 NIL) (-92 162554 162631 162750 "ASTCAT-" 162755 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 160642 162330 162418 "ASTACK" 162497 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 159131 159444 159809 "ASSOCEQ" 160324 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 158077 158790 158914 "ASP9" 159038 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 156859 157682 157824 "ASP80" 157966 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 156587 156807 156846 "ASP8" 156851 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 155455 156264 156382 "ASP78" 156500 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 154338 155135 155252 "ASP77" 155369 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 153164 153976 154107 "ASP74" 154238 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 151978 152799 152931 "ASP73" 153063 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 150790 151613 151745 "ASP7" 151877 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 149808 150616 150716 "ASP6" 150721 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 148669 149485 149603 "ASP55" 149721 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 147532 148343 148462 "ASP50" 148581 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 146534 147233 147343 "ASP49" 147453 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 145232 146073 146241 "ASP42" 146423 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 143923 144765 144935 "ASP41" 145119 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 142925 143624 143734 "ASP4" 143844 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 141789 142602 142720 "ASP35" 142838 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 141518 141737 141776 "ASP34" 141781 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 141237 141322 141398 "ASP33" 141473 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 140045 140872 141004 "ASP31" 141136 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 139774 139993 140032 "ASP30" 140037 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 139491 139578 139654 "ASP29" 139729 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 139220 139439 139478 "ASP28" 139483 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 138949 139168 139207 "ASP27" 139212 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 137947 138647 138758 "ASP24" 138869 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 136938 137749 137861 "ASP20" 137866 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 135795 136612 136731 "ASP19" 136850 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 135514 135599 135675 "ASP12" 135750 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 134280 135113 135257 "ASP10" 135401 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 133282 133981 134091 "ASP1" 134201 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 131008 133126 133217 "ARRAY2" 133222 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 130022 130213 130434 "ARRAY12" 130831 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 125496 129670 129784 "ARRAY1" 129939 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 119652 121698 121773 "ARR2CAT" 124403 NIL ARR2CAT (NIL T T T) -9 NIL 125161 NIL) (-56 117251 118028 118883 "ARR2CAT-" 118888 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 116502 116878 117003 "ARITY" 117144 T ARITY (NIL) -8 NIL NIL NIL) (-54 115260 115430 115729 "APPRULE" 116338 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 114905 114959 115078 "APPLYORE" 115206 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 114159 114306 114463 "ANY1" 114779 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 113459 113752 113872 "ANY" 114057 T ANY (NIL) -8 NIL NIL NIL) (-50 110785 111896 112223 "ANTISYM" 113183 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 110229 110492 110588 "ANON" 110707 T ANON (NIL) -8 NIL NIL NIL) (-48 103401 108768 109222 "AN" 109793 T AN (NIL) -8 NIL NIL NIL) (-47 99064 100673 100724 "AMR" 101472 NIL AMR (NIL T T) -9 NIL 102072 NIL) (-46 98116 98397 98760 "AMR-" 98765 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 81591 98033 98094 "ALIST" 98099 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 77920 81185 81354 "ALGSC" 81509 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 74370 75030 75637 "ALGPKG" 77360 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 73635 73748 73932 "ALGMFACT" 74256 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 69618 70249 70843 "ALGMANIP" 73219 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 58989 69244 69394 "ALGFF" 69551 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 58161 58316 58495 "ALGFACT" 58847 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 56950 57688 57726 "ALGEBRA" 57731 NIL ALGEBRA (NIL T) -9 NIL 57772 NIL) (-37 56650 56727 56859 "ALGEBRA-" 56864 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 37610 54487 54539 "ALAGG" 54675 NIL ALAGG (NIL T T) -9 NIL 54836 NIL) (-35 37110 37259 37285 "AHYP" 37486 T AHYP (NIL) -9 NIL NIL NIL) (-34 36412 36595 36621 "AGG" 36904 T AGG (NIL) -9 NIL 37093 NIL) (-33 36119 36206 36321 "AGG-" 36326 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 33879 34348 34753 "AF" 35761 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33299 33604 33694 "ADDAST" 33807 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32531 32826 32982 "ACPLOT" 33161 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20151 29463 29501 "ACFS" 30108 NIL ACFS (NIL T) -9 NIL 30347 NIL) (-28 18058 18668 19430 "ACFS-" 19435 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13768 16091 16117 "ACF" 16996 T ACF (NIL) -9 NIL 17409 NIL) (-26 12400 12806 13299 "ACF-" 13304 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11910 12153 12179 "ABELSG" 12271 T ABELSG (NIL) -9 NIL 12336 NIL) (-24 11771 11802 11868 "ABELSG-" 11873 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11040 11387 11413 "ABELMON" 11583 T ABELMON (NIL) -9 NIL 11695 NIL) (-22 10680 10788 10926 "ABELMON-" 10931 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9930 10386 10412 "ABELGRP" 10484 T ABELGRP (NIL) -9 NIL 10559 NIL) (-20 9357 9522 9738 "ABELGRP-" 9743 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8619 8658 "A1AGG" 8663 NIL A1AGG (NIL T) -9 NIL 8703 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index d15aa38f..c4ec6984 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,358 +1,358 @@
 
-(724229 . 3521929248)        
-(((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1296 *4)) (-4 *4 (-13 (-1078) (-658 (-558))))
-   (-5 *2 (-1296 (-419 (-558)))) (-5 *1 (-1325 *4))))) 
-(((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-1296 *4)) (-4 *4 (-13 (-1078) (-658 (-558))))
-   (-5 *2 (-1296 (-558))) (-5 *1 (-1325 *4))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-1296 *4)) (-4 *4 (-13 (-1078) (-658 (-558)))) (-5 *2 (-114))
-   (-5 *1 (-1325 *4))))) 
-(((*1 *2 *3)
-  (-12 (-4 *5 (-13 (-631 *2) (-175))) (-5 *2 (-913 *4)) (-5 *1 (-173 *4 *5 *3))
-   (-4 *4 (-1130)) (-4 *3 (-168 *5))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-1118 (-863 (-391)))))
-   (-5 *2 (-661 (-1118 (-863 (-229))))) (-5 *1 (-315))))
- ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 *3)) (-4 *3 (-175)) (-4 *1 (-422 *3 *4))
-   (-4 *4 (-1272 *3))))
- ((*1 *2 *1)
-  (-12 (-4 *1 (-422 *3 *4)) (-4 *3 (-175)) (-4 *4 (-1272 *3))
-   (-5 *2 (-1296 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 *3)) (-4 *3 (-175)) (-4 *1 (-430 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-5 *2 (-1296 *3))))
- ((*1 *1 *2)
-  (-12 (-5 *2 (-417 *1)) (-4 *1 (-433 *3)) (-4 *3 (-569)) (-4 *3 (-1130))))
- ((*1 *1 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-1078))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-475 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-1132)) (-5 *1 (-547))))
- ((*1 *2 *1) (-12 (-4 *1 (-631 *2)) (-4 *2 (-1246))))
- ((*1 *1 *2) (-12 (-4 *1 (-635 *2)) (-4 *2 (-1246))))
- ((*1 *1 *2) (-12 (-4 *3 (-175)) (-4 *1 (-744 *3 *2)) (-4 *2 (-1272 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-661 (-913 *3))) (-5 *1 (-913 *3)) (-4 *3 (-1130))))
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-  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1078)) (-5 *1 (-50 *3 *4))
-   (-14 *4 (-661 (-1206)))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1070)) (-5 *1 (-50 *3 *4))
+   (-14 *4 (-661 (-1198)))))
  ((*1 *1 *2 *1 *1 *3)
-  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1246))
+  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1238))
    (-4 *4 (-385 *3)) (-4 *5 (-385 *3))))
  ((*1 *1 *2 *1 *1)
-  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1246))
+  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1238))
    (-4 *4 (-385 *3)) (-4 *5 (-385 *3))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1246))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1238))
    (-4 *4 (-385 *3)) (-4 *5 (-385 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-58 *5)) (-4 *5 (-1246)) (-4 *6 (-1246))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-58 *5)) (-4 *5 (-1238)) (-4 *6 (-1238))
    (-5 *2 (-58 *6)) (-5 *1 (-59 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *8 *7)) (-5 *4 (-137 *5 *6 *7)) (-14 *5 (-558))
@@ -362,46 +362,46 @@
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-171 *5)) (-4 *5 (-175)) (-4 *6 (-175))
    (-5 *2 (-171 *6)) (-5 *1 (-172 *5 *6))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 (-326 *3) (-326 *3))) (-4 *3 (-13 (-1078) (-869)))
-   (-5 *1 (-227 *3 *4)) (-14 *4 (-661 (-1206)))))
+  (-12 (-5 *2 (-1 (-326 *3) (-326 *3))) (-4 *3 (-13 (-1070) (-861)))
+   (-5 *1 (-227 *3 *4)) (-14 *4 (-661 (-1198)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-246 *5 *6)) (-14 *5 (-791)) (-4 *6 (-1246))
-   (-4 *7 (-1246)) (-5 *2 (-246 *5 *7)) (-5 *1 (-247 *5 *6 *7))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1246)) (-5 *1 (-305 *3))))
+  (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-246 *5 *6)) (-14 *5 (-791)) (-4 *6 (-1238))
+   (-4 *7 (-1238)) (-5 *2 (-246 *5 *7)) (-5 *1 (-247 *5 *6 *7))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1238)) (-5 *1 (-305 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-305 *5)) (-4 *5 (-1246)) (-4 *6 (-1246))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-305 *5)) (-4 *5 (-1238)) (-4 *6 (-1238))
    (-5 *2 (-305 *6)) (-5 *1 (-306 *5 *6))))
  ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *1 *1)) (-5 *3 (-628 *1)) (-4 *1 (-310))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1188)) (-5 *5 (-628 *6)) (-4 *6 (-310))
-   (-4 *2 (-1246)) (-5 *1 (-311 *6 *2))))
+  (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1180)) (-5 *5 (-628 *6)) (-4 *6 (-310))
+   (-4 *2 (-1238)) (-5 *1 (-311 *6 *2))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *2 *5)) (-5 *4 (-628 *5)) (-4 *5 (-310)) (-4 *2 (-310))
    (-5 *1 (-312 *5 *2))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-709 *5)) (-4 *5 (-1078)) (-4 *6 (-1078))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-709 *5)) (-4 *5 (-1070)) (-4 *6 (-1070))
    (-5 *2 (-709 *6)) (-5 *1 (-317 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-326 *5)) (-4 *5 (-1130)) (-4 *6 (-1130))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-326 *5)) (-4 *5 (-1122)) (-4 *6 (-1122))
    (-5 *2 (-326 *6)) (-5 *1 (-327 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-346 *5 *6 *7 *8)) (-4 *5 (-376))
-   (-4 *6 (-1272 *5)) (-4 *7 (-1272 (-419 *6))) (-4 *8 (-355 *5 *6 *7))
-   (-4 *9 (-376)) (-4 *10 (-1272 *9)) (-4 *11 (-1272 (-419 *10)))
+   (-4 *6 (-1264 *5)) (-4 *7 (-1264 (-419 *6))) (-4 *8 (-355 *5 *6 *7))
+   (-4 *9 (-376)) (-4 *10 (-1264 *9)) (-4 *11 (-1264 (-419 *10)))
    (-5 *2 (-346 *9 *10 *11 *12)) (-5 *1 (-347 *5 *6 *7 *8 *9 *10 *11 *12))
    (-4 *12 (-355 *9 *10 *11))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-351 *3)) (-4 *3 (-1130))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-351 *3)) (-4 *3 (-1122))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1251)) (-4 *8 (-1251)) (-4 *6 (-1272 *5))
-   (-4 *7 (-1272 (-419 *6))) (-4 *9 (-1272 *8)) (-4 *2 (-355 *8 *9 *10))
+  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1243)) (-4 *8 (-1243)) (-4 *6 (-1264 *5))
+   (-4 *7 (-1264 (-419 *6))) (-4 *9 (-1264 *8)) (-4 *2 (-355 *8 *9 *10))
    (-5 *1 (-356 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-355 *5 *6 *7))
-   (-4 *10 (-1272 (-419 *9)))))
+   (-4 *10 (-1264 (-419 *9)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1246)) (-4 *6 (-1246)) (-4 *2 (-385 *6))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1238)) (-4 *6 (-1238)) (-4 *2 (-385 *6))
    (-5 *1 (-386 *5 *4 *6 *2)) (-4 *4 (-385 *5))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-397 *3 *4)) (-4 *3 (-1078))
-   (-4 *4 (-1130))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-397 *3 *4)) (-4 *3 (-1070))
+   (-4 *4 (-1122))))
  ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-569)) (-5 *1 (-417 *3))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-417 *5)) (-4 *5 (-569)) (-4 *6 (-569))
@@ -411,29 +411,29 @@
    (-5 *2 (-419 *6)) (-5 *1 (-420 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-425 *5 *6 *7 *8)) (-4 *5 (-319))
-   (-4 *6 (-1020 *5)) (-4 *7 (-1272 *6)) (-4 *8 (-13 (-422 *6 *7) (-1067 *6)))
-   (-4 *9 (-319)) (-4 *10 (-1020 *9)) (-4 *11 (-1272 *10))
+   (-4 *6 (-1012 *5)) (-4 *7 (-1264 *6)) (-4 *8 (-13 (-422 *6 *7) (-1059 *6)))
+   (-4 *9 (-319)) (-4 *10 (-1012 *9)) (-4 *11 (-1264 *10))
    (-5 *2 (-425 *9 *10 *11 *12)) (-5 *1 (-426 *5 *6 *7 *8 *9 *10 *11 *12))
-   (-4 *12 (-13 (-422 *10 *11) (-1067 *10)))))
+   (-4 *12 (-13 (-422 *10 *11) (-1059 *10)))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-175)) (-4 *6 (-175)) (-4 *2 (-430 *6))
    (-5 *1 (-428 *4 *5 *2 *6)) (-4 *4 (-430 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1078)) (-4 *6 (-1078)) (-4 *2 (-433 *6))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1070)) (-4 *6 (-1070)) (-4 *2 (-433 *6))
    (-5 *1 (-434 *5 *4 *6 *2)) (-4 *4 (-433 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *2 (-438 *6))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1122)) (-4 *6 (-1122)) (-4 *2 (-438 *6))
    (-5 *1 (-439 *5 *4 *6 *2)) (-4 *4 (-438 *5))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-501 *3)) (-4 *3 (-1246))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-501 *3)) (-4 *3 (-1238))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-521 *3 *4)) (-4 *3 (-102)) (-4 *4 (-872))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-521 *3 *4)) (-4 *3 (-102)) (-4 *4 (-864))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-595 *5)) (-4 *5 (-376)) (-4 *6 (-376))
    (-5 *2 (-595 *6)) (-5 *1 (-596 *5 *6))))
  ((*1 *2 *3 *4)
   (|partial| -12 (-5 *3 (-1 *6 *5))
-   (-5 *4 (-3 (-2 (|:| -2359 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-376))
-   (-4 *6 (-376)) (-5 *2 (-2 (|:| -2359 *6) (|:| |coeff| *6)))
+   (-5 *4 (-3 (-2 (|:| -2351 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-376))
+   (-4 *6 (-376)) (-5 *2 (-2 (|:| -2351 *6) (|:| |coeff| *6)))
    (-5 *1 (-596 *5 *6))))
  ((*1 *2 *3 *4)
   (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) (-4 *5 (-376))
@@ -451,251 +451,251 @@
      (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *6) (|:| |logand| *6))))))
    (-5 *1 (-596 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-613 *5)) (-4 *5 (-1246)) (-4 *6 (-1246))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-613 *5)) (-4 *5 (-1238)) (-4 *6 (-1238))
    (-5 *2 (-613 *6)) (-5 *1 (-610 *5 *6))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-613 *6)) (-5 *5 (-613 *7))
-   (-4 *6 (-1246)) (-4 *7 (-1246)) (-4 *8 (-1246)) (-5 *2 (-613 *8))
+   (-4 *6 (-1238)) (-4 *7 (-1238)) (-4 *8 (-1238)) (-5 *2 (-613 *8))
    (-5 *1 (-611 *6 *7 *8))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1184 *6)) (-5 *5 (-613 *7))
-   (-4 *6 (-1246)) (-4 *7 (-1246)) (-4 *8 (-1246)) (-5 *2 (-1184 *8))
+  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1176 *6)) (-5 *5 (-613 *7))
+   (-4 *6 (-1238)) (-4 *7 (-1238)) (-4 *8 (-1238)) (-5 *2 (-1176 *8))
    (-5 *1 (-611 *6 *7 *8))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-613 *6)) (-5 *5 (-1184 *7))
-   (-4 *6 (-1246)) (-4 *7 (-1246)) (-4 *8 (-1246)) (-5 *2 (-1184 *8))
+  (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-613 *6)) (-5 *5 (-1176 *7))
+   (-4 *6 (-1238)) (-4 *7 (-1238)) (-4 *8 (-1238)) (-5 *2 (-1176 *8))
    (-5 *1 (-611 *6 *7 *8))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1246)) (-5 *1 (-613 *3))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1238)) (-5 *1 (-613 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-661 *5)) (-4 *5 (-1246)) (-4 *6 (-1246))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-661 *5)) (-4 *5 (-1238)) (-4 *6 (-1238))
    (-5 *2 (-661 *6)) (-5 *1 (-662 *5 *6))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-661 *6)) (-5 *5 (-661 *7))
-   (-4 *6 (-1246)) (-4 *7 (-1246)) (-4 *8 (-1246)) (-5 *2 (-661 *8))
+   (-4 *6 (-1238)) (-4 *7 (-1238)) (-4 *8 (-1238)) (-5 *2 (-661 *8))
    (-5 *1 (-664 *6 *7 *8))))
  ((*1 *1 *2 *1 *1)
-  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-671 *3)) (-4 *3 (-1246))))
+  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-671 *3)) (-4 *3 (-1238))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1078)) (-4 *8 (-1078)) (-4 *6 (-385 *5))
+  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1070)) (-4 *8 (-1070)) (-4 *6 (-385 *5))
    (-4 *7 (-385 *5)) (-4 *2 (-706 *8 *9 *10))
    (-5 *1 (-707 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-706 *5 *6 *7))
    (-4 *9 (-385 *8)) (-4 *10 (-385 *8))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1 (-3 *8 "failed") *5)) (-4 *5 (-1078))
-   (-4 *8 (-1078)) (-4 *6 (-385 *5)) (-4 *7 (-385 *5)) (-4 *2 (-706 *8 *9 *10))
+  (|partial| -12 (-5 *3 (-1 (-3 *8 "failed") *5)) (-4 *5 (-1070))
+   (-4 *8 (-1070)) (-4 *6 (-385 *5)) (-4 *7 (-385 *5)) (-4 *2 (-706 *8 *9 *10))
    (-5 *1 (-707 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-706 *5 *6 *7))
    (-4 *9 (-385 *8)) (-4 *10 (-385 *8))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-569)) (-4 *7 (-569)) (-4 *6 (-1272 *5))
-   (-4 *2 (-1272 (-419 *8))) (-5 *1 (-729 *5 *6 *4 *7 *8 *2))
-   (-4 *4 (-1272 (-419 *6))) (-4 *8 (-1272 *7))))
+  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-569)) (-4 *7 (-569)) (-4 *6 (-1264 *5))
+   (-4 *2 (-1264 (-419 *8))) (-5 *1 (-729 *5 *6 *4 *7 *8 *2))
+   (-4 *4 (-1264 (-419 *6))) (-4 *8 (-1264 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-1078)) (-4 *9 (-1078)) (-4 *5 (-869))
-   (-4 *6 (-815)) (-4 *2 (-977 *9 *7 *5)) (-5 *1 (-748 *5 *6 *7 *8 *9 *4 *2))
-   (-4 *7 (-815)) (-4 *4 (-977 *8 *6 *5))))
+  (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-1070)) (-4 *9 (-1070)) (-4 *5 (-861))
+   (-4 *6 (-815)) (-4 *2 (-969 *9 *7 *5)) (-5 *1 (-748 *5 *6 *7 *8 *9 *4 *2))
+   (-4 *7 (-815)) (-4 *4 (-969 *8 *6 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-869)) (-4 *6 (-869)) (-4 *7 (-815))
-   (-4 *9 (-1078)) (-4 *2 (-977 *9 *8 *6)) (-5 *1 (-749 *5 *6 *7 *8 *9 *4 *2))
-   (-4 *8 (-815)) (-4 *4 (-977 *9 *7 *5))))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-861)) (-4 *6 (-861)) (-4 *7 (-815))
+   (-4 *9 (-1070)) (-4 *2 (-969 *9 *8 *6)) (-5 *1 (-749 *5 *6 *7 *8 *9 *4 *2))
+   (-4 *8 (-815)) (-4 *4 (-969 *9 *7 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-755 *5 *7)) (-4 *5 (-1078)) (-4 *6 (-1078))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-755 *5 *7)) (-4 *5 (-1070)) (-4 *6 (-1070))
    (-4 *7 (-746)) (-5 *2 (-755 *6 *7)) (-5 *1 (-754 *5 *6 *7))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1078)) (-5 *1 (-755 *3 *4)) (-4 *4 (-746))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1070)) (-5 *1 (-755 *3 *4)) (-4 *4 (-746))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-801 *5)) (-4 *5 (-1078)) (-4 *6 (-1078))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-801 *5)) (-4 *5 (-1070)) (-4 *6 (-1070))
    (-5 *2 (-801 *6)) (-5 *1 (-802 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-175)) (-4 *6 (-175)) (-4 *2 (-818 *6))
    (-5 *1 (-821 *4 *5 *2 *6)) (-4 *4 (-818 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-853 *5)) (-4 *5 (-1130)) (-4 *6 (-1130))
-   (-5 *2 (-853 *6)) (-5 *1 (-854 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-845 *5)) (-4 *5 (-1122)) (-4 *6 (-1122))
+   (-5 *2 (-845 *6)) (-5 *1 (-846 *5 *6))))
  ((*1 *2 *3 *4 *2)
-  (-12 (-5 *2 (-853 *6)) (-5 *3 (-1 *6 *5)) (-5 *4 (-853 *5)) (-4 *5 (-1130))
-   (-4 *6 (-1130)) (-5 *1 (-854 *5 *6))))
+  (-12 (-5 *2 (-845 *6)) (-5 *3 (-1 *6 *5)) (-5 *4 (-845 *5)) (-4 *5 (-1122))
+   (-4 *6 (-1122)) (-5 *1 (-846 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-863 *5)) (-4 *5 (-1130)) (-4 *6 (-1130))
-   (-5 *2 (-863 *6)) (-5 *1 (-864 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-855 *5)) (-4 *5 (-1122)) (-4 *6 (-1122))
+   (-5 *2 (-855 *6)) (-5 *1 (-856 *5 *6))))
  ((*1 *2 *3 *4 *2 *2)
-  (-12 (-5 *2 (-863 *6)) (-5 *3 (-1 *6 *5)) (-5 *4 (-863 *5)) (-4 *5 (-1130))
-   (-4 *6 (-1130)) (-5 *1 (-864 *5 *6))))
+  (-12 (-5 *2 (-855 *6)) (-5 *3 (-1 *6 *5)) (-5 *4 (-855 *5)) (-4 *5 (-1122))
+   (-4 *6 (-1122)) (-5 *1 (-856 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-900 *5)) (-4 *5 (-1246)) (-4 *6 (-1246))
-   (-5 *2 (-900 *6)) (-5 *1 (-899 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-892 *5)) (-4 *5 (-1238)) (-4 *6 (-1238))
+   (-5 *2 (-892 *6)) (-5 *1 (-891 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-902 *5)) (-4 *5 (-1246)) (-4 *6 (-1246))
-   (-5 *2 (-902 *6)) (-5 *1 (-901 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-894 *5)) (-4 *5 (-1238)) (-4 *6 (-1238))
+   (-5 *2 (-894 *6)) (-5 *1 (-893 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-905 *5)) (-4 *5 (-1246)) (-4 *6 (-1246))
-   (-5 *2 (-905 *6)) (-5 *1 (-904 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-897 *5)) (-4 *5 (-1238)) (-4 *6 (-1238))
+   (-5 *2 (-897 *6)) (-5 *1 (-896 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-911 *5 *6)) (-4 *5 (-1130)) (-4 *6 (-1130))
-   (-4 *7 (-1130)) (-5 *2 (-911 *5 *7)) (-5 *1 (-912 *5 *6 *7))))
+  (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-903 *5 *6)) (-4 *5 (-1122)) (-4 *6 (-1122))
+   (-4 *7 (-1122)) (-5 *2 (-903 *5 *7)) (-5 *1 (-904 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-913 *5)) (-4 *5 (-1130)) (-4 *6 (-1130))
-   (-5 *2 (-913 *6)) (-5 *1 (-915 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-905 *5)) (-4 *5 (-1122)) (-4 *6 (-1122))
+   (-5 *2 (-905 *6)) (-5 *1 (-907 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-973 *5)) (-4 *5 (-1078)) (-4 *6 (-1078))
-   (-5 *2 (-973 *6)) (-5 *1 (-974 *5 *6))))
+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-965 *5)) (-4 *5 (-1070)) (-4 *6 (-1070))
+   (-5 *2 (-965 *6)) (-5 *1 (-966 *5 *6))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *2 *7)) (-5 *4 (-1 *2 *8)) (-4 *7 (-869)) (-4 *8 (-1078))
+  (-12 (-5 *3 (-1 *2 *7)) (-5 *4 (-1 *2 *8)) (-4 *7 (-861)) (-4 *8 (-1070))
    (-4 *6 (-815))
    (-4 *2
-    (-13 (-1130)
-     (-10 -8 (-15 -4346 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-791))))))
-   (-5 *1 (-979 *6 *7 *8 *5 *2)) (-4 *5 (-977 *8 *6 *7))))
+    (-13 (-1122)
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 (((*1 *2 *1)
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 (((*1 *2 *1)
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 (((*1 *2 *3 *1)
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    (-4 *2 (-175))))
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+ ((*1 *2 *1 *1) (-12 (-4 *1 (-1308 *3 *2)) (-4 *3 (-861)) (-4 *2 (-1070))))
  ((*1 *2 *1 *3)
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+  (-12 (-5 *3 (-841 *4)) (-4 *1 (-1308 *4 *2)) (-4 *4 (-861)) (-4 *2 (-1070))))
+ ((*1 *2 *1 *3) (-12 (-4 *2 (-1070)) (-5 *1 (-1312 *2 *3)) (-4 *3 (-859))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-291))))
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+ ((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-905 *3)) (-4 *3 (-1122))))
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 (((*1 *2 *3)
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- ((*1 *2 *1) (-12 (-4 *2 (-1078)) (-5 *1 (-1320 *2 *3)) (-4 *3 (-867))))) 
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+   (-4 *4 (-1122))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1198)) (-5 *2 (-326 (-558))) (-5 *1 (-948))))
+ ((*1 *2 *2) (-12 (-4 *3 (-1122)) (-5 *1 (-949 *3 *2)) (-4 *2 (-433 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1308 *3 *2)) (-4 *3 (-861)) (-4 *2 (-1070))))
+ ((*1 *2 *1) (-12 (-4 *2 (-1070)) (-5 *1 (-1312 *2 *3)) (-4 *3 (-859))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1316 *3 *4)) (-4 *3 (-869)) (-4 *4 (-1078)) (-5 *2 (-114))))
+  (-12 (-4 *1 (-1308 *3 *4)) (-4 *3 (-861)) (-4 *4 (-1070)) (-5 *2 (-114))))
  ((*1 *2 *1)
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- ((*1 *1 *1) (-12 (-5 *1 (-1320 *2 *3)) (-4 *2 (-1078)) (-4 *3 (-867))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-1312 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-859))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-1308 *2 *3)) (-4 *2 (-861)) (-4 *3 (-1070))))
+ ((*1 *1 *1) (-12 (-5 *1 (-1312 *2 *3)) (-4 *2 (-1070)) (-4 *3 (-859))))) 
 (((*1 *1 *1 *2)
-  (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1078)) (-4 *3 (-814)) (-4 *2 (-376))))
+  (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1070)) (-4 *3 (-814)) (-4 *2 (-376))))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-229))))
  ((*1 *1 *1 *1)
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-   (-12 (-5 *1 (-305 *2)) (-4 *2 (-485)) (-4 *2 (-1246)))))
+  (-3957 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1238)))
+   (-12 (-5 *1 (-305 *2)) (-4 *2 (-485)) (-4 *2 (-1238)))))
  ((*1 *1 *1 *1) (-4 *1 (-376)))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-391))))
  ((*1 *1 *2 *2)
-  (-12 (-5 *2 (-1154 *3 (-628 *1))) (-4 *3 (-569)) (-4 *3 (-1130))
+  (-12 (-5 *2 (-1146 *3 (-628 *1))) (-4 *3 (-569)) (-4 *3 (-1122))
    (-4 *1 (-433 *3))))
  ((*1 *1 *1 *1) (-4 *1 (-485)))
- ((*1 *2 *2 *2) (-12 (-5 *2 (-1296 *3)) (-4 *3 (-363)) (-5 *1 (-540 *3))))
+ ((*1 *2 *2 *2) (-12 (-5 *2 (-1288 *3)) (-4 *3 (-363)) (-5 *1 (-540 *3))))
  ((*1 *1 *1 *1) (-5 *1 (-547)))
  ((*1 *1 *2 *3)
   (-12 (-4 *4 (-175)) (-5 *1 (-636 *2 *4 *3)) (-4 *2 (-38 *4))
@@ -711,136 +711,136 @@
   (-12 (-4 *4 (-175)) (-5 *1 (-672 *3 *4 *2)) (-4 *3 (-737 *4))
    (-4 *2 (|SubsetCategory| (-746) *4))))
  ((*1 *1 *1 *2)
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+  (-12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-385 *2))
    (-4 *4 (-385 *2)) (-4 *2 (-376))))
- ((*1 *1 *1 *1) (-5 *1 (-885)))
+ ((*1 *1 *1 *1) (-5 *1 (-877)))
  ((*1 *1 *1 *1)
-  (|partial| -12 (-5 *1 (-888 *2 *3 *4 *5)) (-4 *2 (-376)) (-4 *2 (-1078))
-   (-14 *3 (-661 (-1206))) (-14 *4 (-661 (-791))) (-14 *5 (-791))))
- ((*1 *1 *1 *1) (-12 (-5 *1 (-913 *2)) (-4 *2 (-1130))))
- ((*1 *1 *2 *2) (-12 (-4 *1 (-1020 *2)) (-4 *2 (-569))))
+  (|partial| -12 (-5 *1 (-880 *2 *3 *4 *5)) (-4 *2 (-376)) (-4 *2 (-1070))
+   (-14 *3 (-661 (-1198))) (-14 *4 (-661 (-791))) (-14 *5 (-791))))
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-905 *2)) (-4 *2 (-1122))))
+ ((*1 *1 *2 *2) (-12 (-4 *1 (-1012 *2)) (-4 *2 (-569))))
  ((*1 *1 *1 *2)
-  (-12 (-4 *1 (-1082 *3 *4 *2 *5 *6)) (-4 *2 (-1078)) (-4 *5 (-245 *4 *2))
+  (-12 (-4 *1 (-1074 *3 *4 *2 *5 *6)) (-4 *2 (-1070)) (-4 *5 (-245 *4 *2))
    (-4 *6 (-245 *3 *2)) (-4 *2 (-376))))
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- ((*1 *1 *1 *2) (-12 (-4 *1 (-1304 *2)) (-4 *2 (-376))))
+ ((*1 *2 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-1296 *2)) (-4 *2 (-376))))
  ((*1 *1 *1 *1)
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-   (-4 *5 (-977 *2 *4 *3)) (-14 *7 (-661 (-791))) (-14 *8 (-791))))
+  (|partial| -12 (-4 *2 (-376)) (-4 *2 (-1070)) (-4 *3 (-861)) (-4 *4 (-815))
+   (-14 *6 (-661 *3)) (-5 *1 (-1301 *2 *3 *4 *5 *6 *7 *8))
+   (-4 *5 (-969 *2 *4 *3)) (-14 *7 (-661 (-791))) (-14 *8 (-791))))
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-(((*1 *2 *1) (-12 (-4 *1 (-47 *3 *2)) (-4 *3 (-1078)) (-4 *2 (-814))))
+  (-12 (-5 *1 (-1312 *2 *3)) (-4 *2 (-376)) (-4 *2 (-1070)) (-4 *3 (-859))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-47 *3 *2)) (-4 *3 (-1070)) (-4 *2 (-814))))
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-  (-12 (-5 *2 (-791)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1078))
-   (-14 *4 (-661 (-1206)))))
+  (-12 (-5 *2 (-791)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1070))
+   (-14 *4 (-661 (-1198)))))
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+   (-14 *4 (-661 (-1198)))))
  ((*1 *2 *1 *3)
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+  (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1070)) (-4 *3 (-861))
    (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-791))))
  ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-286))))
  ((*1 *2 *3 *4)
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-   (-4 *8 (-977 *7 *5 *6)) (-4 *5 (-815)) (-4 *7 (-1078)) (-5 *2 (-661 (-791)))
+  (-12 (-5 *3 (-1192 *8)) (-5 *4 (-661 *6)) (-4 *6 (-861))
+   (-4 *8 (-969 *7 *5 *6)) (-4 *5 (-815)) (-4 *7 (-1070)) (-5 *2 (-661 (-791)))
    (-5 *1 (-333 *5 *6 *7 *8))))
- ((*1 *2 *1) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-946))))
+ ((*1 *2 *1) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-938))))
  ((*1 *2 *1)
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+  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-861)) (-4 *4 (-175)) (-5 *2 (-791))))
  ((*1 *2 *1) (-12 (-4 *1 (-482 *3 *2)) (-4 *3 (-175)) (-4 *2 (-23))))
  ((*1 *2 *1)
-  (-12 (-4 *3 (-569)) (-5 *2 (-558)) (-5 *1 (-640 *3 *4)) (-4 *4 (-1272 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-728 *3)) (-4 *3 (-1078)) (-5 *2 (-791))))
- ((*1 *2 *1) (-12 (-4 *1 (-874 *3)) (-4 *3 (-1078)) (-5 *2 (-791))))
- ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-929 *3)) (-4 *3 (-1130))))
- ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-932 *3)) (-4 *3 (-1130))))
+  (-12 (-4 *3 (-569)) (-5 *2 (-558)) (-5 *1 (-640 *3 *4)) (-4 *4 (-1264 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-728 *3)) (-4 *3 (-1070)) (-5 *2 (-791))))
+ ((*1 *2 *1) (-12 (-4 *1 (-866 *3)) (-4 *3 (-1070)) (-5 *2 (-791))))
+ ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-921 *3)) (-4 *3 (-1122))))
+ ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-924 *3)) (-4 *3 (-1122))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-661 *6)) (-4 *1 (-977 *4 *5 *6)) (-4 *4 (-1078)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-661 (-791)))))
+  (-12 (-5 *3 (-661 *6)) (-4 *1 (-969 *4 *5 *6)) (-4 *4 (-1070)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-661 (-791)))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *1 (-977 *4 *5 *3)) (-4 *4 (-1078)) (-4 *5 (-815)) (-4 *3 (-869))
+  (-12 (-4 *1 (-969 *4 *5 *3)) (-4 *4 (-1070)) (-4 *5 (-815)) (-4 *3 (-861))
    (-5 *2 (-791))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1002 *3 *2 *4)) (-4 *3 (-1078)) (-4 *4 (-869)) (-4 *2 (-814))))
+  (-12 (-4 *1 (-994 *3 *2 *4)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *2 (-814))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1241 *3 *4 *5 *6)) (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-869))
-   (-4 *6 (-1094 *3 *4 *5)) (-5 *2 (-791))))
+  (-12 (-4 *1 (-1233 *3 *4 *5 *6)) (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-4 *6 (-1086 *3 *4 *5)) (-5 *2 (-791))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1260 *3 *4)) (-4 *3 (-1078)) (-4 *4 (-1289 *3))
+  (-12 (-4 *1 (-1252 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-1281 *3))
    (-5 *2 (-558))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1281 *3 *4)) (-4 *3 (-1078)) (-4 *4 (-1258 *3))
+  (-12 (-4 *1 (-1273 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-1250 *3))
    (-5 *2 (-419 (-558)))))
- ((*1 *2 *1) (-12 (-4 *1 (-1315 *3)) (-4 *3 (-376)) (-5 *2 (-853 (-946)))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1307 *3)) (-4 *3 (-376)) (-5 *2 (-845 (-938)))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1319 *3 *4)) (-4 *3 (-869)) (-4 *4 (-1078)) (-5 *2 (-791))))) 
+  (-12 (-4 *1 (-1311 *3 *4)) (-4 *3 (-861)) (-4 *4 (-1070)) (-5 *2 (-791))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-791)) (-4 *1 (-387 *3 *4)) (-4 *3 (-869)) (-4 *4 (-175))))
+  (-12 (-5 *2 (-791)) (-4 *1 (-387 *3 *4)) (-4 *3 (-861)) (-4 *4 (-175))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-791)) (-4 *1 (-1319 *3 *4)) (-4 *3 (-869)) (-4 *4 (-1078))))) 
+  (-12 (-5 *2 (-791)) (-4 *1 (-1311 *3 *4)) (-4 *3 (-861)) (-4 *4 (-1070))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-1296 *3)) (-4 *3 (-376)) (-14 *6 (-1296 (-709 *3)))
-   (-5 *1 (-44 *3 *4 *5 *6)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))))
- ((*1 *1 *2) (-12 (-5 *2 (-1154 (-558) (-628 (-48)))) (-5 *1 (-48))))
- ((*1 *2 *3) (-12 (-5 *2 (-51)) (-5 *1 (-52 *3)) (-4 *3 (-1246))))
+  (-12 (-5 *2 (-1288 *3)) (-4 *3 (-376)) (-14 *6 (-1288 (-709 *3)))
+   (-5 *1 (-44 *3 *4 *5 *6)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1146 (-558) (-628 (-48)))) (-5 *1 (-48))))
+ ((*1 *2 *3) (-12 (-5 *2 (-51)) (-5 *1 (-52 *3)) (-4 *3 (-1238))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-352 (-4027 'X) (-4027) (-719))) (-5 *1 (-61 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-352 (-3950 'X) (-3950) (-719))) (-5 *1 (-61 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027 'JINT 'X 'ELAM) (-4027) (-719))))
-   (-5 *1 (-62 *3)) (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950 'JINT 'X 'ELAM) (-3950) (-719))))
+   (-5 *1 (-62 *3)) (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027) (-4027 'XC) (-719)))) (-5 *1 (-64 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950) (-3950 'XC) (-719)))) (-5 *1 (-64 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-352 (-4027) (-4027 'XC) (-719))) (-5 *1 (-66 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-352 (-3950) (-3950 'XC) (-719))) (-5 *1 (-66 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027 'X) (-4027 '-4473) (-719)))) (-5 *1 (-71 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950 'X) (-3950 '-4396) (-719)))) (-5 *1 (-71 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027) (-4027 'X) (-719)))) (-5 *1 (-74 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950) (-3950 'X) (-719)))) (-5 *1 (-74 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-352 (-4027) (-4027 'X) (-719))) (-5 *1 (-75 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-352 (-3950) (-3950 'X) (-719))) (-5 *1 (-75 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027 'X 'EPS) (-4027 '-4473) (-719))))
-   (-5 *1 (-76 *3 *4 *5)) (-14 *3 (-1206)) (-14 *4 (-1206)) (-14 *5 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950 'X 'EPS) (-3950 '-4396) (-719))))
+   (-5 *1 (-76 *3 *4 *5)) (-14 *3 (-1198)) (-14 *4 (-1198)) (-14 *5 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027 'EPS) (-4027 'YA 'YB) (-719))))
-   (-5 *1 (-77 *3 *4 *5)) (-14 *3 (-1206)) (-14 *4 (-1206)) (-14 *5 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950 'EPS) (-3950 'YA 'YB) (-719))))
+   (-5 *1 (-77 *3 *4 *5)) (-14 *3 (-1198)) (-14 *4 (-1198)) (-14 *5 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-352 (-4027) (-4027 'X) (-719))) (-5 *1 (-78 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-352 (-3950) (-3950 'X) (-719))) (-5 *1 (-78 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027) (-4027 'XC) (-719)))) (-5 *1 (-79 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950) (-3950 'XC) (-719)))) (-5 *1 (-79 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027) (-4027 'X) (-719)))) (-5 *1 (-80 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950) (-3950 'X) (-719)))) (-5 *1 (-80 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027 'X) (-4027 '-4473) (-719)))) (-5 *1 (-82 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950 'X) (-3950 '-4396) (-719)))) (-5 *1 (-82 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027 'X '-4473) (-4027) (-719)))) (-5 *1 (-83 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950 'X '-4396) (-3950) (-719)))) (-5 *1 (-83 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-709 (-352 (-4027 'X '-4473) (-4027) (-719)))) (-5 *1 (-84 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-709 (-352 (-3950 'X '-4396) (-3950) (-719)))) (-5 *1 (-84 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-709 (-352 (-4027 'X) (-4027) (-719)))) (-5 *1 (-85 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-709 (-352 (-3950 'X) (-3950) (-719)))) (-5 *1 (-85 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-352 (-4027 'X) (-4027) (-719)))) (-5 *1 (-86 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-1288 (-352 (-3950 'X) (-3950) (-719)))) (-5 *1 (-86 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-709 (-352 (-4027 'XL 'XR 'ELAM) (-4027) (-719))))
-   (-5 *1 (-88 *3)) (-14 *3 (-1206))))
+  (-12 (-5 *2 (-709 (-352 (-3950 'XL 'XR 'ELAM) (-3950) (-719))))
+   (-5 *1 (-88 *3)) (-14 *3 (-1198))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-352 (-4027 'X) (-4027 '-4473) (-719))) (-5 *1 (-89 *3))
-   (-14 *3 (-1206))))
+  (-12 (-5 *2 (-352 (-3950 'X) (-3950 '-4396) (-719))) (-5 *1 (-89 *3))
+   (-14 *3 (-1198))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-661 (-137 *3 *4 *5))) (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-558))
    (-14 *4 (-791)) (-4 *5 (-175))))
@@ -848,31 +848,31 @@
   (-12 (-5 *2 (-661 *5)) (-4 *5 (-175)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-558))
    (-14 *4 (-791))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1171 *4 *5)) (-14 *4 (-791)) (-4 *5 (-175))
+  (-12 (-5 *2 (-1163 *4 *5)) (-14 *4 (-791)) (-4 *5 (-175))
    (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-558))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-246 *4 *5)) (-14 *4 (-791)) (-4 *5 (-175))
    (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-558))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1296 (-709 *4))) (-4 *4 (-175))
-   (-5 *2 (-1296 (-709 (-419 (-973 *4))))) (-5 *1 (-192 *4))))
+  (-12 (-5 *3 (-1288 (-709 *4))) (-4 *4 (-175))
+   (-5 *2 (-1288 (-709 (-419 (-965 *4))))) (-5 *1 (-192 *4))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1121 (-326 *4))) (-4 *4 (-13 (-869) (-569) (-631 (-391))))
-   (-5 *2 (-1121 (-391))) (-5 *1 (-268 *4))))
- ((*1 *1 *2) (-12 (-4 *1 (-277 *2)) (-4 *2 (-869))))
+  (-12 (-5 *3 (-1113 (-326 *4))) (-4 *4 (-13 (-861) (-569) (-631 (-391))))
+   (-5 *2 (-1113 (-391))) (-5 *1 (-268 *4))))
+ ((*1 *1 *2) (-12 (-4 *1 (-277 *2)) (-4 *2 (-861))))
  ((*1 *1 *2) (-12 (-5 *2 (-661 (-558))) (-5 *1 (-286))))
  ((*1 *2 *1)
-  (-12 (-4 *2 (-1272 *3)) (-5 *1 (-301 *3 *2 *4 *5 *6 *7)) (-4 *3 (-175))
+  (-12 (-4 *2 (-1264 *3)) (-5 *1 (-301 *3 *2 *4 *5 *6 *7)) (-4 *3 (-175))
    (-4 *4 (-23)) (-14 *5 (-1 *2 *2 *4)) (-14 *6 (-1 (-3 *4 "failed") *4 *4))
    (-14 *7 (-1 (-3 *2 "failed") *2 *2 *4))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1277 *4 *5 *6)) (-4 *4 (-13 (-27) (-1232) (-433 *3)))
-   (-14 *5 (-1206)) (-14 *6 *4)
-   (-4 *3 (-13 (-1067 (-558)) (-658 (-558)) (-464)))
+  (-12 (-5 *2 (-1269 *4 *5 *6)) (-4 *4 (-13 (-27) (-1224) (-433 *3)))
+   (-14 *5 (-1198)) (-14 *6 *4)
+   (-4 *3 (-13 (-1059 (-558)) (-658 (-558)) (-464)))
    (-5 *1 (-325 *3 *4 *5 *6))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-326 *5)) (-5 *1 (-352 *3 *4 *5)) (-14 *3 (-661 (-1206)))
-   (-14 *4 (-661 (-1206))) (-4 *5 (-401))))
+  (-12 (-5 *2 (-326 *5)) (-5 *1 (-352 *3 *4 *5)) (-14 *3 (-661 (-1198)))
+   (-14 *4 (-661 (-1198))) (-4 *5 (-401))))
  ((*1 *2 *3)
   (-12 (-4 *4 (-363)) (-4 *2 (-341 *4)) (-5 *1 (-361 *3 *4 *2))
    (-4 *3 (-341 *4))))
@@ -880,163 +880,163 @@
   (-12 (-4 *4 (-363)) (-4 *2 (-341 *4)) (-5 *1 (-361 *2 *4 *3))
    (-4 *3 (-341 *4))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-869)) (-4 *4 (-175))
-   (-5 *2 (-1321 *3 *4))))
+  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-861)) (-4 *4 (-175))
+   (-5 *2 (-1313 *3 *4))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-869)) (-4 *4 (-175))
-   (-5 *2 (-1312 *3 *4))))
- ((*1 *1 *2) (-12 (-4 *1 (-387 *2 *3)) (-4 *2 (-869)) (-4 *3 (-175))))
+  (-12 (-4 *1 (-387 *3 *4)) (-4 *3 (-861)) (-4 *4 (-175))
+   (-5 *2 (-1304 *3 *4))))
+ ((*1 *1 *2) (-12 (-4 *1 (-387 *2 *3)) (-4 *2 (-861)) (-4 *3 (-175))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1210)) (|:| -1821 (-661 (-342)))))
+  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1202)) (|:| -1813 (-661 (-342)))))
    (-4 *1 (-396))))
  ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-396))))
  ((*1 *1 *2) (-12 (-5 *2 (-661 (-342))) (-4 *1 (-396))))
  ((*1 *1 *2) (-12 (-5 *2 (-709 (-719))) (-4 *1 (-396))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1210)) (|:| -1821 (-661 (-342)))))
+  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1202)) (|:| -1813 (-661 (-342)))))
    (-4 *1 (-398))))
  ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-398))))
  ((*1 *1 *2) (-12 (-5 *2 (-661 (-342))) (-4 *1 (-398))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1210)) (|:| -1821 (-661 (-342)))))
+  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1202)) (|:| -1813 (-661 (-342)))))
    (-4 *1 (-409))))
  ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-409))))
  ((*1 *1 *2) (-12 (-5 *2 (-661 (-342))) (-4 *1 (-409))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-305 (-326 (-171 (-391))))) (-5 *1 (-410 *3 *4 *5 *6))
-   (-14 *3 (-1206)) (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1="void")))
-   (-14 *5 (-661 (-1206))) (-14 *6 (-1210))))
+   (-14 *3 (-1198)) (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1="void")))
+   (-14 *5 (-661 (-1198))) (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-305 (-326 (-391)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-305 (-326 (-391)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-305 (-326 (-558)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-305 (-326 (-558)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-326 (-171 (-391)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-326 (-171 (-391)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-326 (-391))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-326 (-391))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-326 (-558))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-326 (-558))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-305 (-326 (-714)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-305 (-326 (-714)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-305 (-326 (-719)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-305 (-326 (-719)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-305 (-326 (-721)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-305 (-326 (-721)))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-326 (-714))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-326 (-714))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-326 (-719))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-326 (-719))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-326 (-721))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-326 (-721))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1210)) (|:| -1821 (-661 (-342)))))
-   (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1202)) (|:| -1813 (-661 (-342)))))
+   (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-661 (-342))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-661 (-342))) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-342)) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1206))
-   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4417 #1#))) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1210))))
+  (-12 (-5 *2 (-342)) (-5 *1 (-410 *3 *4 *5 *6)) (-14 *3 (-1198))
+   (-14 *4 (-3 (|:| |fst| (-446)) (|:| -4340 #1#))) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1202))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-419 (-973 (-419 *3)))) (-4 *3 (-569)) (-4 *3 (-1130))
+  (-12 (-5 *2 (-419 (-965 (-419 *3)))) (-4 *3 (-569)) (-4 *3 (-1122))
    (-4 *1 (-433 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-973 (-419 *3))) (-4 *3 (-569)) (-4 *3 (-1130))
+  (-12 (-5 *2 (-965 (-419 *3))) (-4 *3 (-569)) (-4 *3 (-1122))
    (-4 *1 (-433 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-419 *3)) (-4 *3 (-569)) (-4 *3 (-1130)) (-4 *1 (-433 *3))))
+  (-12 (-5 *2 (-419 *3)) (-4 *3 (-569)) (-4 *3 (-1122)) (-4 *1 (-433 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1154 *3 (-628 *1))) (-4 *3 (-1078)) (-4 *3 (-1130))
+  (-12 (-5 *2 (-1146 *3 (-628 *1))) (-4 *3 (-1070)) (-4 *3 (-1122))
    (-4 *1 (-433 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-343 *4)) (-4 *4 (-13 (-869) (-21))) (-5 *1 (-441 *3 *4))
+  (-12 (-5 *2 (-343 *4)) (-4 *4 (-13 (-861) (-21))) (-5 *1 (-441 *3 *4))
    (-4 *3 (-13 (-175) (-38 (-419 (-558)))))))
  ((*1 *1 *2)
   (-12 (-5 *1 (-441 *2 *3)) (-4 *2 (-13 (-175) (-38 (-419 (-558)))))
-   (-4 *3 (-13 (-869) (-21)))))
- ((*1 *2 *1) (-12 (-5 *2 (-1132)) (-5 *1 (-446))))
- ((*1 *2 *1) (-12 (-5 *2 (-1206)) (-5 *1 (-446))))
- ((*1 *1 *2) (-12 (-5 *2 (-1206)) (-5 *1 (-446))))
- ((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-446))))
+   (-4 *3 (-13 (-861) (-21)))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1124)) (-5 *1 (-446))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1198)) (-5 *1 (-446))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1198)) (-5 *1 (-446))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-446))))
  ((*1 *1 *2) (-12 (-5 *2 (-446)) (-5 *1 (-448))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1210)) (|:| -1821 (-661 (-342)))))
+  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1202)) (|:| -1813 (-661 (-342)))))
    (-4 *1 (-452))))
  ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-452))))
  ((*1 *1 *2) (-12 (-5 *2 (-661 (-342))) (-4 *1 (-452))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 (-719))) (-4 *1 (-452))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1288 (-719))) (-4 *1 (-452))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1210)) (|:| -1821 (-661 (-342)))))
+  (-12 (-5 *2 (-2 (|:| |localSymbols| (-1202)) (|:| -1813 (-661 (-342)))))
    (-4 *1 (-453))))
  ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-453))))
  ((*1 *1 *2) (-12 (-5 *2 (-661 (-342))) (-4 *1 (-453))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-419 (-973 *3)))) (-4 *3 (-175))
-   (-14 *6 (-1296 (-709 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-14 *4 (-946))
-   (-14 *5 (-661 (-1206)))))
- ((*1 *1 *2) (-12 (-5 *2 (-661 (-661 (-970 (-229))))) (-5 *1 (-480))))
- ((*1 *2 *1) (-12 (-5 *2 (-885)) (-5 *1 (-480))))
+  (-12 (-5 *2 (-1288 (-419 (-965 *3)))) (-4 *3 (-175))
+   (-14 *6 (-1288 (-709 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-14 *4 (-938))
+   (-14 *5 (-661 (-1198)))))
+ ((*1 *1 *2) (-12 (-5 *2 (-661 (-661 (-962 (-229))))) (-5 *1 (-480))))
+ ((*1 *2 *1) (-12 (-5 *2 (-877)) (-5 *1 (-480))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1277 *3 *4 *5)) (-4 *3 (-1078)) (-14 *4 (-1206)) (-14 *5 *3)
+  (-12 (-5 *2 (-1269 *3 *4 *5)) (-4 *3 (-1070)) (-14 *4 (-1198)) (-14 *5 *3)
    (-5 *1 (-486 *3 *4 *5))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1293 *4)) (-14 *4 (-1206)) (-5 *1 (-486 *3 *4 *5))
-   (-4 *3 (-1078)) (-14 *5 *3)))
- ((*1 *1 *2) (-12 (-5 *2 (-1154 (-558) (-628 (-507)))) (-5 *1 (-507))))
- ((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-514))))
+  (-12 (-5 *2 (-1285 *4)) (-14 *4 (-1198)) (-5 *1 (-486 *3 *4 *5))
+   (-4 *3 (-1070)) (-14 *5 *3)))
+ ((*1 *1 *2) (-12 (-5 *2 (-1146 (-558) (-628 (-507)))) (-5 *1 (-507))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-514))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-376)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-516 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-661 (-1247))) (-5 *1 (-536))))
- ((*1 *1 *2) (-12 (-5 *2 (-661 (-1247))) (-5 *1 (-617))))
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-376)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-516 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-12 (-5 *2 (-661 (-1239))) (-5 *1 (-536))))
+ ((*1 *1 *2) (-12 (-5 *2 (-661 (-1239))) (-5 *1 (-617))))
  ((*1 *1 *2) (-12 (-4 *3 (-175)) (-5 *1 (-618 *3 *2)) (-4 *2 (-764 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-630 *2)) (-4 *2 (-1246))))
- ((*1 *1 *2) (-12 (-4 *1 (-633 *2)) (-4 *2 (-1246))))
- ((*1 *1 *2) (-12 (-4 *1 (-638 *2)) (-4 *2 (-1078))))
+ ((*1 *2 *1) (-12 (-4 *1 (-630 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *2) (-12 (-4 *1 (-633 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *2) (-12 (-4 *1 (-638 *2)) (-4 *2 (-1070))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-1317 *3 *4)) (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-869))
-   (-4 *4 (-13 (-175) (-737 (-419 (-558))))) (-14 *5 (-946))))
+  (-12 (-5 *2 (-1309 *3 *4)) (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-861))
+   (-4 *4 (-13 (-175) (-737 (-419 (-558))))) (-14 *5 (-938))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-1312 *3 *4)) (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-869))
-   (-4 *4 (-13 (-175) (-737 (-419 (-558))))) (-14 *5 (-946))))
+  (-12 (-5 *2 (-1304 *3 *4)) (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-861))
+   (-4 *4 (-13 (-175) (-737 (-419 (-558))))) (-14 *5 (-938))))
  ((*1 *1 *2) (-12 (-4 *3 (-175)) (-5 *1 (-650 *3 *2)) (-4 *2 (-764 *3))))
- ((*1 *2 *1) (-12 (-5 *2 (-697 *3)) (-5 *1 (-692 *3)) (-4 *3 (-869))))
- ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-692 *3)) (-4 *3 (-869))))
+ ((*1 *2 *1) (-12 (-5 *2 (-697 *3)) (-5 *1 (-692 *3)) (-4 *3 (-861))))
+ ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-692 *3)) (-4 *3 (-861))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-985 (-985 (-985 *3)))) (-5 *1 (-695 *3)) (-4 *3 (-1130))))
+  (-12 (-5 *2 (-977 (-977 (-977 *3)))) (-5 *1 (-695 *3)) (-4 *3 (-1122))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-985 (-985 (-985 *3)))) (-4 *3 (-1130)) (-5 *1 (-695 *3))))
- ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-697 *3)) (-4 *3 (-869))))
- ((*1 *1 *2) (-12 (-5 *2 (-1144)) (-5 *1 (-701))))
- ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-702 *3)) (-4 *3 (-1130))))
+  (-12 (-5 *2 (-977 (-977 (-977 *3)))) (-4 *3 (-1122)) (-5 *1 (-695 *3))))
+ ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-697 *3)) (-4 *3 (-861))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1136)) (-5 *1 (-701))))
+ ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-702 *3)) (-4 *3 (-1122))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-1078)) (-4 *1 (-706 *3 *4 *2)) (-4 *4 (-385 *3))
+  (-12 (-4 *3 (-1070)) (-4 *1 (-706 *3 *4 *2)) (-4 *4 (-385 *3))
    (-4 *2 (-385 *3))))
  ((*1 *2 *1) (-12 (-5 *2 (-171 (-391))) (-5 *1 (-714))))
  ((*1 *1 *2) (-12 (-5 *2 (-171 (-721))) (-5 *1 (-714))))
@@ -1046,7 +1046,7 @@
  ((*1 *1 *2) (-12 (-5 *2 (-721)) (-5 *1 (-719))))
  ((*1 *2 *1) (-12 (-5 *2 (-391)) (-5 *1 (-719))))
  ((*1 *2 *3) (-12 (-5 *3 (-326 (-558))) (-5 *2 (-326 (-721))) (-5 *1 (-721))))
- ((*1 *2 *3) (-12 (-5 *3 (-885)) (-5 *2 (-1188)) (-5 *1 (-730))))
+ ((*1 *2 *3) (-12 (-5 *3 (-877)) (-5 *2 (-1180)) (-5 *1 (-730))))
  ((*1 *2 *1)
   (-12 (-4 *2 (-175)) (-5 *1 (-731 *2 *3 *4 *5 *6)) (-4 *3 (-23))
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
@@ -1056,7 +1056,7 @@
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-661 (-2 (|:| -4461 *3) (|:| -4445 *4)))) (-4 *3 (-1078))
+  (-12 (-5 *2 (-661 (-2 (|:| -4384 *3) (|:| -4368 *4)))) (-4 *3 (-1070))
    (-4 *4 (-746)) (-5 *1 (-755 *3 *4))))
  ((*1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-783))))
  ((*1 *1 *2)
@@ -1064,64 +1064,63 @@
    (-5 *2
     (-3
      (|:| |nia|
-          (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-           (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+          (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+           (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
            (|:| |relerr| (-229))))
      (|:| |mdnia|
-          (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229)))))
+          (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229)))))
            (|:| |abserr| (-229)) (|:| |relerr| (-229))))))
    (-5 *1 (-789))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229)))))
+    (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229)))))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *1 (-789))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *1 (-789))))
- ((*1 *2 *3) (-12 (-5 *2 (-793)) (-5 *1 (-794 *3)) (-4 *3 (-1246))))
+ ((*1 *2 *3) (-12 (-5 *2 (-793)) (-5 *1 (-794 *3)) (-4 *3 (-1238))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *1 (-830))))
- ((*1 *1 *2) (-12 (-5 *2 (-1206)) (-5 *1 (-848))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-3
      (|:| |noa|
-          (-2 (|:| |fn| (-326 (-229))) (|:| -3943 (-661 (-229)))
-           (|:| |lb| (-661 (-863 (-229)))) (|:| |cf| (-661 (-326 (-229))))
-           (|:| |ub| (-661 (-863 (-229))))))
+          (-2 (|:| |fn| (-326 (-229))) (|:| -3866 (-661 (-229)))
+           (|:| |lb| (-661 (-855 (-229)))) (|:| |cf| (-661 (-326 (-229))))
+           (|:| |ub| (-661 (-855 (-229))))))
      (|:| |lsa|
-          (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3943 (-661 (-229)))))))
-   (-5 *1 (-862))))
+          (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3866 (-661 (-229)))))))
+   (-5 *1 (-854))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3943 (-661 (-229)))))
-   (-5 *1 (-862))))
+  (-12 (-5 *2 (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3866 (-661 (-229)))))
+   (-5 *1 (-854))))
  ((*1 *1 *2)
   (-12
    (-5 *2
-    (-2 (|:| |fn| (-326 (-229))) (|:| -3943 (-661 (-229)))
-     (|:| |lb| (-661 (-863 (-229)))) (|:| |cf| (-661 (-326 (-229))))
-     (|:| |ub| (-661 (-863 (-229))))))
-   (-5 *1 (-862))))
- ((*1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-880))))
- ((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-896))))
- ((*1 *2 *3) (-12 (-5 *3 (-973 (-48))) (-5 *2 (-326 (-558))) (-5 *1 (-897))))
+    (-2 (|:| |fn| (-326 (-229))) (|:| -3866 (-661 (-229)))
+     (|:| |lb| (-661 (-855 (-229)))) (|:| |cf| (-661 (-326 (-229))))
+     (|:| |ub| (-661 (-855 (-229))))))
+   (-5 *1 (-854))))
+ ((*1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-872))))
+ ((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-888))))
+ ((*1 *2 *3) (-12 (-5 *3 (-965 (-48))) (-5 *2 (-326 (-558))) (-5 *1 (-889))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-419 (-973 (-48)))) (-5 *2 (-326 (-558))) (-5 *1 (-897))))
- ((*1 *1 *2) (-12 (-5 *1 (-916 *2)) (-4 *2 (-869))))
- ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-916 *3)) (-4 *3 (-869))))
+  (-12 (-5 *3 (-419 (-965 (-48)))) (-5 *2 (-326 (-558))) (-5 *1 (-889))))
+ ((*1 *1 *2) (-12 (-5 *1 (-908 *2)) (-4 *2 (-861))))
+ ((*1 *2 *1) (-12 (-5 *2 (-841 *3)) (-5 *1 (-908 *3)) (-4 *3 (-861))))
  ((*1 *1 *2)
   (-12
    (-5 *2
@@ -1131,341 +1130,341 @@
            (-2 (|:| |start| (-229)) (|:| |finish| (-229)) (|:| |grid| (-791))
             (|:| |boundaryType| (-558)) (|:| |dStart| (-709 (-229)))
             (|:| |dFinish| (-709 (-229))))))
-     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1188))
+     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1180))
      (|:| |tol| (-229))))
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- ((*1 *2) (-12 (-4 *1 (-1315 *3)) (-4 *3 (-376)) (-5 *2 (-853 (-946)))))) 
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 (((*1 *2)
   (-12 (-4 *4 (-376)) (-5 *2 (-791)) (-5 *1 (-340 *3 *4)) (-4 *3 (-341 *4))))
- ((*1 *2) (-12 (-4 *1 (-1315 *3)) (-4 *3 (-376)) (-5 *2 (-791))))) 
+ ((*1 *2) (-12 (-4 *1 (-1307 *3)) (-4 *3 (-376)) (-5 *2 (-791))))) 
 (((*1 *2 *2)
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-  (-12 (-5 *2 (-791)) (-4 *1 (-1315 *3)) (-4 *3 (-376)) (-4 *3 (-381))))
- ((*1 *1 *1) (-12 (-4 *1 (-1315 *2)) (-4 *2 (-376)) (-4 *2 (-381))))) 
+  (-12 (-5 *2 (-791)) (-4 *1 (-1307 *3)) (-4 *3 (-376)) (-4 *3 (-381))))
+ ((*1 *1 *1) (-12 (-4 *1 (-1307 *2)) (-4 *2 (-376)) (-4 *2 (-381))))) 
 (((*1 *2 *2 *2 *3)
-  (-12 (-5 *3 (-791)) (-4 *4 (-13 (-1078) (-737 (-419 (-558))))) (-4 *5 (-869))
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+  (-12 (-5 *3 (-791)) (-4 *4 (-13 (-1070) (-737 (-419 (-558))))) (-4 *5 (-861))
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 (((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-569))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1310 *3 *4 *5 *6))))
+  (|partial| -12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-569))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-1302 *3 *4 *5 *6))))
  ((*1 *1 *2 *3 *4)
   (|partial| -12 (-5 *2 (-661 *8)) (-5 *3 (-1 (-114) *8 *8))
-   (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1094 *5 *6 *7)) (-4 *5 (-569)) (-4 *6 (-815))
-   (-4 *7 (-869)) (-5 *1 (-1310 *5 *6 *7 *8))))) 
+   (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1086 *5 *6 *7)) (-4 *5 (-569)) (-4 *6 (-815))
+   (-4 *7 (-861)) (-5 *1 (-1302 *5 *6 *7 *8))))) 
 (((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-569))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1310 *3 *4 *5 *6))))
+  (|partial| -12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-569))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-1302 *3 *4 *5 *6))))
  ((*1 *1 *2 *3 *4)
   (|partial| -12 (-5 *2 (-661 *8)) (-5 *3 (-1 (-114) *8 *8))
-   (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1094 *5 *6 *7)) (-4 *5 (-569)) (-4 *6 (-815))
-   (-4 *7 (-869)) (-5 *1 (-1310 *5 *6 *7 *8))))) 
+   (-5 *4 (-1 *8 *8 *8)) (-4 *8 (-1086 *5 *6 *7)) (-4 *5 (-569)) (-4 *6 (-815))
+   (-4 *7 (-861)) (-5 *1 (-1302 *5 *6 *7 *8))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-661 (-1310 *4 *5 *6 *7)))
-   (-5 *1 (-1310 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-661 (-1302 *4 *5 *6 *7)))
+   (-5 *1 (-1302 *4 *5 *6 *7))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-661 *9)) (-5 *4 (-1 (-114) *9 *9)) (-5 *5 (-1 *9 *9 *9))
-   (-4 *9 (-1094 *6 *7 *8)) (-4 *6 (-569)) (-4 *7 (-815)) (-4 *8 (-869))
-   (-5 *2 (-661 (-1310 *6 *7 *8 *9))) (-5 *1 (-1310 *6 *7 *8 *9))))) 
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+   (-5 *2 (-661 (-1302 *6 *7 *8 *9))) (-5 *1 (-1302 *6 *7 *8 *9))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-791)) (-5 *2 (-1302)) (-5 *1 (-888 *4 *5 *6 *7))
-   (-4 *4 (-1078)) (-14 *5 (-661 (-1206))) (-14 *6 (-661 *3)) (-14 *7 *3)))
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+   (-4 *4 (-1070)) (-14 *5 (-661 (-1198))) (-14 *6 (-661 *3)) (-14 *7 *3)))
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-  (-12 (-5 *3 (-791)) (-4 *4 (-1078)) (-4 *5 (-869)) (-4 *6 (-815))
-   (-14 *8 (-661 *5)) (-5 *2 (-1302)) (-5 *1 (-1309 *4 *5 *6 *7 *8 *9 *10))
-   (-4 *7 (-977 *4 *6 *5)) (-14 *9 (-661 *3)) (-14 *10 *3)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1164)) (-5 *1 (-529))))
+  (-12 (-5 *3 (-791)) (-4 *4 (-1070)) (-4 *5 (-861)) (-4 *6 (-815))
+   (-14 *8 (-661 *5)) (-5 *2 (-1294)) (-5 *1 (-1301 *4 *5 *6 *7 *8 *9 *10))
+   (-4 *7 (-969 *4 *6 *5)) (-14 *9 (-661 *3)) (-14 *10 *3)))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-529))))
  ((*1 *2 *1)
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-   (-4 *3 (-13 (-1130) (-34)))))
- ((*1 *2 *1) (-12 (-5 *2 (-1164)) (-5 *1 (-1308))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1164)) (-5 *1 (-1307))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1164)) (-5 *1 (-1307))))) 
+  (-12 (-4 *2 (-13 (-1122) (-34))) (-5 *1 (-1161 *3 *2))
+   (-4 *3 (-13 (-1122) (-34)))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-1300))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-1299))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-1299))))) 
 (((*1 *2 *3)
-  (-12 (-4 *3 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $)))))
-   (-4 *4 (-1272 *3))
+  (-12 (-4 *3 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $)))))
+   (-4 *4 (-1264 *3))
    (-5 *2
-    (-2 (|:| -2230 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
+    (-2 (|:| -2222 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
    (-5 *1 (-364 *3 *4 *5)) (-4 *5 (-422 *3 *4))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-558)) (-4 *4 (-1272 *3))
+  (-12 (-5 *3 (-558)) (-4 *4 (-1264 *3))
    (-5 *2
-    (-2 (|:| -2230 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
+    (-2 (|:| -2222 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
    (-5 *1 (-788 *4 *5)) (-4 *5 (-422 *3 *4))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-363)) (-4 *3 (-1272 *4)) (-4 *5 (-1272 *3))
+  (-12 (-4 *4 (-363)) (-4 *3 (-1264 *4)) (-4 *5 (-1264 *3))
    (-5 *2
-    (-2 (|:| -2230 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
-   (-5 *1 (-1014 *4 *3 *5 *6)) (-4 *6 (-744 *3 *5))))
+    (-2 (|:| -2222 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
+   (-5 *1 (-1006 *4 *3 *5 *6)) (-4 *6 (-744 *3 *5))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-363)) (-4 *3 (-1272 *4)) (-4 *5 (-1272 *3))
+  (-12 (-4 *4 (-363)) (-4 *3 (-1264 *4)) (-4 *5 (-1264 *3))
    (-5 *2
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-   (-5 *1 (-1306 *4 *3 *5 *6)) (-4 *6 (-422 *3 *5))))) 
+    (-2 (|:| -2222 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
+   (-5 *1 (-1298 *4 *3 *5 *6)) (-4 *6 (-422 *3 *5))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-1251)) (-4 *4 (-1272 *3)) (-4 *5 (-1272 (-419 *4)))
-   (-5 *2 (-1296 *1)) (-4 *1 (-355 *3 *4 *5))))
+  (-12 (-4 *3 (-1243)) (-4 *4 (-1264 *3)) (-4 *5 (-1264 (-419 *4)))
+   (-5 *2 (-1288 *1)) (-4 *1 (-355 *3 *4 *5))))
  ((*1 *2)
-  (-12 (-4 *3 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $)))))
-   (-4 *4 (-1272 *3))
+  (-12 (-4 *3 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $)))))
+   (-4 *4 (-1264 *3))
    (-5 *2
-    (-2 (|:| -2230 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
+    (-2 (|:| -2222 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
    (-5 *1 (-364 *3 *4 *5)) (-4 *5 (-422 *3 *4))))
  ((*1 *2)
-  (-12 (-4 *3 (-1272 (-558)))
+  (-12 (-4 *3 (-1264 (-558)))
    (-5 *2
-    (-2 (|:| -2230 (-709 (-558))) (|:| |basisDen| (-558))
+    (-2 (|:| -2222 (-709 (-558))) (|:| |basisDen| (-558))
      (|:| |basisInv| (-709 (-558)))))
    (-5 *1 (-788 *3 *4)) (-4 *4 (-422 (-558) *3))))
  ((*1 *2)
-  (-12 (-4 *3 (-363)) (-4 *4 (-1272 *3)) (-4 *5 (-1272 *4))
+  (-12 (-4 *3 (-363)) (-4 *4 (-1264 *3)) (-4 *5 (-1264 *4))
    (-5 *2
-    (-2 (|:| -2230 (-709 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-709 *4))))
-   (-5 *1 (-1014 *3 *4 *5 *6)) (-4 *6 (-744 *4 *5))))
+    (-2 (|:| -2222 (-709 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-709 *4))))
+   (-5 *1 (-1006 *3 *4 *5 *6)) (-4 *6 (-744 *4 *5))))
  ((*1 *2)
-  (-12 (-4 *3 (-363)) (-4 *4 (-1272 *3)) (-4 *5 (-1272 *4))
+  (-12 (-4 *3 (-363)) (-4 *4 (-1264 *3)) (-4 *5 (-1264 *4))
    (-5 *2
-    (-2 (|:| -2230 (-709 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-709 *4))))
-   (-5 *1 (-1306 *3 *4 *5 *6)) (-4 *6 (-422 *4 *5))))) 
+    (-2 (|:| -2222 (-709 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-709 *4))))
+   (-5 *1 (-1298 *3 *4 *5 *6)) (-4 *6 (-422 *4 *5))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-791)) (-4 *6 (-376)) (-5 *4 (-1239 *6))
-   (-5 *2 (-1 (-1184 *4) (-1184 *4))) (-5 *1 (-1305 *6)) (-5 *5 (-1184 *4))))) 
+  (-12 (-5 *3 (-791)) (-4 *6 (-376)) (-5 *4 (-1231 *6))
+   (-5 *2 (-1 (-1176 *4) (-1176 *4))) (-5 *1 (-1297 *6)) (-5 *5 (-1176 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1206)) (-4 *5 (-376)) (-5 *2 (-661 (-1239 *5)))
-   (-5 *1 (-1305 *5)) (-5 *4 (-1239 *5))))) 
+  (-12 (-5 *3 (-1198)) (-4 *5 (-376)) (-5 *2 (-661 (-1231 *5)))
+   (-5 *1 (-1297 *5)) (-5 *4 (-1231 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1206)) (-5 *2 (-1 (-1200 (-973 *4)) (-973 *4)))
-   (-5 *1 (-1305 *4)) (-4 *4 (-376))))) 
+  (-12 (-5 *3 (-1198)) (-5 *2 (-1 (-1192 (-965 *4)) (-965 *4)))
+   (-5 *1 (-1297 *4)) (-4 *4 (-376))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1206)) (-4 *5 (-376)) (-5 *2 (-1184 (-1184 (-973 *5))))
-   (-5 *1 (-1305 *5)) (-5 *4 (-1184 (-973 *5)))))) 
+  (-12 (-5 *3 (-1198)) (-4 *5 (-376)) (-5 *2 (-1176 (-1176 (-965 *5))))
+   (-5 *1 (-1297 *5)) (-5 *4 (-1176 (-965 *5)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-791)) (-5 *2 (-1 (-1184 (-973 *4)) (-1184 (-973 *4))))
-   (-5 *1 (-1305 *4)) (-4 *4 (-376))))) 
+  (-12 (-5 *3 (-791)) (-5 *2 (-1 (-1176 (-965 *4)) (-1176 (-965 *4))))
+   (-5 *1 (-1297 *4)) (-4 *4 (-376))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-791)) (-5 *2 (-1 (-1184 (-973 *4)) (-1184 (-973 *4))))
-   (-5 *1 (-1305 *4)) (-4 *4 (-376))))) 
+  (-12 (-5 *3 (-791)) (-5 *2 (-1 (-1176 (-965 *4)) (-1176 (-965 *4))))
+   (-5 *1 (-1297 *4)) (-4 *4 (-376))))) 
 (((*1 *2)
-  (-12 (-14 *4 (-791)) (-4 *5 (-1246)) (-5 *2 (-136)) (-5 *1 (-244 *3 *4 *5))
+  (-12 (-14 *4 (-791)) (-4 *5 (-1238)) (-5 *2 (-136)) (-5 *1 (-244 *3 *4 *5))
    (-4 *3 (-245 *4 *5))))
  ((*1 *2)
   (-12 (-4 *4 (-376)) (-5 *2 (-136)) (-5 *1 (-340 *3 *4)) (-4 *3 (-341 *4))))
@@ -1473,256 +1472,256 @@
   (-12 (-5 *2 (-791)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 *2) (-14 *4 *2)
    (-4 *5 (-175))))
  ((*1 *2 *1)
-  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *2 (-558))
-   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-977 *3 *4 *5))))
+  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *2 (-558))
+   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-969 *3 *4 *5))))
  ((*1 *2 *1 *3)
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 (((*1 *2 *1 *3 *3 *4 *4)
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 (((*1 *1 *2)
   (-12
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   (-12
    (-5 *2
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    (-5 *3 (-661 (-270))) (-5 *1 (-271))))
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    (-5 *2
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+ ((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-1291))))
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-(((*1 *1 *2 *3) (-12 (-5 *2 (-480)) (-5 *3 (-661 (-270))) (-5 *1 (-1299))))
- ((*1 *1 *1) (-5 *1 (-1299)))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-558)) (-5 *1 (-1291))))
+ ((*1 *2 *1) (-12 (-5 *2 (-558)) (-5 *1 (-1292))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-661 (-962 (-229)))) (-5 *1 (-1291))))) 
+(((*1 *1) (-5 *1 (-1291)))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-480)) (-5 *3 (-661 (-270))) (-5 *1 (-1291))))
+ ((*1 *1 *1) (-5 *1 (-1291)))) 
 (((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5)
-  (-12 (-5 *3 (-946)) (-5 *4 (-229)) (-5 *5 (-558)) (-5 *6 (-896))
-   (-5 *2 (-1302)) (-5 *1 (-1299))))) 
+  (-12 (-5 *3 (-938)) (-5 *4 (-229)) (-5 *5 (-558)) (-5 *6 (-888))
+   (-5 *2 (-1294)) (-5 *1 (-1291))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
-    (-1296
+    (-1288
      (-2 (|:| |scaleX| (-229)) (|:| |scaleY| (-229)) (|:| |deltaX| (-229))
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-      (|:| |spline| (-558)) (|:| -4386 (-558)) (|:| |axesColor| (-896))
-      (|:| -4358 (-558)) (|:| |unitsColor| (-896)) (|:| |showing| (-558)))))
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- ((*1 *2 *1) (-12 (-5 *2 (-1296 (-3 (-480) "undefined"))) (-5 *1 (-1299))))) 
+      (|:| |deltaY| (-229)) (|:| -4280 (-558)) (|:| -4278 (-558))
+      (|:| |spline| (-558)) (|:| -4309 (-558)) (|:| |axesColor| (-888))
+      (|:| -4281 (-558)) (|:| |unitsColor| (-888)) (|:| |showing| (-558)))))
+   (-5 *1 (-1291))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-938)) (-5 *2 (-1200 (-419 (-558)))) (-5 *1 (-193))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1288 (-3 (-480) "undefined"))) (-5 *1 (-1291))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-480)) (-5 *4 (-946)) (-5 *2 (-1302)) (-5 *1 (-1299))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-946)) (-5 *2 (-480)) (-5 *1 (-1299))))) 
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 (((*1 *2 *3 *2)
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  ((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-946)) (-5 *4 (-896)) (-5 *2 (-1302)) (-5 *1 (-1299))))
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-  (-12 (-5 *3 (-946)) (-5 *4 (-1188)) (-5 *2 (-1302)) (-5 *1 (-1299))))) 
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 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-946)) (-5 *4 (-1188)) (-5 *2 (-1302)) (-5 *1 (-1299))))) 
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 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-946)) (-5 *4 (-1188)) (-5 *2 (-1302)) (-5 *1 (-1299))))) 
+  (-12 (-5 *3 (-938)) (-5 *4 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1291))))) 
 (((*1 *2 *1 *3 *4)
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-  (-12 (-5 *3 (-946)) (-5 *4 (-391)) (-5 *2 (-1302)) (-5 *1 (-1299))))) 
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 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-946)) (-5 *4 (-1188)) (-5 *2 (-1302)) (-5 *1 (-1299))))) 
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 (((*1 *2 *1 *3 *4)
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 (((*1 *2 *3 *4 *4 *5 *6)
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+  (-12 (-5 *3 (-661 (-661 (-962 (-229))))) (-5 *4 (-661 (-270)))
+   (-5 *2 (-1291)) (-5 *1 (-1290))))) 
 (((*1 *2 *3 *4 *4 *5 *6)
-  (-12 (-5 *3 (-661 (-661 (-970 (-229))))) (-5 *4 (-896)) (-5 *5 (-946))
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 (((*1 *1 *1) (-5 *1 (-48)))
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-   (-4 *2 (-1246))))
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+   (-4 *2 (-1238))))
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+  (-12 (-4 *4 (-1070)) (-5 *2 (-2 (|:| -2214 (-1192 *4)) (|:| |deg| (-938))))
+   (-5 *1 (-225 *4 *5)) (-5 *3 (-1192 *4)) (-4 *5 (-569))))
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+   (-4 *6 (-1238)) (-4 *2 (-1238)) (-5 *1 (-247 *5 *6 *2))))
  ((*1 *1 *2 *3)
-  (-12 (-4 *4 (-175)) (-5 *1 (-301 *4 *2 *3 *5 *6 *7)) (-4 *2 (-1272 *4))
+  (-12 (-4 *4 (-175)) (-5 *1 (-301 *4 *2 *3 *5 *6 *7)) (-4 *2 (-1264 *4))
    (-4 *3 (-23)) (-14 *5 (-1 *2 *2 *3)) (-14 *6 (-1 (-3 *3 "failed") *3 *3))
    (-14 *7 (-1 (-3 *2 "failed") *2 *2 *3))))
- ((*1 *1 *1) (-12 (-5 *1 (-326 *2)) (-4 *2 (-569)) (-4 *2 (-1130))))
+ ((*1 *1 *1) (-12 (-5 *1 (-326 *2)) (-4 *2 (-569)) (-4 *2 (-1122))))
  ((*1 *1 *1)
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-   (-4 *4 (-1272 (-419 *3))) (-4 *5 (-355 *2 *3 *4))))
+  (-12 (-4 *1 (-349 *2 *3 *4 *5)) (-4 *2 (-376)) (-4 *3 (-1264 *2))
+   (-4 *4 (-1264 (-419 *3))) (-4 *5 (-355 *2 *3 *4))))
  ((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1246)) (-4 *2 (-1246))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1238)) (-4 *2 (-1238))
    (-5 *1 (-386 *5 *4 *2 *6)) (-4 *4 (-385 *5)) (-4 *6 (-385 *2))))
  ((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1130)) (-4 *2 (-1130))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1122)) (-4 *2 (-1122))
    (-5 *1 (-439 *5 *4 *2 *6)) (-4 *4 (-438 *5)) (-4 *6 (-438 *2))))
  ((*1 *1 *1) (-5 *1 (-507)))
  ((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-661 *5)) (-4 *5 (-1246)) (-4 *2 (-1246))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-661 *5)) (-4 *5 (-1238)) (-4 *2 (-1238))
    (-5 *1 (-662 *5 *2))))
  ((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1078)) (-4 *2 (-1078)) (-4 *6 (-385 *5))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1070)) (-4 *2 (-1070)) (-4 *6 (-385 *5))
    (-4 *7 (-385 *5)) (-4 *8 (-385 *2)) (-4 *9 (-385 *2))
    (-5 *1 (-707 *5 *6 *7 *4 *2 *8 *9 *10)) (-4 *4 (-706 *5 *6 *7))
    (-4 *10 (-706 *2 *8 *9))))
@@ -1730,559 +1729,559 @@
   (-12 (-5 *1 (-731 *2 *3 *4 *5 *6)) (-4 *2 (-175)) (-4 *3 (-23))
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
- ((*1 *1 *2) (-12 (-4 *3 (-1078)) (-5 *1 (-732 *3 *2)) (-4 *2 (-1272 *3))))
+ ((*1 *1 *2) (-12 (-4 *3 (-1070)) (-5 *1 (-732 *3 *2)) (-4 *2 (-1264 *3))))
  ((*1 *1 *2 *3)
   (-12 (-5 *1 (-735 *2 *3 *4 *5 *6)) (-4 *2 (-175)) (-4 *3 (-23))
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
  ((*1 *1 *2)
-  (|partial| -12 (-5 *2 (-419 *4)) (-4 *4 (-1272 *3)) (-4 *3 (-376))
+  (|partial| -12 (-5 *2 (-419 *4)) (-4 *4 (-1264 *3)) (-4 *3 (-376))
    (-4 *3 (-175)) (-4 *1 (-744 *3 *4))))
- ((*1 *1 *2) (-12 (-4 *3 (-175)) (-4 *1 (-744 *3 *2)) (-4 *2 (-1272 *3))))
+ ((*1 *1 *2) (-12 (-4 *3 (-175)) (-4 *1 (-744 *3 *2)) (-4 *2 (-1264 *3))))
  ((*1 *2 *3 *4 *2)
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-   (-5 *1 (-986 *5 *2))))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-977 *5)) (-4 *5 (-1238)) (-4 *2 (-1238))
+   (-5 *1 (-978 *5 *2))))
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-   (-5 *1 (-1063 *3 *4 *5 *2 *6)) (-4 *2 (-977 *3 *4 *5)) (-14 *6 (-661 *2))))
+  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861))
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+   (-5 *1 (-1076 *5 *6 *7 *8 *9 *4 *2 *10 *11 *12))
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-   (-5 *1 (-1186 *5 *2))))
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+   (-5 *1 (-1178 *5 *2))))
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-   (-4 *2 (-1094 *5 *6 *7))))
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+   (-4 *2 (-1086 *5 *6 *7))))
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+  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-1288 *5)) (-4 *5 (-1238)) (-4 *2 (-1238))
+   (-5 *1 (-1289 *5 *2))))) 
 (((*1 *2 *3 *4 *5)
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+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1238)) (-5 *1 (-1288 *3))))) 
 (((*1 *1 *1 *1) (-4 *1 (-25))) ((*1 *1 *1 *1) (-5 *1 (-159)))
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    (-4 *2
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- ((*1 *1 *2 *1) (-12 (-4 *1 (-335 *2 *3)) (-4 *2 (-1130)) (-4 *3 (-133))))
+    (-13 (-861)
+     (-10 -8 (-15 -4230 ((-1180) $ (-1198))) (-15 -4047 ((-1294) $))
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+ ((*1 *1 *1 *2) (-12 (-5 *1 (-305 *2)) (-4 *2 (-25)) (-4 *2 (-1238))))
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+ ((*1 *1 *1 *1) (-5 *1 (-877)))
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-905 *2)) (-4 *2 (-1122))))
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-  (-12 (-5 *2 (-1206)) (-5 *1 (-1239 *3)) (-4 *3 (-38 (-419 (-558))))
-   (-4 *3 (-1078))))
+  (-12 (-5 *2 (-1198)) (-5 *1 (-1231 *3)) (-4 *3 (-38 (-419 (-558))))
+   (-4 *3 (-1070))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1293 *4)) (-14 *4 (-1206)) (-5 *1 (-1256 *3 *4 *5))
-   (-4 *3 (-38 (-419 (-558)))) (-4 *3 (-1078)) (-14 *5 *3)))
+  (-12 (-5 *2 (-1285 *4)) (-14 *4 (-1198)) (-5 *1 (-1248 *3 *4 *5))
+   (-4 *3 (-38 (-419 (-558)))) (-4 *3 (-1070)) (-14 *5 *3)))
  ((*1 *1 *1 *2)
-  (-4034
-   (-12 (-5 *2 (-1206)) (-4 *1 (-1258 *3)) (-4 *3 (-1078))
-    (-12 (-4 *3 (-29 (-558))) (-4 *3 (-987)) (-4 *3 (-1232))
+  (-3957
+   (-12 (-5 *2 (-1198)) (-4 *1 (-1250 *3)) (-4 *3 (-1070))
+    (-12 (-4 *3 (-29 (-558))) (-4 *3 (-979)) (-4 *3 (-1224))
      (-4 *3 (-38 (-419 (-558))))))
-   (-12 (-5 *2 (-1206)) (-4 *1 (-1258 *3)) (-4 *3 (-1078))
-    (-12 (|has| *3 (-15 -3561 ((-661 *2) *3)))
-     (|has| *3 (-15 -4319 (*3 *3 *2))) (-4 *3 (-38 (-419 (-558))))))))
+   (-12 (-5 *2 (-1198)) (-4 *1 (-1250 *3)) (-4 *3 (-1070))
+    (-12 (|has| *3 (-15 -3484 ((-661 *2) *3)))
+     (|has| *3 (-15 -4242 (*3 *3 *2))) (-4 *3 (-38 (-419 (-558))))))))
  ((*1 *1 *1)
-  (-12 (-4 *1 (-1258 *2)) (-4 *2 (-1078)) (-4 *2 (-38 (-419 (-558))))))
+  (-12 (-4 *1 (-1250 *2)) (-4 *2 (-1070)) (-4 *2 (-38 (-419 (-558))))))
  ((*1 *1 *1)
-  (-12 (-4 *1 (-1272 *2)) (-4 *2 (-1078)) (-4 *2 (-38 (-419 (-558))))))
+  (-12 (-4 *1 (-1264 *2)) (-4 *2 (-1070)) (-4 *2 (-38 (-419 (-558))))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1293 *4)) (-14 *4 (-1206)) (-5 *1 (-1277 *3 *4 *5))
-   (-4 *3 (-38 (-419 (-558)))) (-4 *3 (-1078)) (-14 *5 *3)))
+  (-12 (-5 *2 (-1285 *4)) (-14 *4 (-1198)) (-5 *1 (-1269 *3 *4 *5))
+   (-4 *3 (-38 (-419 (-558)))) (-4 *3 (-1070)) (-14 *5 *3)))
  ((*1 *1 *1 *2)
-  (-4034
-   (-12 (-5 *2 (-1206)) (-4 *1 (-1279 *3)) (-4 *3 (-1078))
-    (-12 (-4 *3 (-29 (-558))) (-4 *3 (-987)) (-4 *3 (-1232))
+  (-3957
+   (-12 (-5 *2 (-1198)) (-4 *1 (-1271 *3)) (-4 *3 (-1070))
+    (-12 (-4 *3 (-29 (-558))) (-4 *3 (-979)) (-4 *3 (-1224))
      (-4 *3 (-38 (-419 (-558))))))
-   (-12 (-5 *2 (-1206)) (-4 *1 (-1279 *3)) (-4 *3 (-1078))
-    (-12 (|has| *3 (-15 -3561 ((-661 *2) *3)))
-     (|has| *3 (-15 -4319 (*3 *3 *2))) (-4 *3 (-38 (-419 (-558))))))))
+   (-12 (-5 *2 (-1198)) (-4 *1 (-1271 *3)) (-4 *3 (-1070))
+    (-12 (|has| *3 (-15 -3484 ((-661 *2) *3)))
+     (|has| *3 (-15 -4242 (*3 *3 *2))) (-4 *3 (-38 (-419 (-558))))))))
  ((*1 *1 *1)
-  (-12 (-4 *1 (-1279 *2)) (-4 *2 (-1078)) (-4 *2 (-38 (-419 (-558))))))
+  (-12 (-4 *1 (-1271 *2)) (-4 *2 (-1070)) (-4 *2 (-38 (-419 (-558))))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1293 *4)) (-14 *4 (-1206)) (-5 *1 (-1286 *3 *4 *5))
-   (-4 *3 (-38 (-419 (-558)))) (-4 *3 (-1078)) (-14 *5 *3)))
+  (-12 (-5 *2 (-1285 *4)) (-14 *4 (-1198)) (-5 *1 (-1278 *3 *4 *5))
+   (-4 *3 (-38 (-419 (-558)))) (-4 *3 (-1070)) (-14 *5 *3)))
  ((*1 *1 *1 *2)
-  (-4034
-   (-12 (-5 *2 (-1206)) (-4 *1 (-1289 *3)) (-4 *3 (-1078))
-    (-12 (-4 *3 (-29 (-558))) (-4 *3 (-987)) (-4 *3 (-1232))
+  (-3957
+   (-12 (-5 *2 (-1198)) (-4 *1 (-1281 *3)) (-4 *3 (-1070))
+    (-12 (-4 *3 (-29 (-558))) (-4 *3 (-979)) (-4 *3 (-1224))
      (-4 *3 (-38 (-419 (-558))))))
-   (-12 (-5 *2 (-1206)) (-4 *1 (-1289 *3)) (-4 *3 (-1078))
-    (-12 (|has| *3 (-15 -3561 ((-661 *2) *3)))
-     (|has| *3 (-15 -4319 (*3 *3 *2))) (-4 *3 (-38 (-419 (-558))))))))
+   (-12 (-5 *2 (-1198)) (-4 *1 (-1281 *3)) (-4 *3 (-1070))
+    (-12 (|has| *3 (-15 -3484 ((-661 *2) *3)))
+     (|has| *3 (-15 -4242 (*3 *3 *2))) (-4 *3 (-38 (-419 (-558))))))))
  ((*1 *1 *1)
-  (-12 (-4 *1 (-1289 *2)) (-4 *2 (-1078)) (-4 *2 (-38 (-419 (-558))))))) 
+  (-12 (-4 *1 (-1281 *2)) (-4 *2 (-1070)) (-4 *2 (-38 (-419 (-558))))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-791)) (-5 *2 (-1265 *5 *4)) (-5 *1 (-1204 *4 *5 *6))
-   (-4 *4 (-1078)) (-14 *5 (-1206)) (-14 *6 *4)))
+  (-12 (-5 *3 (-791)) (-5 *2 (-1257 *5 *4)) (-5 *1 (-1196 *4 *5 *6))
+   (-4 *4 (-1070)) (-14 *5 (-1198)) (-14 *6 *4)))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-791)) (-5 *2 (-1265 *5 *4)) (-5 *1 (-1286 *4 *5 *6))
-   (-4 *4 (-1078)) (-14 *5 (-1206)) (-14 *6 *4)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))
+  (-12 (-5 *3 (-791)) (-5 *2 (-1257 *5 *4)) (-5 *1 (-1278 *4 *5 *6))
+   (-4 *4 (-1070)) (-14 *5 (-1198)) (-14 *6 *4)))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1286 *2 *3 *4)) (-4 *2 (-1078)) (-14 *3 (-1206)) (-14 *4 *2)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))
+  (-12 (-5 *1 (-1278 *2 *3 *4)) (-4 *2 (-1070)) (-14 *3 (-1198)) (-14 *4 *2)))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1286 *2 *3 *4)) (-4 *2 (-1078)) (-14 *3 (-1206)) (-14 *4 *2)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))
+  (-12 (-5 *1 (-1278 *2 *3 *4)) (-4 *2 (-1070)) (-14 *3 (-1198)) (-14 *4 *2)))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1286 *2 *3 *4)) (-4 *2 (-1078)) (-14 *3 (-1206)) (-14 *4 *2)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))
+  (-12 (-5 *1 (-1278 *2 *3 *4)) (-4 *2 (-1070)) (-14 *3 (-1198)) (-14 *4 *2)))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1286 *2 *3 *4)) (-4 *2 (-1078)) (-14 *3 (-1206)) (-14 *4 *2)))) 
+  (-12 (-5 *1 (-1278 *2 *3 *4)) (-4 *2 (-1070)) (-14 *3 (-1198)) (-14 *4 *2)))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-1184 *4)) (-5 *3 (-558)) (-4 *4 (-1078)) (-5 *1 (-1190 *4))))
+  (-12 (-5 *2 (-1176 *4)) (-5 *3 (-558)) (-4 *4 (-1070)) (-5 *1 (-1182 *4))))
  ((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-558)) (-5 *1 (-1286 *3 *4 *5)) (-4 *3 (-1078)) (-14 *4 (-1206))
+  (-12 (-5 *2 (-558)) (-5 *1 (-1278 *3 *4 *5)) (-4 *3 (-1070)) (-14 *4 (-1198))
    (-14 *5 *3)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))
+(((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1286 *2 *3 *4)) (-4 *2 (-1078)) (-14 *3 (-1206)) (-14 *4 *2)))) 
+  (-12 (-5 *1 (-1278 *2 *3 *4)) (-4 *2 (-1070)) (-14 *3 (-1198)) (-14 *4 *2)))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-1184 *4)) (-5 *3 (-558)) (-4 *4 (-1078)) (-5 *1 (-1190 *4))))
+  (-12 (-5 *2 (-1176 *4)) (-5 *3 (-558)) (-4 *4 (-1070)) (-5 *1 (-1182 *4))))
  ((*1 *1 *2 *2 *1)
-  (-12 (-5 *2 (-558)) (-5 *1 (-1286 *3 *4 *5)) (-4 *3 (-1078)) (-14 *4 (-1206))
+  (-12 (-5 *2 (-558)) (-5 *1 (-1278 *3 *4 *5)) (-4 *3 (-1070)) (-14 *4 (-1198))
    (-14 *5 *3)))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-1184 *4)) (-5 *3 (-558)) (-4 *4 (-1078)) (-5 *1 (-1190 *4))))
+  (-12 (-5 *2 (-1176 *4)) (-5 *3 (-558)) (-4 *4 (-1070)) (-5 *1 (-1182 *4))))
  ((*1 *1 *2 *2 *1)
-  (-12 (-5 *2 (-558)) (-5 *1 (-1286 *3 *4 *5)) (-4 *3 (-1078)) (-14 *4 (-1206))
+  (-12 (-5 *2 (-558)) (-5 *1 (-1278 *3 *4 *5)) (-4 *3 (-1070)) (-14 *4 (-1198))
    (-14 *5 *3)))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-1064)) (-5 *1 (-315))))
- ((*1 *2 *3) (-12 (-5 *3 (-661 (-1064))) (-5 *2 (-1064)) (-5 *1 (-315))))
- ((*1 *1 *2) (-12 (-5 *2 (-661 *1)) (-4 *1 (-671 *3)) (-4 *3 (-1246))))
- ((*1 *1 *1 *1) (-12 (-4 *1 (-671 *2)) (-4 *2 (-1246))))
- ((*1 *1 *2 *1) (-12 (-4 *1 (-671 *2)) (-4 *2 (-1246))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-671 *2)) (-4 *2 (-1246))))
- ((*1 *1 *1 *1) (-5 *1 (-1092)))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1184 (-1184 *4))) (-5 *2 (-1184 *4)) (-5 *1 (-1185 *4))
-   (-4 *4 (-1246))))
- ((*1 *1 *2 *1) (-12 (-4 *1 (-1285 *2)) (-4 *2 (-1246))))
- ((*1 *1 *1 *1) (-12 (-4 *1 (-1285 *2)) (-4 *2 (-1246))))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-616 *3 *2)) (-4 *3 (-1130)) (-4 *3 (-869)) (-4 *2 (-1246))))
- ((*1 *2 *1) (-12 (-5 *1 (-697 *2)) (-4 *2 (-869))))
- ((*1 *2 *1) (-12 (-5 *1 (-841 *2)) (-4 *2 (-869))))
- ((*1 *2 *1) (-12 (-4 *2 (-1246)) (-5 *1 (-895 *2 *3)) (-4 *3 (-1246))))
- ((*1 *2 *1) (-12 (-5 *2 (-692 *3)) (-5 *1 (-916 *3)) (-4 *3 (-869))))
- ((*1 *2 *1)
-  (|partial| -12 (-4 *1 (-1241 *3 *4 *5 *2)) (-4 *3 (-569)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-4 *2 (-1094 *3 *4 *5))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-791)) (-4 *1 (-1285 *3)) (-4 *3 (-1246))))
- ((*1 *2 *1) (-12 (-4 *1 (-1285 *2)) (-4 *2 (-1246))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-1056)) (-5 *1 (-315))))
+ ((*1 *2 *3) (-12 (-5 *3 (-661 (-1056))) (-5 *2 (-1056)) (-5 *1 (-315))))
+ ((*1 *1 *2) (-12 (-5 *2 (-661 *1)) (-4 *1 (-671 *3)) (-4 *3 (-1238))))
+ ((*1 *1 *1 *1) (-12 (-4 *1 (-671 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *2 *1) (-12 (-4 *1 (-671 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-671 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *1 *1) (-5 *1 (-1084)))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1176 (-1176 *4))) (-5 *2 (-1176 *4)) (-5 *1 (-1177 *4))
+   (-4 *4 (-1238))))
+ ((*1 *1 *2 *1) (-12 (-4 *1 (-1277 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *1 *1) (-12 (-4 *1 (-1277 *2)) (-4 *2 (-1238))))) 
+(((*1 *2 *1)
+  (-12 (-4 *1 (-616 *3 *2)) (-4 *3 (-1122)) (-4 *3 (-861)) (-4 *2 (-1238))))
+ ((*1 *2 *1) (-12 (-5 *1 (-697 *2)) (-4 *2 (-861))))
+ ((*1 *2 *1) (-12 (-5 *1 (-841 *2)) (-4 *2 (-861))))
+ ((*1 *2 *1) (-12 (-4 *2 (-1238)) (-5 *1 (-887 *2 *3)) (-4 *3 (-1238))))
+ ((*1 *2 *1) (-12 (-5 *2 (-692 *3)) (-5 *1 (-908 *3)) (-4 *3 (-861))))
+ ((*1 *2 *1)
+  (|partial| -12 (-4 *1 (-1233 *3 *4 *5 *2)) (-4 *3 (-569)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-4 *2 (-1086 *3 *4 *5))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-791)) (-4 *1 (-1277 *3)) (-4 *3 (-1238))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1277 *2)) (-4 *2 (-1238))))) 
 (((*1 *2 *1 *3 *3 *2)
-  (-12 (-5 *3 (-558)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1246)) (-4 *4 (-385 *2))
+  (-12 (-5 *3 (-558)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1238)) (-4 *4 (-385 *2))
    (-4 *5 (-385 *2))))
  ((*1 *2 *1 *3 *3)
   (-12 (-5 *3 (-558)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-385 *2))
-   (-4 *5 (-385 *2)) (-4 *2 (-1246))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "right") (-4 *1 (-121 *3)) (-4 *3 (-1246))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "left") (-4 *1 (-121 *3)) (-4 *3 (-1246))))
+   (-4 *5 (-385 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 "right") (-4 *1 (-121 *3)) (-4 *3 (-1238))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 "left") (-4 *1 (-121 *3)) (-4 *3 (-1238))))
  ((*1 *2 *1 *3)
   (-12 (-5 *3 (-661 (-558))) (-4 *2 (-175)) (-5 *1 (-137 *4 *5 *2))
    (-14 *4 (-558)) (-14 *5 (-791))))
@@ -2298,358 +2297,358 @@
  ((*1 *2 *1)
   (-12 (-4 *2 (-175)) (-5 *1 (-137 *3 *4 *2)) (-14 *3 (-558)) (-14 *4 (-791))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1206)) (-5 *2 (-252 (-1188))) (-5 *1 (-217 *4))
+  (-12 (-5 *3 (-1198)) (-5 *2 (-252 (-1180))) (-5 *1 (-217 *4))
    (-4 *4
-    (-13 (-869)
-     (-10 -8 (-15 -4307 ((-1188) $ *3)) (-15 -4124 ((-1302) $))
-      (-15 -2183 ((-1302) $)))))))
+    (-13 (-861)
+     (-10 -8 (-15 -4230 ((-1180) $ *3)) (-15 -4047 ((-1294) $))
+      (-15 -2175 ((-1294) $)))))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1018)) (-5 *1 (-217 *3))
+  (-12 (-5 *2 (-1010)) (-5 *1 (-217 *3))
    (-4 *3
-    (-13 (-869)
-     (-10 -8 (-15 -4307 ((-1188) $ (-1206))) (-15 -4124 ((-1302) $))
-      (-15 -2183 ((-1302) $)))))))
+    (-13 (-861)
+     (-10 -8 (-15 -4230 ((-1180) $ (-1198))) (-15 -4047 ((-1294) $))
+      (-15 -2175 ((-1294) $)))))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 "count") (-5 *2 (-791)) (-5 *1 (-252 *4)) (-4 *4 (-869))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-252 *3)) (-4 *3 (-869))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "unique") (-5 *1 (-252 *3)) (-4 *3 (-869))))
- ((*1 *2 *1 *3) (-12 (-4 *1 (-298 *3 *2)) (-4 *3 (-1246)) (-4 *2 (-1246))))
- ((*1 *2 *1 *3 *2) (-12 (-4 *1 (-300 *3 *2)) (-4 *3 (-1130)) (-4 *2 (-1246))))
+  (-12 (-5 *3 "count") (-5 *2 (-791)) (-5 *1 (-252 *4)) (-4 *4 (-861))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-252 *3)) (-4 *3 (-861))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 "unique") (-5 *1 (-252 *3)) (-4 *3 (-861))))
+ ((*1 *2 *1 *3) (-12 (-4 *1 (-298 *3 *2)) (-4 *3 (-1238)) (-4 *2 (-1238))))
+ ((*1 *2 *1 *3 *2) (-12 (-4 *1 (-300 *3 *2)) (-4 *3 (-1122)) (-4 *2 (-1238))))
  ((*1 *1 *2 *3) (-12 (-5 *2 (-115)) (-5 *3 (-661 *1)) (-4 *1 (-310))))
  ((*1 *1 *2 *1 *1 *1 *1) (-12 (-4 *1 (-310)) (-5 *2 (-115))))
  ((*1 *1 *2 *1 *1 *1) (-12 (-4 *1 (-310)) (-5 *2 (-115))))
  ((*1 *1 *2 *1 *1) (-12 (-4 *1 (-310)) (-5 *2 (-115))))
  ((*1 *1 *2 *1) (-12 (-4 *1 (-310)) (-5 *2 (-115))))
  ((*1 *2 *1 *2 *2)
-  (-12 (-4 *1 (-355 *2 *3 *4)) (-4 *2 (-1251)) (-4 *3 (-1272 *2))
-   (-4 *4 (-1272 (-419 *3)))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1206)) (-5 *2 (-1188)) (-5 *1 (-514))))
- ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-791)) (-5 *1 (-695 *2)) (-4 *2 (-1130))))
+  (-12 (-4 *1 (-355 *2 *3 *4)) (-4 *2 (-1243)) (-4 *3 (-1264 *2))
+   (-4 *4 (-1264 (-419 *3)))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1198)) (-5 *2 (-1180)) (-5 *1 (-514))))
+ ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-791)) (-5 *1 (-695 *2)) (-4 *2 (-1122))))
  ((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-661 (-558))) (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1078))
+  (-12 (-5 *2 (-661 (-558))) (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1070))
    (-4 *4 (-385 *3)) (-4 *5 (-385 *3))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-661 (-885))) (-5 *1 (-885))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-661 (-877))) (-5 *1 (-877))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-115)) (-5 *3 (-661 (-913 *4))) (-5 *1 (-913 *4))
-   (-4 *4 (-1130))))
+  (-12 (-5 *2 (-115)) (-5 *3 (-661 (-905 *4))) (-5 *1 (-905 *4))
+   (-4 *4 (-1122))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-791)) (-5 *2 (-929 *4)) (-5 *1 (-932 *4)) (-4 *4 (-1130))))
- ((*1 *2 *1 *3) (-12 (-5 *3 "value") (-4 *1 (-1039 *2)) (-4 *2 (-1246))))
- ((*1 *2 *1) (-12 (-5 *1 (-1055 *2)) (-4 *2 (-1246))))
+  (-12 (-5 *3 (-791)) (-5 *2 (-921 *4)) (-5 *1 (-924 *4)) (-4 *4 (-1122))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 "value") (-4 *1 (-1031 *2)) (-4 *2 (-1238))))
+ ((*1 *2 *1) (-12 (-5 *1 (-1047 *2)) (-4 *2 (-1238))))
  ((*1 *2 *1 *3 *3 *2)
-  (-12 (-5 *3 (-558)) (-4 *1 (-1082 *4 *5 *2 *6 *7)) (-4 *2 (-1078))
+  (-12 (-5 *3 (-558)) (-4 *1 (-1074 *4 *5 *2 *6 *7)) (-4 *2 (-1070))
    (-4 *6 (-245 *5 *2)) (-4 *7 (-245 *4 *2))))
  ((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-558)) (-4 *1 (-1082 *4 *5 *2 *6 *7)) (-4 *6 (-245 *5 *2))
-   (-4 *7 (-245 *4 *2)) (-4 *2 (-1078))))
+  (-12 (-5 *3 (-558)) (-4 *1 (-1074 *4 *5 *2 *6 *7)) (-4 *6 (-245 *5 *2))
+   (-4 *7 (-245 *4 *2)) (-4 *2 (-1070))))
  ((*1 *2 *1 *2 *3)
-  (-12 (-5 *3 (-946)) (-4 *4 (-1130))
-   (-4 *5 (-13 (-1078) (-909 *4) (-631 (-913 *4)))) (-5 *1 (-1104 *4 *5 *2))
-   (-4 *2 (-13 (-433 *5) (-909 *4) (-631 (-913 *4))))))
+  (-12 (-5 *3 (-938)) (-4 *4 (-1122))
+   (-4 *5 (-13 (-1070) (-901 *4) (-631 (-905 *4)))) (-5 *1 (-1096 *4 *5 *2))
+   (-4 *2 (-13 (-433 *5) (-901 *4) (-631 (-905 *4))))))
  ((*1 *2 *1 *2 *3)
-  (-12 (-5 *3 (-946)) (-4 *4 (-1130))
-   (-4 *5 (-13 (-1078) (-909 *4) (-631 (-913 *4)))) (-5 *1 (-1106 *4 *5 *2))
-   (-4 *2 (-13 (-433 *5) (-909 *4) (-631 (-913 *4))))))
- ((*1 *1 *1 *1) (-4 *1 (-1173)))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-661 (-885))) (-5 *1 (-1206))))
+  (-12 (-5 *3 (-938)) (-4 *4 (-1122))
+   (-4 *5 (-13 (-1070) (-901 *4) (-631 (-905 *4)))) (-5 *1 (-1098 *4 *5 *2))
+   (-4 *2 (-13 (-433 *5) (-901 *4) (-631 (-905 *4))))))
+ ((*1 *1 *1 *1) (-4 *1 (-1165)))
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-419 (-558))) (-4 *1 (-1279 *3)) (-4 *3 (-1078))))) 
+  (-12 (-5 *2 (-938)) (-4 *1 (-1267 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-814))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-419 (-558))) (-4 *1 (-1271 *3)) (-4 *3 (-1070))))) 
 (((*1 *2 *2)
   (-12
    (-5 *2
     (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4)
      (|:| |xpnt| (-558))))
-   (-4 *4 (-13 (-1272 *3) (-569) (-10 -8 (-15 -3639 ($ $ $))))) (-4 *3 (-569))
-   (-5 *1 (-1276 *3 *4))))) 
+   (-4 *4 (-13 (-1264 *3) (-569) (-10 -8 (-15 -3562 ($ $ $))))) (-4 *3 (-569))
+   (-5 *1 (-1268 *3 *4))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-977 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-969 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-464))))
  ((*1 *2 *3 *1)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *3 (-1094 *4 *5 *6))
-   (-5 *2 (-661 (-2 (|:| |val| *3) (|:| -1751 *1))))
-   (-4 *1 (-1100 *4 *5 *6 *3))))
- ((*1 *1 *1) (-4 *1 (-1251)))
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *3 (-1086 *4 *5 *6))
+   (-5 *2 (-661 (-2 (|:| |val| *3) (|:| -1743 *1))))
+   (-4 *1 (-1092 *4 *5 *6 *3))))
+ ((*1 *1 *1) (-4 *1 (-1243)))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-1276 *3 *2))
-   (-4 *2 (-13 (-1272 *3) (-569) (-10 -8 (-15 -3639 ($ $ $)))))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-1268 *3 *2))
+   (-4 *2 (-13 (-1264 *3) (-569) (-10 -8 (-15 -3562 ($ $ $)))))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-335 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-133))
-   (-5 *2 (-661 (-2 (|:| |gen| *3) (|:| -4450 *4))))))
+  (-12 (-4 *1 (-335 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-133))
+   (-5 *2 (-661 (-2 (|:| |gen| *3) (|:| -4373 *4))))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-521 *3 *4)) (-4 *3 (-102)) (-4 *4 (-872))
-   (-5 *2 (-661 (-895 *4 *3)))))
+  (-12 (-4 *1 (-521 *3 *4)) (-4 *3 (-102)) (-4 *4 (-864))
+   (-5 *2 (-661 (-887 *4 *3)))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-661 (-2 (|:| -4461 *3) (|:| -4445 *4)))) (-5 *1 (-755 *3 *4))
-   (-4 *3 (-1078)) (-4 *4 (-746))))
+  (-12 (-5 *2 (-661 (-2 (|:| -4384 *3) (|:| -4368 *4)))) (-5 *1 (-755 *3 *4))
+   (-4 *3 (-1070)) (-4 *4 (-746))))
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-  (-12 (-4 *1 (-1275 *3 *4)) (-4 *3 (-1078)) (-4 *4 (-814))
-   (-5 *2 (-1184 (-2 (|:| |k| *4) (|:| |c| *3))))))) 
-(((*1 *2 *2 *3 *2) (-12 (-5 *2 (-1188)) (-5 *3 (-558)) (-5 *1 (-248))))
+  (-12 (-4 *1 (-1267 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-814))
+   (-5 *2 (-1176 (-2 (|:| |k| *4) (|:| |c| *3))))))) 
+(((*1 *2 *2 *3 *2) (-12 (-5 *2 (-1180)) (-5 *3 (-558)) (-5 *1 (-248))))
  ((*1 *2 *2 *3 *4)
-  (-12 (-5 *2 (-661 (-1188))) (-5 *3 (-558)) (-5 *4 (-1188)) (-5 *1 (-248))))
- ((*1 *1 *1) (-5 *1 (-885)))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-885))))
- ((*1 *2 *1) (-12 (-4 *1 (-1275 *2 *3)) (-4 *3 (-814)) (-4 *2 (-1078))))) 
+  (-12 (-5 *2 (-661 (-1180))) (-5 *3 (-558)) (-5 *4 (-1180)) (-5 *1 (-248))))
+ ((*1 *1 *1) (-5 *1 (-877)))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-877))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1267 *2 *3)) (-4 *3 (-814)) (-4 *2 (-1070))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1078)) (-4 *4 (-869))
+  (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-861))
    (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-791))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1078)) (-4 *3 (-869))
+  (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1070)) (-4 *3 (-861))
    (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-791))))
- ((*1 *2 *1) (-12 (-4 *1 (-277 *3)) (-4 *3 (-869)) (-5 *2 (-791))))
- ((*1 *2 *1) (-12 (-4 *1 (-363)) (-5 *2 (-946))))
+ ((*1 *2 *1) (-12 (-4 *1 (-277 *3)) (-4 *3 (-861)) (-5 *2 (-791))))
+ ((*1 *2 *1) (-12 (-4 *1 (-363)) (-5 *2 (-938))))
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   (-12 (-5 *3 (-346 *4 *5 *6 *7)) (-4 *4 (-13 (-381) (-376)))
-   (-4 *5 (-1272 *4)) (-4 *6 (-1272 (-419 *5))) (-4 *7 (-355 *4 *5 *6))
+   (-4 *5 (-1264 *4)) (-4 *6 (-1264 (-419 *5))) (-4 *7 (-355 *4 *5 *6))
    (-5 *2 (-791)) (-5 *1 (-406 *4 *5 *6 *7))))
- ((*1 *2 *1) (-12 (-4 *1 (-414)) (-5 *2 (-853 (-946)))))
+ ((*1 *2 *1) (-12 (-4 *1 (-414)) (-5 *2 (-845 (-938)))))
  ((*1 *2 *1) (-12 (-4 *1 (-416)) (-5 *2 (-558))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-608 *3)) (-4 *3 (-1078))))
- ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-608 *3)) (-4 *3 (-1078))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-608 *3)) (-4 *3 (-1070))))
+ ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-608 *3)) (-4 *3 (-1070))))
  ((*1 *2 *1)
-  (-12 (-4 *3 (-569)) (-5 *2 (-558)) (-5 *1 (-640 *3 *4)) (-4 *4 (-1272 *3))))
+  (-12 (-4 *3 (-569)) (-5 *2 (-558)) (-5 *1 (-640 *3 *4)) (-4 *4 (-1264 *3))))
  ((*1 *2 *1 *3 *2)
-  (-12 (-5 *2 (-791)) (-4 *1 (-760 *4 *3)) (-4 *4 (-1078)) (-4 *3 (-869))))
+  (-12 (-5 *2 (-791)) (-4 *1 (-760 *4 *3)) (-4 *4 (-1070)) (-4 *3 (-861))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *1 (-760 *4 *3)) (-4 *4 (-1078)) (-4 *3 (-869)) (-5 *2 (-791))))
- ((*1 *2 *1) (-12 (-4 *1 (-892 *3)) (-5 *2 (-791))))
- ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-929 *3)) (-4 *3 (-1130))))
- ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-932 *3)) (-4 *3 (-1130))))
+  (-12 (-4 *1 (-760 *4 *3)) (-4 *4 (-1070)) (-4 *3 (-861)) (-5 *2 (-791))))
+ ((*1 *2 *1) (-12 (-4 *1 (-884 *3)) (-5 *2 (-791))))
+ ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-921 *3)) (-4 *3 (-1122))))
+ ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-924 *3)) (-4 *3 (-1122))))
  ((*1 *2 *3)
   (|partial| -12 (-5 *3 (-346 *5 *6 *7 *8)) (-4 *5 (-433 *4))
-   (-4 *6 (-1272 *5)) (-4 *7 (-1272 (-419 *6))) (-4 *8 (-355 *5 *6 *7))
-   (-4 *4 (-13 (-569) (-1067 (-558)))) (-5 *2 (-791))
-   (-5 *1 (-938 *4 *5 *6 *7 *8))))
+   (-4 *6 (-1264 *5)) (-4 *7 (-1264 (-419 *6))) (-4 *8 (-355 *5 *6 *7))
+   (-4 *4 (-13 (-569) (-1059 (-558)))) (-5 *2 (-791))
+   (-5 *1 (-930 *4 *5 *6 *7 *8))))
  ((*1 *2 *3)
   (|partial| -12 (-5 *3 (-346 (-419 (-558)) *4 *5 *6))
-   (-4 *4 (-1272 (-419 (-558)))) (-4 *5 (-1272 (-419 *4)))
-   (-4 *6 (-355 (-419 (-558)) *4 *5)) (-5 *2 (-791)) (-5 *1 (-939 *4 *5 *6))))
+   (-4 *4 (-1264 (-419 (-558)))) (-4 *5 (-1264 (-419 *4)))
+   (-4 *6 (-355 (-419 (-558)) *4 *5)) (-5 *2 (-791)) (-5 *1 (-931 *4 *5 *6))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-346 *6 *7 *4 *8)) (-5 *5 (-1 *9 *6)) (-4 *6 (-376))
-   (-4 *7 (-1272 *6)) (-4 *4 (-1272 (-419 *7))) (-4 *8 (-355 *6 *7 *4))
-   (-4 *9 (-13 (-381) (-376))) (-5 *2 (-791)) (-5 *1 (-1047 *6 *7 *4 *8 *9))))
+   (-4 *7 (-1264 *6)) (-4 *4 (-1264 (-419 *7))) (-4 *8 (-355 *6 *7 *4))
+   (-4 *9 (-13 (-381) (-376))) (-5 *2 (-791)) (-5 *1 (-1039 *6 *7 *4 *8 *9))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1272 *3)) (-4 *3 (-1078)) (-4 *3 (-569)) (-5 *2 (-791))))
- ((*1 *2 *1 *2) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1078)) (-4 *2 (-814))))
- ((*1 *2 *1) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1078)) (-4 *2 (-814))))) 
-(((*1 *1 *1) (-4 *1 (-1089)))
- ((*1 *1 *1 *2 *2) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1078)) (-4 *2 (-814))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1078)) (-4 *2 (-814))))) 
+  (-12 (-4 *1 (-1264 *3)) (-4 *3 (-1070)) (-4 *3 (-569)) (-5 *2 (-791))))
+ ((*1 *2 *1 *2) (-12 (-4 *1 (-1267 *3 *2)) (-4 *3 (-1070)) (-4 *2 (-814))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1267 *3 *2)) (-4 *3 (-1070)) (-4 *2 (-814))))) 
+(((*1 *1 *1) (-4 *1 (-1081)))
+ ((*1 *1 *1 *2 *2) (-12 (-4 *1 (-1267 *3 *2)) (-4 *3 (-1070)) (-4 *2 (-814))))
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-1267 *3 *2)) (-4 *3 (-1070)) (-4 *2 (-814))))) 
 (((*1 *2 *1 *3)
   (-12 (-5 *2 (-419 (-558))) (-5 *1 (-119 *4)) (-14 *4 *3) (-5 *3 (-558))))
- ((*1 *2 *1 *2) (-12 (-4 *1 (-892 *3)) (-5 *2 (-558))))
+ ((*1 *2 *1 *2) (-12 (-4 *1 (-884 *3)) (-5 *2 (-558))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *2 (-419 (-558))) (-5 *1 (-893 *4)) (-14 *4 *3) (-5 *3 (-558))))
+  (-12 (-5 *2 (-419 (-558))) (-5 *1 (-885 *4)) (-14 *4 *3) (-5 *3 (-558))))
  ((*1 *2 *1 *3)
-  (-12 (-14 *4 *3) (-5 *2 (-419 (-558))) (-5 *1 (-894 *4 *5)) (-5 *3 (-558))
-   (-4 *5 (-892 *4))))
- ((*1 *2 *1 *1) (-12 (-4 *1 (-1041)) (-5 *2 (-419 (-558)))))
+  (-12 (-14 *4 *3) (-5 *2 (-419 (-558))) (-5 *1 (-886 *4 *5)) (-5 *3 (-558))
+   (-4 *5 (-884 *4))))
+ ((*1 *2 *1 *1) (-12 (-4 *1 (-1033)) (-5 *2 (-419 (-558)))))
  ((*1 *2 *3 *1 *2)
-  (-12 (-4 *1 (-1097 *2 *3)) (-4 *2 (-13 (-868) (-376))) (-4 *3 (-1272 *2))))
+  (-12 (-4 *1 (-1089 *2 *3)) (-4 *2 (-13 (-860) (-376))) (-4 *3 (-1264 *2))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *1 (-1275 *2 *3)) (-4 *3 (-814)) (|has| *2 (-15 ** (*2 *2 *3)))
-   (|has| *2 (-15 -4453 (*2 (-1206)))) (-4 *2 (-1078))))) 
+  (-12 (-4 *1 (-1267 *2 *3)) (-4 *3 (-814)) (|has| *2 (-15 ** (*2 *2 *3)))
+   (|has| *2 (-15 -4376 (*2 (-1198)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-177 *3)) (-4 *3 (-319))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-694 *3)) (-4 *3 (-1246))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-694 *3)) (-4 *3 (-1238))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-791)) (-4 *1 (-760 *3 *4)) (-4 *3 (-1078)) (-4 *4 (-869))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-892 *3)) (-5 *2 (-558))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *1 (-1009 *3)) (-4 *3 (-1078))))
+  (-12 (-5 *2 (-791)) (-4 *1 (-760 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-861))))
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-884 *3)) (-5 *2 (-558))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *1 (-1001 *3)) (-4 *3 (-1070))))
  ((*1 *2 *3 *2)
-  (-12 (-5 *2 (-661 *1)) (-5 *3 (-661 *7)) (-4 *1 (-1100 *4 *5 *6 *7))
-   (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))))
+  (-12 (-5 *2 (-661 *1)) (-5 *3 (-661 *7)) (-4 *1 (-1092 *4 *5 *6 *7))
+   (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))))
  ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-661 *1)) (-4 *1 (-1100 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-661 *1)) (-4 *1 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *2)
-  (-12 (-5 *2 (-661 *1)) (-4 *1 (-1100 *4 *5 *6 *3)) (-4 *4 (-464))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-4 *3 (-1094 *4 *5 *6))))
+  (-12 (-5 *2 (-661 *1)) (-4 *1 (-1092 *4 *5 *6 *3)) (-4 *4 (-464))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-4 *3 (-1086 *4 *5 *6))))
  ((*1 *2 *3 *1)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *3 (-1094 *4 *5 *6))
-   (-5 *2 (-661 *1)) (-4 *1 (-1100 *4 *5 *6 *3))))
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *3 (-1086 *4 *5 *6))
+   (-5 *2 (-661 *1)) (-4 *1 (-1092 *4 *5 *6 *3))))
  ((*1 *1 *1 *2)
-  (-12 (-4 *1 (-1241 *3 *4 *5 *2)) (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-869))
-   (-4 *2 (-1094 *3 *4 *5))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1078)) (-4 *2 (-814))))) 
+  (-12 (-4 *1 (-1233 *3 *4 *5 *2)) (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-4 *2 (-1086 *3 *4 *5))))
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-1267 *3 *2)) (-4 *3 (-1070)) (-4 *2 (-814))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *3 (-419 *5)) (-4 *4 (-1251)) (-4 *5 (-1272 *4))
-   (-5 *1 (-150 *4 *5 *2)) (-4 *2 (-1272 *3))))
+  (-12 (-5 *3 (-419 *5)) (-4 *4 (-1243)) (-4 *5 (-1264 *4))
+   (-5 *1 (-150 *4 *5 *2)) (-4 *2 (-1264 *3))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1208 (-419 (-558)))) (-5 *2 (-419 (-558))) (-5 *1 (-193))))
+  (-12 (-5 *3 (-1200 (-419 (-558)))) (-5 *2 (-419 (-558))) (-5 *1 (-193))))
  ((*1 *2 *2 *3 *4)
-  (-12 (-5 *2 (-709 (-326 (-229)))) (-5 *3 (-661 (-1206)))
-   (-5 *4 (-1296 (-326 (-229)))) (-5 *1 (-208))))
+  (-12 (-5 *2 (-709 (-326 (-229)))) (-5 *3 (-661 (-1198)))
+   (-5 *4 (-1288 (-326 (-229)))) (-5 *1 (-208))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-661 (-305 *3))) (-4 *3 (-321 *3)) (-4 *3 (-1130))
-   (-4 *3 (-1246)) (-5 *1 (-305 *3))))
+  (-12 (-5 *2 (-661 (-305 *3))) (-4 *3 (-321 *3)) (-4 *3 (-1122))
+   (-4 *3 (-1238)) (-5 *1 (-305 *3))))
  ((*1 *1 *1 *1)
-  (-12 (-4 *2 (-321 *2)) (-4 *2 (-1130)) (-4 *2 (-1246)) (-5 *1 (-305 *2))))
+  (-12 (-4 *2 (-321 *2)) (-4 *2 (-1122)) (-4 *2 (-1238)) (-5 *1 (-305 *2))))
  ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-115)) (-5 *3 (-1 *1 *1)) (-4 *1 (-310))))
  ((*1 *1 *1 *2 *3)
   (-12 (-5 *2 (-115)) (-5 *3 (-1 *1 (-661 *1))) (-4 *1 (-310))))
@@ -2657,1098 +2656,1098 @@
   (-12 (-5 *2 (-661 (-115))) (-5 *3 (-661 (-1 *1 (-661 *1)))) (-4 *1 (-310))))
  ((*1 *1 *1 *2 *3)
   (-12 (-5 *2 (-661 (-115))) (-5 *3 (-661 (-1 *1 *1))) (-4 *1 (-310))))
- ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1206)) (-5 *3 (-1 *1 *1)) (-4 *1 (-310))))
+ ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1198)) (-5 *3 (-1 *1 *1)) (-4 *1 (-310))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-1206)) (-5 *3 (-1 *1 (-661 *1))) (-4 *1 (-310))))
+  (-12 (-5 *2 (-1198)) (-5 *3 (-1 *1 (-661 *1))) (-4 *1 (-310))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-661 (-1206))) (-5 *3 (-661 (-1 *1 (-661 *1)))) (-4 *1 (-310))))
+  (-12 (-5 *2 (-661 (-1198))) (-5 *3 (-661 (-1 *1 (-661 *1)))) (-4 *1 (-310))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-661 (-1206))) (-5 *3 (-661 (-1 *1 *1))) (-4 *1 (-310))))
+  (-12 (-5 *2 (-661 (-1198))) (-5 *3 (-661 (-1 *1 *1))) (-4 *1 (-310))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-661 (-305 *3))) (-4 *1 (-321 *3)) (-4 *3 (-1130))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-305 *3)) (-4 *1 (-321 *3)) (-4 *3 (-1130))))
+  (-12 (-5 *2 (-661 (-305 *3))) (-4 *1 (-321 *3)) (-4 *3 (-1122))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-305 *3)) (-4 *1 (-321 *3)) (-4 *3 (-1122))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *2 (-558))) (-5 *4 (-1208 (-419 (-558)))) (-5 *1 (-322 *2))
+  (-12 (-5 *3 (-1 *2 (-558))) (-5 *4 (-1200 (-419 (-558)))) (-5 *1 (-322 *2))
    (-4 *2 (-38 (-419 (-558))))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-661 *4)) (-5 *3 (-661 *1)) (-4 *1 (-387 *4 *5)) (-4 *4 (-869))
+  (-12 (-5 *2 (-661 *4)) (-5 *3 (-661 *1)) (-4 *1 (-387 *4 *5)) (-4 *4 (-861))
    (-4 *5 (-175))))
- ((*1 *1 *1 *2 *1) (-12 (-4 *1 (-387 *2 *3)) (-4 *2 (-869)) (-4 *3 (-175))))
+ ((*1 *1 *1 *2 *1) (-12 (-4 *1 (-387 *2 *3)) (-4 *2 (-861)) (-4 *3 (-175))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-1206)) (-5 *3 (-791)) (-5 *4 (-1 *1 *1)) (-4 *1 (-433 *5))
-   (-4 *5 (-1130)) (-4 *5 (-1078))))
+  (-12 (-5 *2 (-1198)) (-5 *3 (-791)) (-5 *4 (-1 *1 *1)) (-4 *1 (-433 *5))
+   (-4 *5 (-1122)) (-4 *5 (-1070))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-1206)) (-5 *3 (-791)) (-5 *4 (-1 *1 (-661 *1)))
-   (-4 *1 (-433 *5)) (-4 *5 (-1130)) (-4 *5 (-1078))))
+  (-12 (-5 *2 (-1198)) (-5 *3 (-791)) (-5 *4 (-1 *1 (-661 *1)))
+   (-4 *1 (-433 *5)) (-4 *5 (-1122)) (-4 *5 (-1070))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-661 (-1206))) (-5 *3 (-661 (-791)))
-   (-5 *4 (-661 (-1 *1 (-661 *1)))) (-4 *1 (-433 *5)) (-4 *5 (-1130))
-   (-4 *5 (-1078))))
+  (-12 (-5 *2 (-661 (-1198))) (-5 *3 (-661 (-791)))
+   (-5 *4 (-661 (-1 *1 (-661 *1)))) (-4 *1 (-433 *5)) (-4 *5 (-1122))
+   (-4 *5 (-1070))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-661 (-1206))) (-5 *3 (-661 (-791))) (-5 *4 (-661 (-1 *1 *1)))
-   (-4 *1 (-433 *5)) (-4 *5 (-1130)) (-4 *5 (-1078))))
+  (-12 (-5 *2 (-661 (-1198))) (-5 *3 (-661 (-791))) (-5 *4 (-661 (-1 *1 *1)))
+   (-4 *1 (-433 *5)) (-4 *5 (-1122)) (-4 *5 (-1070))))
  ((*1 *1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-661 (-115))) (-5 *3 (-661 *1)) (-5 *4 (-1206))
-   (-4 *1 (-433 *5)) (-4 *5 (-1130)) (-4 *5 (-631 (-547)))))
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   (-12 (-5 *3 (-1 *6 (-558))) (-5 *4 (-305 *6))
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    (-5 *1 (-471 *5 *6))))
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-   (-4 *6 (-13 (-569) (-1067 (-558)) (-658 (-558)))) (-5 *2 (-51))
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    (-5 *1 (-471 *6 *3))))
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-   (-4 *6 (-13 (-569) (-1067 (-558)) (-658 (-558)))) (-5 *2 (-51))
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    (-5 *1 (-471 *6 *7))))
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-  (-12 (-5 *4 (-1206)) (-5 *5 (-305 *3)) (-5 *6 (-1263 (-791)))
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-   (-4 *7 (-13 (-569) (-1067 (-558)) (-658 (-558)))) (-5 *2 (-51))
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+   (-4 *3 (-13 (-27) (-1224) (-433 *7)))
+   (-4 *7 (-13 (-569) (-1059 (-558)) (-658 (-558)))) (-5 *2 (-51))
    (-5 *1 (-471 *7 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-1260 *3 *2)) (-4 *3 (-1078)) (-4 *2 (-1289 *3))))) 
+ ((*1 *2 *1) (-12 (-4 *1 (-1252 *3 *2)) (-4 *3 (-1070)) (-4 *2 (-1281 *3))))) 
 (((*1 *2 *1)
-  (|partial| -12 (-4 *1 (-1260 *3 *2)) (-4 *3 (-1078)) (-4 *2 (-1289 *3))))) 
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 (((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-558)) (-4 *1 (-1258 *4)) (-4 *4 (-1078)) (-4 *4 (-569))
-   (-5 *2 (-419 (-973 *4)))))
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+   (-5 *2 (-419 (-965 *4)))))
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-  (-12 (-5 *3 (-558)) (-4 *1 (-1258 *4)) (-4 *4 (-1078)) (-4 *4 (-569))
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+  (-12 (-5 *3 (-558)) (-4 *1 (-1250 *4)) (-4 *4 (-1070)) (-4 *4 (-569))
+   (-5 *2 (-419 (-965 *4)))))) 
 (((*1 *1 *1 *1) (-5 *1 (-130)))
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- ((*1 *1 *1 *1) (-5 *1 (-1252))) ((*1 *1 *1 *1) (-5 *1 (-1253)))
- ((*1 *1 *1 *1) (-5 *1 (-1254))) ((*1 *1 *1 *1) (-5 *1 (-1255)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1205 *2)) (-14 *2 (-938))))
+ ((*1 *1 *1 *1) (-5 *1 (-1244))) ((*1 *1 *1 *1) (-5 *1 (-1245)))
+ ((*1 *1 *1 *1) (-5 *1 (-1246))) ((*1 *1 *1 *1) (-5 *1 (-1247)))) 
 (((*1 *1 *1 *1) (-5 *1 (-130)))
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- ((*1 *1 *1 *1) (-5 *1 (-1254))) ((*1 *1 *1 *1) (-5 *1 (-1255)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1205 *2)) (-14 *2 (-938))))
+ ((*1 *1 *1 *1) (-5 *1 (-1244))) ((*1 *1 *1 *1) (-5 *1 (-1245)))
+ ((*1 *1 *1 *1) (-5 *1 (-1246))) ((*1 *1 *1 *1) (-5 *1 (-1247)))) 
 (((*1 *1) (-4 *1 (-23))) ((*1 *1) (-4 *1 (-34))) ((*1 *1) (-5 *1 (-130)))
  ((*1 *1)
   (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-558)) (-14 *3 (-791)) (-4 *4 (-175))))
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- ((*1 *1) (-5 *1 (-1253))) ((*1 *1) (-5 *1 (-1254))) ((*1 *1) (-5 *1 (-1255)))) 
+ ((*1 *1) (-5 *1 (-562))) ((*1 *1) (-4 *1 (-746))) ((*1 *1) (-5 *1 (-1198)))
+ ((*1 *1) (-12 (-5 *1 (-1204 *2)) (-14 *2 (-938))))
+ ((*1 *1) (-12 (-5 *1 (-1205 *2)) (-14 *2 (-938)))) ((*1 *1) (-5 *1 (-1244)))
+ ((*1 *1) (-5 *1 (-1245))) ((*1 *1) (-5 *1 (-1246))) ((*1 *1) (-5 *1 (-1247)))) 
 (((*1 *2 *3) (-12 (-5 *3 (-171 (-558))) (-5 *2 (-114)) (-5 *1 (-458))))
  ((*1 *2 *3)
   (-12
    (-5 *3
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-   (-14 *4 (-661 (-1206))) (-14 *5 (-791)) (-5 *2 (-114))
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+   (-14 *4 (-661 (-1198))) (-14 *5 (-791)) (-5 *2 (-114))
    (-5 *1 (-517 *4 *5))))
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- ((*1 *2 *1) (-12 (-4 *1 (-1251)) (-5 *2 (-114))))) 
-(((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-1249))))) 
+ ((*1 *2 *3) (-12 (-5 *2 (-114)) (-5 *1 (-981 *3)) (-4 *3 (-557))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1243)) (-5 *2 (-114))))) 
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 (((*1 *2)
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- ((*1 *2 *3 *3) (-12 (-5 *3 (-661 (-1206))) (-5 *2 (-1302)) (-5 *1 (-1249))))) 
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+   (-5 *1 (-1241))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-661 (-1198))) (-5 *2 (-1294)) (-5 *1 (-1241))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-661 (-1198))) (-5 *2 (-1294)) (-5 *1 (-1241))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-791)) (-4 *1 (-1179 *4)) (-4 *4 (-1246)) (-5 *2 (-114))))
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  ((*1 *2 *3 *3)
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 (((*1 *2 *3 *4)
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-   (-4 *2 (-1130))))
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 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-791)) (-4 *1 (-1179 *4)) (-4 *4 (-1246)) (-5 *2 (-114))))
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-  (|partial| -12 (-5 *2 (-114)) (-5 *1 (-1248 *3)) (-4 *3 (-1130))))
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-   (-5 *1 (-1248 *3))))) 
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 (((*1 *2)
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 (((*1 *2 *3)
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 (((*1 *2 *3 *4)
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+   (-5 *3 (-1192 (-1192 *4)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-363)) (-5 *2 (-417 (-1200 (-1200 *4)))) (-5 *1 (-1245 *4))
-   (-5 *3 (-1200 (-1200 *4)))))) 
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- ((*1 *2 *1 *3) (-12 (-5 *3 (-791)) (-5 *1 (-1244 *2)) (-4 *2 (-1246))))) 
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+   (-4 *3 (-861)) (-4 *2 (-1086 *4 *5 *3))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-791)) (-5 *1 (-1236 *2)) (-4 *2 (-1238))))) 
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 (((*1 *1 *2)
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  ((*1 *1 *2)
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    (-14 *6
-    (-1 (-114) (-2 (|:| -2639 *2) (|:| -2640 *5))
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-   (-4 *7 (-977 *4 *5 (-886 *3)))))
- ((*1 *2 *2) (-12 (-5 *2 (-970 (-229))) (-5 *1 (-1243))))) 
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+     (-2 (|:| -2631 *2) (|:| -2632 *5))))
+   (-5 *1 (-473 *3 *4 *2 *5 *6 *7)) (-4 *2 (-861))
+   (-4 *7 (-969 *4 *5 (-878 *3)))))
+ ((*1 *2 *2) (-12 (-5 *2 (-962 (-229))) (-5 *1 (-1235))))) 
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-  (-12 (-5 *3 (-970 (-229))) (-5 *4 (-896)) (-5 *2 (-1302)) (-5 *1 (-480))))
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+ ((*1 *1 *1 *2) (-12 (-5 *2 (-791)) (-4 *1 (-1155 *3)) (-4 *3 (-1070))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *1 (-1155 *3)) (-4 *3 (-1070))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-962 *3)) (-4 *1 (-1155 *3)) (-4 *3 (-1070))))
  ((*1 *2 *3 *3 *3 *3)
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+  (-12 (-5 *2 (-962 (-229))) (-5 *1 (-1235)) (-5 *3 (-229))))) 
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-   (-4 *3 (-1003))))
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+   (-4 *3 (-995))))
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 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-174))))
- ((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1242 *3)) (-4 *3 (-1003))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1234 *3)) (-4 *3 (-995))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-661 (-661 (-970 (-229))))) (-5 *1 (-1242 *3)) (-4 *3 (-1003))))) 
-(((*1 *2 *1) (-12 (-5 *1 (-1242 *2)) (-4 *2 (-1003))))) 
+  (-12 (-5 *2 (-661 (-661 (-962 (-229))))) (-5 *1 (-1234 *3)) (-4 *3 (-995))))) 
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 (((*1 *2 *3 *3)
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-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))
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+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1094 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-815)) (-4 *5 (-869))
+  (-12 (-4 *1 (-1086 *3 *4 *5)) (-4 *3 (-1070)) (-4 *4 (-815)) (-4 *5 (-861))
    (-5 *2 (-114))))
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   (|partial| -12 (-5 *4 (-1 (-114) *9)) (-5 *5 (-1 (-114) *9 *9))
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 (((*1 *2 *2 *1)
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+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-51)) (-5 *1 (-1217))))) 
+(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *2 *1) (-12 (-5 *1 (-123 *2)) (-4 *2 (-861))))
+ ((*1 *1 *2 *1) (-12 (-5 *1 (-128 *2)) (-4 *2 (-861))))
+ ((*1 *1 *1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-294 *3)) (-4 *3 (-1238))))
+ ((*1 *1 *2 *1 *3) (-12 (-5 *3 (-558)) (-4 *1 (-294 *2)) (-4 *2 (-1238))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-2
-     (|:| -4367
-          (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-           (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+     (|:| -4290
+          (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+           (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
            (|:| |relerr| (-229))))
-     (|:| -2294
+     (|:| -2286
           (-2
            (|:| |endPointContinuity|
                 (-3 (|:| |continuous| "Continuous at the end points")
@@ -3761,1159 +3760,1159 @@
                  (|:| |notEvaluated|
                       "End point continuity not yet evaluated")))
            (|:| |singularitiesStream|
-                (-3 (|:| |str| (-1184 (-229)))
+                (-3 (|:| |str| (-1176 (-229)))
                  (|:| |notEvaluated|
                       "Internal singularities not yet evaluated")))
-           (|:| -1646
+           (|:| -1638
                 (-3 (|:| |finite| "The range is finite")
                  (|:| |lowerInfinite| "The bottom of range is infinite")
                  (|:| |upperInfinite| "The top of range is infinite")
                  (|:| |bothInfinite| "Both top and bottom points are infinite")
                  (|:| |notEvaluated| "Range not yet evaluated")))))))
    (-5 *1 (-572))))
- ((*1 *1 *2 *1 *3) (-12 (-5 *3 (-791)) (-4 *1 (-715 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *2 *1 *3) (-12 (-5 *3 (-791)) (-4 *1 (-715 *2)) (-4 *2 (-1122))))
  ((*1 *1 *2)
   (-12
    (-5 *2
     (-2
-     (|:| -4367
+     (|:| -4290
           (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-           (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+           (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
            (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
            (|:| |abserr| (-229)) (|:| |relerr| (-229))))
-     (|:| -2294
+     (|:| -2286
           (-2 (|:| |stiffness| (-391)) (|:| |stability| (-391))
            (|:| |expense| (-391)) (|:| |accuracy| (-391))
            (|:| |intermediateResults| (-391))))))
    (-5 *1 (-825))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *2 (-1302)) (-5 *1 (-1224 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+  (-12 (-5 *2 (-1294)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-4 *2 (-1130)) (-5 *1 (-1224 *3 *2)) (-4 *3 (-1130))))) 
+  (|partial| -12 (-4 *2 (-1122)) (-5 *1 (-1216 *3 *2)) (-4 *3 (-1122))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-114)) (-5 *1 (-1224 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-114)) (-5 *1 (-1224 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-114)) (-5 *1 (-1224 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-1302)) (-5 *1 (-1224 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+  (-12 (-5 *2 (-1294)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-1302)) (-5 *1 (-1224 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+  (-12 (-5 *2 (-1294)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-1224 *4 *5)) (-4 *4 (-1130))
-   (-4 *5 (-1130))))) 
+  (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1216 *4 *5)) (-4 *4 (-1122))
+   (-4 *5 (-1122))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-1224 *4 *5)) (-4 *4 (-1130))
-   (-4 *5 (-1130))))) 
+  (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1216 *4 *5)) (-4 *4 (-1122))
+   (-4 *5 (-1122))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-1302)) (-5 *1 (-1224 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+  (-12 (-5 *2 (-1294)) (-5 *1 (-1216 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-661 (-2 (|:| -4367 *3) (|:| -2294 *4)))) (-4 *3 (-1130))
-   (-4 *4 (-1130)) (-4 *1 (-1223 *3 *4))))
- ((*1 *1) (-12 (-4 *1 (-1223 *2 *3)) (-4 *2 (-1130)) (-4 *3 (-1130))))) 
-(((*1 *2 *2 *3) (-12 (-5 *3 (-558)) (-5 *1 (-1221 *2)) (-4 *2 (-376))))) 
+  (-12 (-5 *2 (-661 (-2 (|:| -4290 *3) (|:| -2286 *4)))) (-4 *3 (-1122))
+   (-4 *4 (-1122)) (-4 *1 (-1215 *3 *4))))
+ ((*1 *1) (-12 (-4 *1 (-1215 *2 *3)) (-4 *2 (-1122)) (-4 *3 (-1122))))) 
+(((*1 *2 *2 *3) (-12 (-5 *3 (-558)) (-5 *1 (-1213 *2)) (-4 *2 (-376))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-946)) (-5 *2 (-1200 *3)) (-5 *1 (-1221 *3)) (-4 *3 (-376))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-661 *2)) (-5 *1 (-1221 *2)) (-4 *2 (-376))))) 
+  (-12 (-5 *4 (-938)) (-5 *2 (-1192 *3)) (-5 *1 (-1213 *3)) (-4 *3 (-376))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-661 *2)) (-5 *1 (-1213 *2)) (-4 *2 (-376))))) 
 (((*1 *2 *2)
   (-12 (-5 *2 (-115)) (-4 *3 (-569)) (-5 *1 (-32 *3 *4)) (-4 *4 (-433 *3))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-1206)) (-5 *3 (-55)) (-5 *1 (-115))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-1206)) (-5 *3 (-791)) (-5 *1 (-115))))
- ((*1 *1 *2) (-12 (-5 *2 (-1206)) (-5 *1 (-115))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-1198)) (-5 *3 (-55)) (-5 *1 (-115))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-1198)) (-5 *3 (-791)) (-5 *1 (-115))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1198)) (-5 *1 (-115))))
  ((*1 *2 *2)
   (-12 (-5 *2 (-115)) (-4 *3 (-569)) (-5 *1 (-160 *3 *4)) (-4 *4 (-433 *3))))
- ((*1 *2 *3) (-12 (-5 *3 (-1206)) (-5 *2 (-115)) (-5 *1 (-165))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1198)) (-5 *2 (-115)) (-5 *1 (-165))))
  ((*1 *2 *2)
   (-12 (-5 *2 (-115)) (-4 *3 (-569)) (-5 *1 (-287 *3 *4))
-   (-4 *4 (-13 (-433 *3) (-1031)))))
+   (-4 *4 (-13 (-433 *3) (-1023)))))
  ((*1 *2 *2) (-12 (-5 *2 (-115)) (-5 *1 (-309 *3)) (-4 *3 (-310))))
  ((*1 *2 *2) (-12 (-4 *1 (-310)) (-5 *2 (-115))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-115)) (-4 *4 (-1130)) (-5 *1 (-432 *3 *4)) (-4 *3 (-433 *4))))
+  (-12 (-5 *2 (-115)) (-4 *4 (-1122)) (-5 *1 (-432 *3 *4)) (-4 *3 (-433 *4))))
  ((*1 *2 *2)
   (-12 (-5 *2 (-115)) (-4 *3 (-569)) (-5 *1 (-443 *3 *4)) (-4 *4 (-433 *3))))
- ((*1 *2 *1) (-12 (-5 *2 (-115)) (-5 *1 (-628 *3)) (-4 *3 (-1130))))
+ ((*1 *2 *1) (-12 (-5 *2 (-115)) (-5 *1 (-628 *3)) (-4 *3 (-1122))))
  ((*1 *2 *2)
   (-12 (-5 *2 (-115)) (-4 *3 (-569)) (-5 *1 (-646 *3 *4))
-   (-4 *4 (-13 (-433 *3) (-1031) (-1232)))))
- ((*1 *2 *1) (-12 (-5 *2 (-1164)) (-5 *1 (-1048))))
- ((*1 *1 *2 *3) (-12 (-5 *3 (-55)) (-5 *1 (-1220 *2)) (-4 *2 (-1130))))) 
+   (-4 *4 (-13 (-433 *3) (-1023) (-1224)))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-1040))))
+ ((*1 *1 *2 *3) (-12 (-5 *3 (-55)) (-5 *1 (-1212 *2)) (-4 *2 (-1122))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-385 *3))
+  (-12 (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1070)) (-4 *4 (-385 *3))
    (-4 *5 (-385 *3)) (-5 *2 (-661 (-661 *3)))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1082 *3 *4 *5 *6 *7)) (-4 *5 (-1078)) (-4 *6 (-245 *4 *5))
+  (-12 (-4 *1 (-1074 *3 *4 *5 *6 *7)) (-4 *5 (-1070)) (-4 *6 (-245 *4 *5))
    (-4 *7 (-245 *3 *5)) (-5 *2 (-661 (-661 *5)))))
- ((*1 *2 *1) (-12 (-5 *2 (-661 (-661 *3))) (-5 *1 (-1219 *3)) (-4 *3 (-1130))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 (-661 *3))) (-4 *3 (-1130)) (-5 *1 (-1219 *3))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-661 (-661 *3))) (-5 *1 (-1211 *3)) (-4 *3 (-1122))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 (-661 *3))) (-4 *3 (-1122)) (-5 *1 (-1211 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-869))
+  (-12 (-4 *4 (-861))
    (-5 *2
     (-2 (|:| |f1| (-661 *4)) (|:| |f2| (-661 (-661 (-661 *4))))
      (|:| |f3| (-661 (-661 *4))) (|:| |f4| (-661 (-661 (-661 *4))))))
-   (-5 *1 (-1217 *4)) (-5 *3 (-661 (-661 (-661 *4))))))) 
+   (-5 *1 (-1209 *4)) (-5 *3 (-661 (-661 (-661 *4))))))) 
 (((*1 *2 *3 *4 *5 *4 *4 *4)
-  (-12 (-4 *6 (-869)) (-5 *3 (-661 *6)) (-5 *5 (-661 *3))
+  (-12 (-4 *6 (-861)) (-5 *3 (-661 *6)) (-5 *5 (-661 *3))
    (-5 *2
     (-2 (|:| |f1| *3) (|:| |f2| (-661 *5)) (|:| |f3| *5) (|:| |f4| (-661 *5))))
-   (-5 *1 (-1217 *6)) (-5 *4 (-661 *5))))) 
+   (-5 *1 (-1209 *6)) (-5 *4 (-661 *5))))) 
 (((*1 *2 *2)
   (|partial| -12 (-4 *3 (-376)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3))
    (-5 *1 (-533 *3 *4 *5 *2)) (-4 *2 (-706 *3 *4 *5))))
  ((*1 *2 *3)
   (|partial| -12 (-4 *4 (-569)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))
-   (-4 *7 (-1020 *4)) (-4 *2 (-706 *7 *8 *9))
+   (-4 *7 (-1012 *4)) (-4 *2 (-706 *7 *8 *9))
    (-5 *1 (-534 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-706 *4 *5 *6))
    (-4 *8 (-385 *7)) (-4 *9 (-385 *7))))
  ((*1 *1 *1)
-  (|partial| -12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-385 *2))
+  (|partial| -12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-385 *2))
    (-4 *4 (-385 *2)) (-4 *2 (-376))))
  ((*1 *2 *2)
   (|partial| -12 (-4 *3 (-376)) (-4 *3 (-175)) (-4 *4 (-385 *3))
    (-4 *5 (-385 *3)) (-5 *1 (-708 *3 *4 *5 *2)) (-4 *2 (-706 *3 *4 *5))))
- ((*1 *1 *1) (|partial| -12 (-5 *1 (-709 *2)) (-4 *2 (-376)) (-4 *2 (-1078))))
+ ((*1 *1 *1) (|partial| -12 (-5 *1 (-709 *2)) (-4 *2 (-376)) (-4 *2 (-1070))))
  ((*1 *1 *1)
-  (|partial| -12 (-4 *1 (-1152 *2 *3 *4 *5)) (-4 *3 (-1078))
+  (|partial| -12 (-4 *1 (-1144 *2 *3 *4 *5)) (-4 *3 (-1070))
    (-4 *4 (-245 *2 *3)) (-4 *5 (-245 *2 *3)) (-4 *3 (-376))))
- ((*1 *2 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-869)) (-5 *1 (-1217 *3))))) 
+ ((*1 *2 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-861)) (-5 *1 (-1209 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-869)) (-5 *2 (-661 (-661 *4))) (-5 *1 (-1217 *4))
+  (-12 (-4 *4 (-861)) (-5 *2 (-661 (-661 *4))) (-5 *1 (-1209 *4))
    (-5 *3 (-661 *4))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-661 (-661 *3))) (-4 *3 (-869)) (-5 *1 (-1217 *3))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-661 (-661 *3))) (-4 *3 (-861)) (-5 *1 (-1209 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-869)) (-5 *2 (-1219 (-661 *4))) (-5 *1 (-1217 *4))
+  (-12 (-4 *4 (-861)) (-5 *2 (-1211 (-661 *4))) (-5 *1 (-1209 *4))
    (-5 *3 (-661 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-869)) (-5 *2 (-661 (-661 (-661 *4)))) (-5 *1 (-1217 *4))
+  (-12 (-4 *4 (-861)) (-5 *2 (-661 (-661 (-661 *4)))) (-5 *1 (-1209 *4))
    (-5 *3 (-661 (-661 *4)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1219 (-661 *4))) (-4 *4 (-869)) (-5 *2 (-661 (-661 *4)))
-   (-5 *1 (-1217 *4))))) 
+  (-12 (-5 *3 (-1211 (-661 *4))) (-4 *4 (-861)) (-5 *2 (-661 (-661 *4)))
+   (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3)
   (-12 (-5 *3 (-661 (-661 (-661 *4)))) (-5 *2 (-661 (-661 *4)))
-   (-5 *1 (-1217 *4)) (-4 *4 (-869))))) 
+   (-5 *1 (-1209 *4)) (-4 *4 (-861))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-661 (-661 (-661 *4)))) (-5 *2 (-661 (-661 *4))) (-4 *4 (-869))
-   (-5 *1 (-1217 *4))))) 
+  (-12 (-5 *3 (-661 (-661 (-661 *4)))) (-5 *2 (-661 (-661 *4))) (-4 *4 (-861))
+   (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *2 (-661 (-661 (-661 *4)))) (-5 *3 (-661 *4)) (-4 *4 (-869))
-   (-5 *1 (-1217 *4))))) 
+  (-12 (-5 *2 (-661 (-661 (-661 *4)))) (-5 *3 (-661 *4)) (-4 *4 (-861))
+   (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3 *4 *2)
   (-12 (-5 *2 (-661 (-661 (-661 *5)))) (-5 *3 (-1 (-114) *5 *5))
-   (-5 *4 (-661 *5)) (-4 *5 (-869)) (-5 *1 (-1217 *5))))) 
+   (-5 *4 (-661 *5)) (-4 *5 (-861)) (-5 *1 (-1209 *5))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 (-114) *6 *6)) (-4 *6 (-869)) (-5 *4 (-661 *6))
+  (-12 (-5 *3 (-1 (-114) *6 *6)) (-4 *6 (-861)) (-5 *4 (-661 *6))
    (-5 *2 (-2 (|:| |fs| (-114)) (|:| |sd| *4) (|:| |td| (-661 *4))))
-   (-5 *1 (-1217 *6)) (-5 *5 (-661 *4))))) 
-(((*1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-1216))))) 
-(((*1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-1216))))) 
-(((*1 *2) (-12 (-5 *2 (-132)) (-5 *1 (-1216))))) 
-(((*1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-1216))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-1216))))) 
+   (-5 *1 (-1209 *6)) (-5 *5 (-661 *4))))) 
+(((*1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-1208))))) 
+(((*1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-1208))))) 
+(((*1 *2) (-12 (-5 *2 (-132)) (-5 *1 (-1208))))) 
+(((*1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-1208))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-1208))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-419 (-973 *5)))) (-5 *4 (-661 (-1206))) (-4 *5 (-569))
-   (-5 *2 (-661 (-661 (-973 *5)))) (-5 *1 (-1215 *5))))) 
+  (-12 (-5 *3 (-661 (-419 (-965 *5)))) (-5 *4 (-661 (-1198))) (-4 *5 (-569))
+   (-5 *2 (-661 (-661 (-965 *5)))) (-5 *1 (-1207 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-419 (-973 (-558)))))
-   (-5 *2 (-661 (-661 (-305 (-973 *4))))) (-5 *1 (-393 *4))
-   (-4 *4 (-13 (-868) (-376)))))
+  (-12 (-5 *3 (-661 (-419 (-965 (-558)))))
+   (-5 *2 (-661 (-661 (-305 (-965 *4))))) (-5 *1 (-393 *4))
+   (-4 *4 (-13 (-860) (-376)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-305 (-419 (-973 (-558))))))
-   (-5 *2 (-661 (-661 (-305 (-973 *4))))) (-5 *1 (-393 *4))
-   (-4 *4 (-13 (-868) (-376)))))
+  (-12 (-5 *3 (-661 (-305 (-419 (-965 (-558))))))
+   (-5 *2 (-661 (-661 (-305 (-965 *4))))) (-5 *1 (-393 *4))
+   (-4 *4 (-13 (-860) (-376)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-973 (-558)))) (-5 *2 (-661 (-305 (-973 *4))))
-   (-5 *1 (-393 *4)) (-4 *4 (-13 (-868) (-376)))))
+  (-12 (-5 *3 (-419 (-965 (-558)))) (-5 *2 (-661 (-305 (-965 *4))))
+   (-5 *1 (-393 *4)) (-4 *4 (-13 (-860) (-376)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-305 (-419 (-973 (-558))))) (-5 *2 (-661 (-305 (-973 *4))))
-   (-5 *1 (-393 *4)) (-4 *4 (-13 (-868) (-376)))))
+  (-12 (-5 *3 (-305 (-419 (-965 (-558))))) (-5 *2 (-661 (-305 (-965 *4))))
+   (-5 *1 (-393 *4)) (-4 *4 (-13 (-860) (-376)))))
  ((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *5 (-1206))
-   (-4 *6 (-13 (-319) (-1067 (-558)) (-658 (-558)) (-149)))
-   (-4 *4 (-13 (-29 *6) (-1232) (-987)))
-   (-5 *2 (-2 (|:| |particular| *4) (|:| -2230 (-661 *4))))
+  (|partial| -12 (-5 *5 (-1198))
+   (-4 *6 (-13 (-319) (-1059 (-558)) (-658 (-558)) (-149)))
+   (-4 *4 (-13 (-29 *6) (-1224) (-979)))
+   (-5 *2 (-2 (|:| |particular| *4) (|:| -2222 (-661 *4))))
    (-5 *1 (-673 *6 *4 *3)) (-4 *3 (-678 *4))))
  ((*1 *2 *3 *2 *4 *2 *5)
-  (|partial| -12 (-5 *4 (-1206)) (-5 *5 (-661 *2))
-   (-4 *2 (-13 (-29 *6) (-1232) (-987)))
-   (-4 *6 (-13 (-319) (-1067 (-558)) (-658 (-558)) (-149)))
+  (|partial| -12 (-5 *4 (-1198)) (-5 *5 (-661 *2))
+   (-4 *2 (-13 (-29 *6) (-1224) (-979)))
+   (-4 *6 (-13 (-319) (-1059 (-558)) (-658 (-558)) (-149)))
    (-5 *1 (-673 *6 *2 *3)) (-4 *3 (-678 *2))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-376)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4503))))
-   (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4503))))
-   (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2230 (-661 *4))))
+  (-12 (-4 *5 (-376)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4426))))
+   (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4426))))
+   (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2222 (-661 *4))))
    (-5 *1 (-687 *5 *6 *4 *3)) (-4 *3 (-706 *5 *6 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-376)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4503))))
-   (-4 *7 (-13 (-385 *5) (-10 -7 (-6 -4503))))
-   (-5 *2 (-661 (-2 (|:| |particular| (-3 *7 #1#)) (|:| -2230 (-661 *7)))))
+  (-12 (-4 *5 (-376)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4426))))
+   (-4 *7 (-13 (-385 *5) (-10 -7 (-6 -4426))))
+   (-5 *2 (-661 (-2 (|:| |particular| (-3 *7 #1#)) (|:| -2222 (-661 *7)))))
    (-5 *1 (-687 *5 *6 *7 *3)) (-5 *4 (-661 *7)) (-4 *3 (-706 *5 *6 *7))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-709 *5)) (-4 *5 (-376))
    (-5 *2
-    (-2 (|:| |particular| (-3 (-1296 *5) #2="failed"))
-     (|:| -2230 (-661 (-1296 *5)))))
-   (-5 *1 (-688 *5)) (-5 *4 (-1296 *5))))
+    (-2 (|:| |particular| (-3 (-1288 *5) #2="failed"))
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-   (-5 *1 (-290 *3 *4 *2 *5)) (-4 *2 (-1281 *3 *4)) (-4 *5 (-1012 *4))))
+  (-12 (-4 *3 (-38 (-419 (-558)))) (-4 *4 (-1250 *3))
+   (-5 *1 (-290 *3 *4 *2 *5)) (-4 *2 (-1273 *3 *4)) (-4 *5 (-1004 *4))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-661 (-1206))) (-14 *3 (-661 (-1206)))
+  (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-661 (-1198))) (-14 *3 (-661 (-1198)))
    (-4 *4 (-401))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-38 (-419 (-558)))) (-5 *1 (-1191 *3))))
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-558)))) (-5 *1 (-1183 *3))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-38 (-419 (-558)))) (-5 *1 (-1192 *3))))) 
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-558)))) (-5 *1 (-1184 *3))))) 
 (((*1 *1 *1) (-4 *1 (-95)))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-38 (-419 (-558)))) (-4 *4 (-1289 *3)) (-5 *1 (-289 *3 *4 *2))
-   (-4 *2 (-1260 *3 *4))))
+  (-12 (-4 *3 (-38 (-419 (-558)))) (-4 *4 (-1281 *3)) (-5 *1 (-289 *3 *4 *2))
+   (-4 *2 (-1252 *3 *4))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-38 (-419 (-558)))) (-4 *4 (-1258 *3))
-   (-5 *1 (-290 *3 *4 *2 *5)) (-4 *2 (-1281 *3 *4)) (-4 *5 (-1012 *4))))
+  (-12 (-4 *3 (-38 (-419 (-558)))) (-4 *4 (-1250 *3))
+   (-5 *1 (-290 *3 *4 *2 *5)) (-4 *2 (-1273 *3 *4)) (-4 *5 (-1004 *4))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-661 (-1206))) (-14 *3 (-661 (-1206)))
+  (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-661 (-1198))) (-14 *3 (-661 (-1198)))
    (-4 *4 (-401))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-38 (-419 (-558)))) (-5 *1 (-1191 *3))))
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-558)))) (-5 *1 (-1183 *3))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-38 (-419 (-558)))) (-5 *1 (-1192 *3))))) 
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-38 (-419 (-558)))) (-5 *1 (-1184 *3))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-38 (-419 (-558))))
-   (-5 *2 (-2 (|:| -3987 (-1184 *4)) (|:| -3988 (-1184 *4))))
-   (-5 *1 (-1191 *4)) (-5 *3 (-1184 *4))))) 
+   (-5 *2 (-2 (|:| -3910 (-1176 *4)) (|:| -3911 (-1176 *4))))
+   (-5 *1 (-1183 *4)) (-5 *3 (-1176 *4))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-38 (-419 (-558))))
-   (-5 *2 (-2 (|:| -4145 (-1184 *4)) (|:| -4141 (-1184 *4))))
-   (-5 *1 (-1191 *4)) (-5 *3 (-1184 *4))))) 
+   (-5 *2 (-2 (|:| -4068 (-1176 *4)) (|:| -4064 (-1176 *4))))
+   (-5 *1 (-1183 *4)) (-5 *3 (-1176 *4))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-376)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))) 
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-376)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1 *4 (-558))) (-5 *5 (-1 (-1184 *4))) (-4 *4 (-376))
-   (-4 *4 (-1078)) (-5 *2 (-1184 *4)) (-5 *1 (-1190 *4))))) 
+  (-12 (-5 *3 (-1 *4 (-558))) (-5 *5 (-1 (-1176 *4))) (-4 *4 (-376))
+   (-4 *4 (-1070)) (-5 *2 (-1176 *4)) (-5 *1 (-1182 *4))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-376)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))) 
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-376)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *2 (-1184 *4)) (-4 *4 (-38 *3)) (-4 *4 (-1078))
-   (-5 *3 (-419 (-558))) (-5 *1 (-1190 *4))))) 
+  (-12 (-5 *2 (-1176 *4)) (-4 *4 (-38 *3)) (-4 *4 (-1070))
+   (-5 *3 (-419 (-558))) (-5 *1 (-1182 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1184 (-1184 *4))) (-5 *2 (-1184 *4)) (-5 *1 (-1190 *4))
-   (-4 *4 (-38 (-419 (-558)))) (-4 *4 (-1078))))) 
+  (-12 (-5 *3 (-1176 (-1176 *4))) (-5 *2 (-1176 *4)) (-5 *1 (-1182 *4))
+   (-4 *4 (-38 (-419 (-558)))) (-4 *4 (-1070))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 (-1184 *3))) (-5 *2 (-1184 *3)) (-5 *1 (-1190 *3))
-   (-4 *3 (-38 (-419 (-558)))) (-4 *3 (-1078))))) 
+  (-12 (-5 *4 (-1 (-1176 *3))) (-5 *2 (-1176 *3)) (-5 *1 (-1182 *3))
+   (-4 *3 (-38 (-419 (-558)))) (-4 *3 (-1070))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1184 (-1184 *4))) (-5 *2 (-1184 *4)) (-5 *1 (-1190 *4))
-   (-4 *4 (-1078))))) 
-(((*1 *2 *2 *2) (-12 (-4 *3 (-1078)) (-5 *1 (-917 *2 *3)) (-4 *2 (-1272 *3))))
- ((*1 *2 *2 *2) (-12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))) 
+  (-12 (-5 *3 (-1176 (-1176 *4))) (-5 *2 (-1176 *4)) (-5 *1 (-1182 *4))
+   (-4 *4 (-1070))))) 
+(((*1 *2 *2 *2) (-12 (-4 *3 (-1070)) (-5 *1 (-909 *2 *3)) (-4 *2 (-1264 *3))))
+ ((*1 *2 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *2 (-1184 *4)) (-5 *3 (-1 *4 (-558))) (-4 *4 (-1078))
-   (-5 *1 (-1190 *4))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))) 
+  (-12 (-5 *2 (-1176 *4)) (-5 *3 (-1 *4 (-558))) (-4 *4 (-1070))
+   (-5 *1 (-1182 *4))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-13 (-319) (-1067 (-558)) (-658 (-558)) (-149)))
-   (-5 *1 (-826 *4 *2)) (-4 *2 (-13 (-29 *4) (-1232) (-987)))))
- ((*1 *1 *1 *1 *1) (-5 *1 (-885))) ((*1 *1 *1 *1) (-5 *1 (-885)))
- ((*1 *1 *1) (-5 *1 (-885)))
- ((*1 *2 *3) (-12 (-5 *2 (-1184 *3)) (-5 *1 (-1190 *3)) (-4 *3 (-1078))))) 
+  (-12 (-5 *3 (-1198)) (-4 *4 (-13 (-319) (-1059 (-558)) (-658 (-558)) (-149)))
+   (-5 *1 (-826 *4 *2)) (-4 *2 (-13 (-29 *4) (-1224) (-979)))))
+ ((*1 *1 *1 *1 *1) (-5 *1 (-877))) ((*1 *1 *1 *1) (-5 *1 (-877)))
+ ((*1 *1 *1) (-5 *1 (-877)))
+ ((*1 *2 *3) (-12 (-5 *2 (-1176 *3)) (-5 *1 (-1182 *3)) (-4 *3 (-1070))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-1184 (-558))) (-5 *1 (-1190 *4)) (-4 *4 (-1078))
+  (-12 (-5 *2 (-1176 (-558))) (-5 *1 (-1182 *4)) (-4 *4 (-1070))
    (-5 *3 (-558))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-1184 (-558))) (-5 *1 (-1190 *4)) (-4 *4 (-1078))
+  (-12 (-5 *2 (-1176 (-558))) (-5 *1 (-1182 *4)) (-4 *4 (-1070))
    (-5 *3 (-558))))) 
 (((*1 *1 *1)
-  (|partial| -12 (-5 *1 (-154 *2 *3 *4)) (-14 *2 (-946)) (-4 *3 (-376))
-   (-14 *4 (-1022 *2 *3))))
+  (|partial| -12 (-5 *1 (-154 *2 *3 *4)) (-14 *2 (-938)) (-4 *3 (-376))
+   (-14 *4 (-1014 *2 *3))))
  ((*1 *1 *1)
   (|partial| -12 (-4 *2 (-175)) (-5 *1 (-301 *2 *3 *4 *5 *6 *7))
-   (-4 *3 (-1272 *2)) (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4))
+   (-4 *3 (-1264 *2)) (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4))
    (-14 *6 (-1 (-3 *4 "failed") *4 *4))
    (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4))))
  ((*1 *1 *1) (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-175)) (-4 *2 (-569))))
@@ -4925,1831 +4924,1831 @@
  ((*1 *1) (-12 (-5 *1 (-738 *2)) (-4 *2 (-376))))
  ((*1 *1 *1) (|partial| -4 *1 (-742))) ((*1 *1 *1) (|partial| -4 *1 (-746)))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869)) (-4 *3 (-1094 *5 *6 *7))
+  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861)) (-4 *3 (-1086 *5 *6 *7))
    (-5 *2 (-2 (|:| |num| *3) (|:| |den| *3))) (-5 *1 (-796 *5 *6 *7 *3 *4))
-   (-4 *4 (-1100 *5 *6 *7 *3))))
+   (-4 *4 (-1092 *5 *6 *7 *3))))
  ((*1 *2 *2 *1)
-  (|partial| -12 (-4 *1 (-1097 *3 *2)) (-4 *3 (-13 (-868) (-376)))
-   (-4 *2 (-1272 *3))))
+  (|partial| -12 (-4 *1 (-1089 *3 *2)) (-4 *3 (-13 (-860) (-376)))
+   (-4 *2 (-1264 *3))))
  ((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))) 
+  (|partial| -12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))) 
 (((*1 *1 *1 *2)
   (|partial| -12 (-4 *1 (-168 *2)) (-4 *2 (-175)) (-4 *2 (-569))))
  ((*1 *1 *1 *2)
-  (|partial| -12 (-4 *1 (-338 *2 *3)) (-4 *2 (-1078)) (-4 *3 (-814))
+  (|partial| -12 (-4 *1 (-338 *2 *3)) (-4 *2 (-1070)) (-4 *3 (-814))
    (-4 *2 (-569))))
  ((*1 *1 *1 *1) (|partial| -4 *1 (-569)))
  ((*1 *1 *1 *2)
-  (|partial| -12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-385 *2))
+  (|partial| -12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-385 *2))
    (-4 *4 (-385 *2)) (-4 *2 (-569))))
  ((*1 *1 *1 *1) (|partial| -5 *1 (-791)))
  ((*1 *1 *1 *2)
-  (|partial| -12 (-4 *1 (-874 *2)) (-4 *2 (-1078)) (-4 *2 (-569))))
- ((*1 *1 *1 *1) (-5 *1 (-885)))
+  (|partial| -12 (-4 *1 (-866 *2)) (-4 *2 (-1070)) (-4 *2 (-569))))
+ ((*1 *1 *1 *1) (-5 *1 (-877)))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1296 *4)) (-4 *4 (-1272 *3)) (-4 *3 (-569))
-   (-5 *1 (-998 *3 *4))))
+  (-12 (-5 *2 (-1288 *4)) (-4 *4 (-1264 *3)) (-4 *3 (-569))
+   (-5 *1 (-990 *3 *4))))
  ((*1 *1 *1 *2)
-  (|partial| -12 (-4 *1 (-1082 *3 *4 *2 *5 *6)) (-4 *2 (-1078))
+  (|partial| -12 (-4 *1 (-1074 *3 *4 *2 *5 *6)) (-4 *2 (-1070))
    (-4 *5 (-245 *4 *2)) (-4 *6 (-245 *3 *2)) (-4 *2 (-569))))
  ((*1 *2 *2 *2)
-  (|partial| -12 (-5 *2 (-1184 *3)) (-4 *3 (-1078)) (-5 *1 (-1190 *3))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1246)) (-5 *1 (-1184 *3))))) 
+  (|partial| -12 (-5 *2 (-1176 *3)) (-4 *3 (-1070)) (-5 *1 (-1182 *3))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1238)) (-5 *1 (-1176 *3))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-661 *4)) (-4 *4 (-1130)) (-4 *4 (-1246)) (-5 *2 (-114))
-   (-5 *1 (-1184 *4))))) 
+  (-12 (-5 *3 (-661 *4)) (-4 *4 (-1122)) (-4 *4 (-1238)) (-5 *2 (-114))
+   (-5 *1 (-1176 *4))))) 
 (((*1 *2 *3 *1)
   (-12
-   (-5 *2 (-2 (|:| |cycle?| (-114)) (|:| -3071 (-791)) (|:| |period| (-791))))
-   (-5 *1 (-1184 *4)) (-4 *4 (-1246)) (-5 *3 (-791))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1 (-1184 *3))) (-5 *1 (-1184 *3)) (-4 *3 (-1246))))) 
-(((*1 *1 *2 *1) (-12 (-5 *1 (-661 *2)) (-4 *2 (-1246))))
- ((*1 *1 *2 *1) (-12 (-5 *1 (-1184 *2)) (-4 *2 (-1246))))) 
+   (-5 *2 (-2 (|:| |cycle?| (-114)) (|:| -2994 (-791)) (|:| |period| (-791))))
+   (-5 *1 (-1176 *4)) (-4 *4 (-1238)) (-5 *3 (-791))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1 (-1176 *3))) (-5 *1 (-1176 *3)) (-4 *3 (-1238))))) 
+(((*1 *1 *2 *1) (-12 (-5 *1 (-661 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *2 *1) (-12 (-5 *1 (-1176 *2)) (-4 *2 (-1238))))) 
 (((*1 *1) (-5 *1 (-590)))
- ((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-881))))
- ((*1 *2 *3) (-12 (-5 *3 (-885)) (-5 *2 (-1302)) (-5 *1 (-881))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-873))))
+ ((*1 *2 *3) (-12 (-5 *3 (-877)) (-5 *2 (-1294)) (-5 *1 (-873))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1188)) (-5 *4 (-885)) (-5 *2 (-1302)) (-5 *1 (-881))))
+  (-12 (-5 *3 (-1180)) (-5 *4 (-877)) (-5 *2 (-1294)) (-5 *1 (-873))))
  ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-558)) (-5 *2 (-1302)) (-5 *1 (-1184 *4)) (-4 *4 (-1130))
-   (-4 *4 (-1246))))) 
+  (-12 (-5 *3 (-558)) (-5 *2 (-1294)) (-5 *1 (-1176 *4)) (-4 *4 (-1122))
+   (-4 *4 (-1238))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-885)) (-5 *1 (-1184 *3)) (-4 *3 (-1130)) (-4 *3 (-1246))))) 
+  (-12 (-5 *2 (-877)) (-5 *1 (-1176 *3)) (-4 *3 (-1122)) (-4 *3 (-1238))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-114)) (-5 *1 (-1184 *3)) (-4 *3 (-1130)) (-4 *3 (-1246))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-1176 *3)) (-4 *3 (-1122)) (-4 *3 (-1238))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-791)) (-5 *2 (-1296 (-661 (-558)))) (-5 *1 (-492))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1246)) (-5 *1 (-613 *3))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1246)) (-5 *1 (-1184 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1246)) (-5 *1 (-1184 *3))))) 
-(((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1246)) (-5 *1 (-613 *3))))
+  (-12 (-5 *3 (-791)) (-5 *2 (-1288 (-661 (-558)))) (-5 *1 (-492))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1238)) (-5 *1 (-613 *3))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1238)) (-5 *1 (-1176 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1238)) (-5 *1 (-1176 *3))))) 
+(((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1238)) (-5 *1 (-613 *3))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1246)) (-5 *1 (-1184 *3))))) 
-(((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1246)) (-5 *1 (-613 *3))))
+  (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1238)) (-5 *1 (-1176 *3))))) 
+(((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1238)) (-5 *1 (-613 *3))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1246)) (-5 *1 (-1184 *3))))) 
+  (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1238)) (-5 *1 (-1176 *3))))) 
 (((*1 *2 *2 *3 *3)
   (-12 (-5 *3 (-558)) (-4 *4 (-13 (-569) (-149))) (-5 *1 (-549 *4 *2))
-   (-4 *2 (-1289 *4))))
+   (-4 *2 (-1281 *4))))
  ((*1 *2 *2 *3 *3)
-  (-12 (-5 *3 (-558)) (-4 *4 (-13 (-376) (-381) (-631 *3))) (-4 *5 (-1272 *4))
-   (-4 *6 (-744 *4 *5)) (-5 *1 (-553 *4 *5 *6 *2)) (-4 *2 (-1289 *6))))
+  (-12 (-5 *3 (-558)) (-4 *4 (-13 (-376) (-381) (-631 *3))) (-4 *5 (-1264 *4))
+   (-4 *6 (-744 *4 *5)) (-5 *1 (-553 *4 *5 *6 *2)) (-4 *2 (-1281 *6))))
  ((*1 *2 *2 *3 *3)
   (-12 (-5 *3 (-558)) (-4 *4 (-13 (-376) (-381) (-631 *3)))
-   (-5 *1 (-554 *4 *2)) (-4 *2 (-1289 *4))))
+   (-5 *1 (-554 *4 *2)) (-4 *2 (-1281 *4))))
  ((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-1184 *4)) (-5 *3 (-558)) (-4 *4 (-13 (-569) (-149)))
-   (-5 *1 (-1183 *4))))) 
+  (-12 (-5 *2 (-1176 *4)) (-5 *3 (-558)) (-4 *4 (-13 (-569) (-149)))
+   (-5 *1 (-1175 *4))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-569) (-149))) (-5 *1 (-549 *3 *2)) (-4 *2 (-1289 *3))))
+  (-12 (-4 *3 (-13 (-569) (-149))) (-5 *1 (-549 *3 *2)) (-4 *2 (-1281 *3))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-4 *4 (-1272 *3))
-   (-4 *5 (-744 *3 *4)) (-5 *1 (-553 *3 *4 *5 *2)) (-4 *2 (-1289 *5))))
+  (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-4 *4 (-1264 *3))
+   (-4 *5 (-744 *3 *4)) (-5 *1 (-553 *3 *4 *5 *2)) (-4 *2 (-1281 *5))))
  ((*1 *2 *2)
   (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-5 *1 (-554 *3 *2))
-   (-4 *2 (-1289 *3))))
+   (-4 *2 (-1281 *3))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-13 (-569) (-149))) (-5 *1 (-1183 *3))))) 
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-13 (-569) (-149))) (-5 *1 (-1175 *3))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-569) (-149))) (-5 *1 (-549 *3 *2)) (-4 *2 (-1289 *3))))
+  (-12 (-4 *3 (-13 (-569) (-149))) (-5 *1 (-549 *3 *2)) (-4 *2 (-1281 *3))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-4 *4 (-1272 *3))
-   (-4 *5 (-744 *3 *4)) (-5 *1 (-553 *3 *4 *5 *2)) (-4 *2 (-1289 *5))))
+  (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-4 *4 (-1264 *3))
+   (-4 *5 (-744 *3 *4)) (-5 *1 (-553 *3 *4 *5 *2)) (-4 *2 (-1281 *5))))
  ((*1 *2 *2)
   (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-5 *1 (-554 *3 *2))
-   (-4 *2 (-1289 *3))))
+   (-4 *2 (-1281 *3))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-13 (-569) (-149))) (-5 *1 (-1183 *3))))) 
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-13 (-569) (-149))) (-5 *1 (-1175 *3))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-569) (-149))) (-5 *1 (-549 *3 *2)) (-4 *2 (-1289 *3))))
+  (-12 (-4 *3 (-13 (-569) (-149))) (-5 *1 (-549 *3 *2)) (-4 *2 (-1281 *3))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-4 *4 (-1272 *3))
-   (-4 *5 (-744 *3 *4)) (-5 *1 (-553 *3 *4 *5 *2)) (-4 *2 (-1289 *5))))
+  (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-4 *4 (-1264 *3))
+   (-4 *5 (-744 *3 *4)) (-5 *1 (-553 *3 *4 *5 *2)) (-4 *2 (-1281 *5))))
  ((*1 *2 *2)
   (-12 (-4 *3 (-13 (-376) (-381) (-631 (-558)))) (-5 *1 (-554 *3 *2))
-   (-4 *2 (-1289 *3))))
+   (-4 *2 (-1281 *3))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1184 *3)) (-4 *3 (-13 (-569) (-149))) (-5 *1 (-1183 *3))))) 
+  (-12 (-5 *2 (-1176 *3)) (-4 *3 (-13 (-569) (-149))) (-5 *1 (-1175 *3))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-537))))
- ((*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-1182))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1164)) (-5 *1 (-1182))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-711 (-1164))) (-5 *1 (-1182))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1164)) (-5 *1 (-1182))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-1174))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-1174))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-711 (-1156))) (-5 *1 (-1174))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-1174))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))))
- ((*1 *1) (-4 *1 (-1181)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-711 *1)) (-4 *1 (-1181))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-1179 *3)) (-4 *3 (-1246)) (-5 *2 (-114))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-1179 *3)) (-4 *3 (-1246)) (-5 *2 (-114))))) 
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))))
+ ((*1 *1) (-4 *1 (-1173)))) 
+(((*1 *2 *1) (-12 (-5 *2 (-711 *1)) (-4 *1 (-1173))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-1171 *3)) (-4 *3 (-1238)) (-5 *2 (-114))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-1171 *3)) (-4 *3 (-1238)) (-5 *2 (-114))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-791)) (-4 *1 (-1179 *4)) (-4 *4 (-1246)) (-5 *2 (-114))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1246)) (-5 *1 (-1177 *3))))) 
+  (-12 (-5 *3 (-791)) (-4 *1 (-1171 *4)) (-4 *4 (-1238)) (-5 *2 (-114))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1238)) (-5 *1 (-1169 *3))))) 
 (((*1 *2 *3 *1 *4 *4 *4 *4 *4)
-  (-12 (-5 *4 (-114)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869))
-   (-5 *2 (-661 (-1056 *5 *6 *7 *3))) (-5 *1 (-1056 *5 *6 *7 *3))
-   (-4 *3 (-1094 *5 *6 *7))))
+  (-12 (-5 *4 (-114)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861))
+   (-5 *2 (-661 (-1048 *5 *6 *7 *3))) (-5 *1 (-1048 *5 *6 *7 *3))
+   (-4 *3 (-1086 *5 *6 *7))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-661 *6)) (-4 *1 (-1100 *3 *4 *5 *6)) (-4 *3 (-464))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5))))
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+   (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-1086 *3 *4 *5))))
  ((*1 *1 *2 *1)
-  (-12 (-4 *1 (-1100 *3 *4 *5 *2)) (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-869))
-   (-4 *2 (-1094 *3 *4 *5))))
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+   (-4 *2 (-1086 *3 *4 *5))))
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-  (-12 (-5 *4 (-114)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869))
-   (-5 *2 (-661 (-1175 *5 *6 *7 *3))) (-5 *1 (-1175 *5 *6 *7 *3))
-   (-4 *3 (-1094 *5 *6 *7))))) 
+  (-12 (-5 *4 (-114)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861))
+   (-5 *2 (-661 (-1167 *5 *6 *7 *3))) (-5 *1 (-1167 *5 *6 *7 *3))
+   (-4 *3 (-1086 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *4 *4)
-  (-12 (-5 *3 (-661 *8)) (-5 *4 (-114)) (-4 *8 (-1094 *5 *6 *7)) (-4 *5 (-464))
-   (-4 *6 (-815)) (-4 *7 (-869)) (-5 *2 (-661 (-1056 *5 *6 *7 *8)))
-   (-5 *1 (-1056 *5 *6 *7 *8))))
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+   (-4 *6 (-815)) (-4 *7 (-861)) (-5 *2 (-661 (-1048 *5 *6 *7 *8)))
+   (-5 *1 (-1048 *5 *6 *7 *8))))
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-  (-12 (-5 *3 (-661 *8)) (-5 *4 (-114)) (-4 *8 (-1094 *5 *6 *7)) (-4 *5 (-464))
-   (-4 *6 (-815)) (-4 *7 (-869)) (-5 *2 (-661 (-1175 *5 *6 *7 *8)))
-   (-5 *1 (-1175 *5 *6 *7 *8))))) 
+  (-12 (-5 *3 (-661 *8)) (-5 *4 (-114)) (-4 *8 (-1086 *5 *6 *7)) (-4 *5 (-464))
+   (-4 *6 (-815)) (-4 *7 (-861)) (-5 *2 (-661 (-1167 *5 *6 *7 *8)))
+   (-5 *1 (-1167 *5 *6 *7 *8))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-114)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869))
-   (-4 *8 (-1094 *5 *6 *7))
-   (-5 *2 (-2 (|:| |val| (-661 *8)) (|:| |towers| (-661 (-1056 *5 *6 *7 *8)))))
-   (-5 *1 (-1056 *5 *6 *7 *8)) (-5 *3 (-661 *8))))
+  (-12 (-5 *4 (-114)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861))
+   (-4 *8 (-1086 *5 *6 *7))
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-  (-12 (-5 *4 (-114)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869))
-   (-4 *8 (-1094 *5 *6 *7))
-   (-5 *2 (-2 (|:| |val| (-661 *8)) (|:| |towers| (-661 (-1175 *5 *6 *7 *8)))))
-   (-5 *1 (-1175 *5 *6 *7 *8)) (-5 *3 (-661 *8))))) 
-(((*1 *2 *3 *4)
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-   (-4 *6 (-815)) (-4 *7 (-869)) (-5 *2 (-1302))
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- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-2 (|:| |val| (-661 *8)) (|:| -1751 *9)))) (-5 *4 (-791))
-   (-4 *8 (-1094 *5 *6 *7)) (-4 *9 (-1138 *5 *6 *7 *8)) (-4 *5 (-464))
-   (-4 *6 (-815)) (-4 *7 (-869)) (-5 *2 (-1302))
-   (-5 *1 (-1174 *5 *6 *7 *8 *9))))) 
+  (-12 (-5 *4 (-114)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861))
+   (-4 *8 (-1086 *5 *6 *7))
+   (-5 *2 (-2 (|:| |val| (-661 *8)) (|:| |towers| (-661 (-1167 *5 *6 *7 *8)))))
+   (-5 *1 (-1167 *5 *6 *7 *8)) (-5 *3 (-661 *8))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *3 (-661 (-2 (|:| |val| (-661 *8)) (|:| -1743 *9)))) (-5 *4 (-791))
+   (-4 *8 (-1086 *5 *6 *7)) (-4 *9 (-1092 *5 *6 *7 *8)) (-4 *5 (-464))
+   (-4 *6 (-815)) (-4 *7 (-861)) (-5 *2 (-1294))
+   (-5 *1 (-1090 *5 *6 *7 *8 *9))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-661 (-2 (|:| |val| (-661 *8)) (|:| -1743 *9)))) (-5 *4 (-791))
+   (-4 *8 (-1086 *5 *6 *7)) (-4 *9 (-1130 *5 *6 *7 *8)) (-4 *5 (-464))
+   (-4 *6 (-815)) (-4 *7 (-861)) (-5 *2 (-1294))
+   (-5 *1 (-1166 *5 *6 *7 *8 *9))))) 
 (((*1 *2 *3 *4 *2 *5 *6)
   (-12
    (-5 *5
     (-2 (|:| |done| (-661 *11))
-     (|:| |todo| (-661 (-2 (|:| |val| *3) (|:| -1751 *11))))))
-   (-5 *6 (-791)) (-5 *2 (-661 (-2 (|:| |val| (-661 *10)) (|:| -1751 *11))))
-   (-5 *3 (-661 *10)) (-5 *4 (-661 *11)) (-4 *10 (-1094 *7 *8 *9))
-   (-4 *11 (-1100 *7 *8 *9 *10)) (-4 *7 (-464)) (-4 *8 (-815)) (-4 *9 (-869))
-   (-5 *1 (-1098 *7 *8 *9 *10 *11))))
+     (|:| |todo| (-661 (-2 (|:| |val| *3) (|:| -1743 *11))))))
+   (-5 *6 (-791)) (-5 *2 (-661 (-2 (|:| |val| (-661 *10)) (|:| -1743 *11))))
+   (-5 *3 (-661 *10)) (-5 *4 (-661 *11)) (-4 *10 (-1086 *7 *8 *9))
+   (-4 *11 (-1092 *7 *8 *9 *10)) (-4 *7 (-464)) (-4 *8 (-815)) (-4 *9 (-861))
+   (-5 *1 (-1090 *7 *8 *9 *10 *11))))
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   (-12
    (-5 *5
     (-2 (|:| |done| (-661 *11))
-     (|:| |todo| (-661 (-2 (|:| |val| *3) (|:| -1751 *11))))))
-   (-5 *6 (-791)) (-5 *2 (-661 (-2 (|:| |val| (-661 *10)) (|:| -1751 *11))))
-   (-5 *3 (-661 *10)) (-5 *4 (-661 *11)) (-4 *10 (-1094 *7 *8 *9))
-   (-4 *11 (-1138 *7 *8 *9 *10)) (-4 *7 (-464)) (-4 *8 (-815)) (-4 *9 (-869))
-   (-5 *1 (-1174 *7 *8 *9 *10 *11))))) 
+     (|:| |todo| (-661 (-2 (|:| |val| *3) (|:| -1743 *11))))))
+   (-5 *6 (-791)) (-5 *2 (-661 (-2 (|:| |val| (-661 *10)) (|:| -1743 *11))))
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+   (-4 *11 (-1130 *7 *8 *9 *10)) (-4 *7 (-464)) (-4 *8 (-815)) (-4 *9 (-861))
+   (-5 *1 (-1166 *7 *8 *9 *10 *11))))) 
 (((*1 *2 *1)
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-   (-4 *5 (-1272 (-419 *4))) (-4 *6 (-355 *3 *4 *5))
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+   (-4 *5 (-1264 (-419 *4))) (-4 *6 (-355 *3 *4 *5))
    (-5 *2
-    (-2 (|:| -2563 (-425 *4 (-419 *4) *5 *6)) (|:| |principalPart| *6)))))
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  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1272 *5)) (-4 *5 (-376))
-   (-5 *2 (-2 (|:| |poly| *6) (|:| -3569 (-419 *6)) (|:| |special| (-419 *6))))
+  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5)) (-4 *5 (-376))
+   (-5 *2 (-2 (|:| |poly| *6) (|:| -3492 (-419 *6)) (|:| |special| (-419 *6))))
    (-5 *1 (-747 *5 *6)) (-5 *3 (-419 *6))))
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-   (-4 *3 (-1272 *4))))
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+   (-4 *3 (-1264 *4))))
  ((*1 *2 *3 *4 *4)
   (|partial| -12 (-5 *4 (-791)) (-4 *5 (-376))
-   (-5 *2 (-2 (|:| -3617 *3) (|:| -3616 *3))) (-5 *1 (-921 *3 *5))
-   (-4 *3 (-1272 *5))))
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   (-12 (-5 *2 (-661 *9)) (-5 *3 (-661 *8)) (-5 *4 (-114))
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-   (-4 *6 (-815)) (-4 *7 (-869)) (-5 *1 (-1098 *5 *6 *7 *8 *9))))
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   (-12 (-5 *2 (-661 *9)) (-5 *3 (-661 *8)) (-5 *4 (-114))
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   (-12 (-5 *2 (-661 *9)) (-5 *3 (-661 *8)) (-5 *4 (-114))
-   (-4 *8 (-1094 *5 *6 *7)) (-4 *9 (-1138 *5 *6 *7 *8)) (-4 *5 (-464))
-   (-4 *6 (-815)) (-4 *7 (-869)) (-5 *1 (-1174 *5 *6 *7 *8 *9))))
+   (-4 *8 (-1086 *5 *6 *7)) (-4 *9 (-1130 *5 *6 *7 *8)) (-4 *5 (-464))
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   (-12 (-5 *2 (-661 *9)) (-5 *3 (-661 *8)) (-5 *4 (-114))
-   (-4 *8 (-1094 *5 *6 *7)) (-4 *9 (-1138 *5 *6 *7 *8)) (-4 *5 (-464))
-   (-4 *6 (-815)) (-4 *7 (-869)) (-5 *1 (-1174 *5 *6 *7 *8 *9))))) 
+   (-4 *8 (-1086 *5 *6 *7)) (-4 *9 (-1130 *5 *6 *7 *8)) (-4 *5 (-464))
+   (-4 *6 (-815)) (-4 *7 (-861)) (-5 *1 (-1166 *5 *6 *7 *8 *9))))) 
 (((*1 *2 *3 *4 *5 *6)
   (-12 (-5 *5 (-791)) (-5 *6 (-114)) (-4 *7 (-464)) (-4 *8 (-815))
-   (-4 *9 (-869)) (-4 *3 (-1094 *7 *8 *9))
+   (-4 *9 (-861)) (-4 *3 (-1086 *7 *8 *9))
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     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1098 *7 *8 *9 *3 *4)) (-4 *4 (-1100 *7 *8 *9 *3))))
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
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-   (-4 *3 (-1094 *6 *7 *8))
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     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1098 *6 *7 *8 *3 *4)) (-4 *4 (-1100 *6 *7 *8 *3))))
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
+   (-5 *1 (-1090 *6 *7 *8 *3 *4)) (-4 *4 (-1092 *6 *7 *8 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869)) (-4 *3 (-1094 *5 *6 *7))
+  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861)) (-4 *3 (-1086 *5 *6 *7))
    (-5 *2
     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1098 *5 *6 *7 *3 *4)) (-4 *4 (-1100 *5 *6 *7 *3))))
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
+   (-5 *1 (-1090 *5 *6 *7 *3 *4)) (-4 *4 (-1092 *5 *6 *7 *3))))
  ((*1 *2 *3 *4 *5 *6)
   (-12 (-5 *5 (-791)) (-5 *6 (-114)) (-4 *7 (-464)) (-4 *8 (-815))
-   (-4 *9 (-869)) (-4 *3 (-1094 *7 *8 *9))
+   (-4 *9 (-861)) (-4 *3 (-1086 *7 *8 *9))
    (-5 *2
     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1174 *7 *8 *9 *3 *4)) (-4 *4 (-1138 *7 *8 *9 *3))))
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
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-  (-12 (-5 *5 (-791)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-869))
-   (-4 *3 (-1094 *6 *7 *8))
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+   (-4 *3 (-1086 *6 *7 *8))
    (-5 *2
     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1174 *6 *7 *8 *3 *4)) (-4 *4 (-1138 *6 *7 *8 *3))))
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
+   (-5 *1 (-1166 *6 *7 *8 *3 *4)) (-4 *4 (-1130 *6 *7 *8 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869)) (-4 *3 (-1094 *5 *6 *7))
+  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861)) (-4 *3 (-1086 *5 *6 *7))
    (-5 *2
     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1174 *5 *6 *7 *3 *4)) (-4 *4 (-1138 *5 *6 *7 *3))))) 
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
+   (-5 *1 (-1166 *5 *6 *7 *3 *4)) (-4 *4 (-1130 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *5 (-791)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-869))
-   (-4 *3 (-1094 *6 *7 *8))
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    (-5 *2
     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1098 *6 *7 *8 *3 *4)) (-4 *4 (-1100 *6 *7 *8 *3))))
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
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  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869)) (-4 *3 (-1094 *5 *6 *7))
+  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861)) (-4 *3 (-1086 *5 *6 *7))
    (-5 *2
     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1098 *5 *6 *7 *3 *4)) (-4 *4 (-1100 *5 *6 *7 *3))))
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
+   (-5 *1 (-1090 *5 *6 *7 *3 *4)) (-4 *4 (-1092 *5 *6 *7 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *5 (-791)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-869))
-   (-4 *3 (-1094 *6 *7 *8))
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+   (-4 *3 (-1086 *6 *7 *8))
    (-5 *2
     (-2 (|:| |done| (-661 *4))
-     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1751 *4))))))
-   (-5 *1 (-1174 *6 *7 *8 *3 *4)) (-4 *4 (-1138 *6 *7 *8 *3))))
+     (|:| |todo| (-661 (-2 (|:| |val| (-661 *3)) (|:| -1743 *4))))))
+   (-5 *1 (-1166 *6 *7 *8 *3 *4)) (-4 *4 (-1130 *6 *7 *8 *3))))
  ((*1 *2 *3 *4)
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+  (-12 (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861)) (-4 *3 (-1086 *5 *6 *7))
    (-5 *2
     (-2 (|:| |done| (-661 *4))
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 (((*1 *2 *3)
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 (((*1 *2 *2 *2 *3)
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 (((*1 *2 *3 *3 *3)
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-   (-4 *8 (-1100 *4 *5 *6 *7))))
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-   (-4 *8 (-1100 *4 *5 *6 *7))))) 
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 (((*1 *2)
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-   (-4 *8 (-1100 *4 *5 *6 *7))))
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  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1188)) (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-1094 *4 *5 *6)) (-5 *2 (-1302)) (-5 *1 (-1137 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1180)) (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-1086 *4 *5 *6)) (-5 *2 (-1294)) (-5 *1 (-1129 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-114)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-869))
-   (-4 *9 (-1094 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3761 (-661 *9)) (|:| -1751 *4) (|:| |ineq| (-661 *9))))
-   (-5 *1 (-1017 *6 *7 *8 *9 *4)) (-5 *3 (-661 *9))
-   (-4 *4 (-1100 *6 *7 *8 *9))))
+  (|partial| -12 (-5 *5 (-114)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-861))
+   (-4 *9 (-1086 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3684 (-661 *9)) (|:| -1743 *4) (|:| |ineq| (-661 *9))))
+   (-5 *1 (-1009 *6 *7 *8 *9 *4)) (-5 *3 (-661 *9))
+   (-4 *4 (-1092 *6 *7 *8 *9))))
  ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-114)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-869))
-   (-4 *9 (-1094 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3761 (-661 *9)) (|:| -1751 *4) (|:| |ineq| (-661 *9))))
-   (-5 *1 (-1136 *6 *7 *8 *9 *4)) (-5 *3 (-661 *9))
-   (-4 *4 (-1100 *6 *7 *8 *9))))) 
+  (|partial| -12 (-5 *5 (-114)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-861))
+   (-4 *9 (-1086 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3684 (-661 *9)) (|:| -1743 *4) (|:| |ineq| (-661 *9))))
+   (-5 *1 (-1128 *6 *7 *8 *9 *4)) (-5 *3 (-661 *9))
+   (-4 *4 (-1092 *6 *7 *8 *9))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-661 *10)) (-5 *5 (-114)) (-4 *10 (-1100 *6 *7 *8 *9))
-   (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-869)) (-4 *9 (-1094 *6 *7 *8))
+  (-12 (-5 *4 (-661 *10)) (-5 *5 (-114)) (-4 *10 (-1092 *6 *7 *8 *9))
+   (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-861)) (-4 *9 (-1086 *6 *7 *8))
    (-5 *2
-    (-661 (-2 (|:| -3761 (-661 *9)) (|:| -1751 *10) (|:| |ineq| (-661 *9)))))
-   (-5 *1 (-1017 *6 *7 *8 *9 *10)) (-5 *3 (-661 *9))))
+    (-661 (-2 (|:| -3684 (-661 *9)) (|:| -1743 *10) (|:| |ineq| (-661 *9)))))
+   (-5 *1 (-1009 *6 *7 *8 *9 *10)) (-5 *3 (-661 *9))))
  ((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-661 *10)) (-5 *5 (-114)) (-4 *10 (-1100 *6 *7 *8 *9))
-   (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-869)) (-4 *9 (-1094 *6 *7 *8))
+  (-12 (-5 *4 (-661 *10)) (-5 *5 (-114)) (-4 *10 (-1092 *6 *7 *8 *9))
+   (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-861)) (-4 *9 (-1086 *6 *7 *8))
    (-5 *2
-    (-661 (-2 (|:| -3761 (-661 *9)) (|:| -1751 *10) (|:| |ineq| (-661 *9)))))
-   (-5 *1 (-1136 *6 *7 *8 *9 *10)) (-5 *3 (-661 *9))))) 
+    (-661 (-2 (|:| -3684 (-661 *9)) (|:| -1743 *10) (|:| |ineq| (-661 *9)))))
+   (-5 *1 (-1128 *6 *7 *8 *9 *10)) (-5 *3 (-661 *9))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 (-2 (|:| |val| (-661 *6)) (|:| -1751 *7))))
-   (-4 *6 (-1094 *3 *4 *5)) (-4 *7 (-1100 *3 *4 *5 *6)) (-4 *3 (-464))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1017 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-661 (-2 (|:| |val| (-661 *6)) (|:| -1743 *7))))
+   (-4 *6 (-1086 *3 *4 *5)) (-4 *7 (-1092 *3 *4 *5 *6)) (-4 *3 (-464))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-1009 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-661 (-2 (|:| |val| (-661 *6)) (|:| -1751 *7))))
-   (-4 *6 (-1094 *3 *4 *5)) (-4 *7 (-1100 *3 *4 *5 *6)) (-4 *3 (-464))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1136 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-661 (-2 (|:| |val| (-661 *6)) (|:| -1743 *7))))
+   (-4 *6 (-1086 *3 *4 *5)) (-4 *7 (-1092 *3 *4 *5 *6)) (-4 *3 (-464))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-1128 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-661 *7)) (|:| -1751 *8)))
-   (-4 *7 (-1094 *4 *5 *6)) (-4 *8 (-1100 *4 *5 *6 *7)) (-4 *4 (-464))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-114))
-   (-5 *1 (-1017 *4 *5 *6 *7 *8))))
+  (-12 (-5 *3 (-2 (|:| |val| (-661 *7)) (|:| -1743 *8)))
+   (-4 *7 (-1086 *4 *5 *6)) (-4 *8 (-1092 *4 *5 *6 *7)) (-4 *4 (-464))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-114))
+   (-5 *1 (-1009 *4 *5 *6 *7 *8))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-661 *7)) (|:| -1751 *8)))
-   (-4 *7 (-1094 *4 *5 *6)) (-4 *8 (-1100 *4 *5 *6 *7)) (-4 *4 (-464))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-114))
-   (-5 *1 (-1136 *4 *5 *6 *7 *8))))) 
-(((*1 *2 *2)
-  (-12 (-5 *2 (-661 *7)) (-4 *7 (-1100 *3 *4 *5 *6)) (-4 *3 (-464))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5))
-   (-5 *1 (-1017 *3 *4 *5 *6 *7))))
- ((*1 *2 *2)
-  (-12 (-5 *2 (-661 *7)) (-4 *7 (-1100 *3 *4 *5 *6)) (-4 *3 (-464))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5))
-   (-5 *1 (-1136 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-2 (|:| |val| (-661 *7)) (|:| -1743 *8)))
+   (-4 *7 (-1086 *4 *5 *6)) (-4 *8 (-1092 *4 *5 *6 *7)) (-4 *4 (-464))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-114))
+   (-5 *1 (-1128 *4 *5 *6 *7 *8))))) 
+(((*1 *2 *2)
+  (-12 (-5 *2 (-661 *7)) (-4 *7 (-1092 *3 *4 *5 *6)) (-4 *3 (-464))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-1086 *3 *4 *5))
+   (-5 *1 (-1009 *3 *4 *5 *6 *7))))
+ ((*1 *2 *2)
+  (-12 (-5 *2 (-661 *7)) (-4 *7 (-1092 *3 *4 *5 *6)) (-4 *3 (-464))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-1086 *3 *4 *5))
+   (-5 *1 (-1128 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-1100 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *3)) (-4 *3 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1100 *5 *6 *7 *8)) (-4 *5 (-464))
-   (-4 *6 (-815)) (-4 *7 (-869)) (-4 *8 (-1094 *5 *6 *7)) (-5 *2 (-114))
-   (-5 *1 (-1017 *5 *6 *7 *8 *3))))
+  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1092 *5 *6 *7 *8)) (-4 *5 (-464))
+   (-4 *6 (-815)) (-4 *7 (-861)) (-4 *8 (-1086 *5 *6 *7)) (-5 *2 (-114))
+   (-5 *1 (-1009 *5 *6 *7 *8 *3))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-114)) (-5 *1 (-1136 *4 *5 *6 *7 *3)) (-4 *3 (-1100 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-114)) (-5 *1 (-1128 *4 *5 *6 *7 *3)) (-4 *3 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1100 *5 *6 *7 *8)) (-4 *5 (-464))
-   (-4 *6 (-815)) (-4 *7 (-869)) (-4 *8 (-1094 *5 *6 *7)) (-5 *2 (-114))
-   (-5 *1 (-1136 *5 *6 *7 *8 *3))))) 
+  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1092 *5 *6 *7 *8)) (-4 *5 (-464))
+   (-4 *6 (-815)) (-4 *7 (-861)) (-4 *8 (-1086 *5 *6 *7)) (-5 *2 (-114))
+   (-5 *1 (-1128 *5 *6 *7 *8 *3))))) 
 (((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-1094 *4 *5 *6)) (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *3))
-   (-4 *3 (-1100 *4 *5 *6 *7))))
+  (|partial| -12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-1086 *4 *5 *6)) (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *3))
+   (-4 *3 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-1094 *4 *5 *6)) (-5 *2 (-114)) (-5 *1 (-1136 *4 *5 *6 *7 *3))
-   (-4 *3 (-1100 *4 *5 *6 *7))))) 
+  (|partial| -12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-1086 *4 *5 *6)) (-5 *2 (-114)) (-5 *1 (-1128 *4 *5 *6 *7 *3))
+   (-4 *3 (-1092 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1136 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-1128 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1136 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-1128 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1136 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-1128 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-1100 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *3)) (-4 *3 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-114)) (-5 *1 (-1136 *4 *5 *6 *7 *3)) (-4 *3 (-1100 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-114)) (-5 *1 (-1128 *4 *5 *6 *7 *3)) (-4 *3 (-1092 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-1100 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *3)) (-4 *3 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-114)) (-5 *1 (-1136 *4 *5 *6 *7 *3)) (-4 *3 (-1100 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-114)) (-5 *1 (-1128 *4 *5 *6 *7 *3)) (-4 *3 (-1092 *4 *5 *6 *7))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *7)) (-4 *7 (-1100 *3 *4 *5 *6)) (-4 *3 (-464))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5))
-   (-5 *1 (-1017 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-661 *7)) (-4 *7 (-1092 *3 *4 *5 *6)) (-4 *3 (-464))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-1086 *3 *4 *5))
+   (-5 *1 (-1009 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-661 *7)) (-4 *7 (-1100 *3 *4 *5 *6)) (-4 *3 (-464))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5))
-   (-5 *1 (-1136 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-661 *7)) (-4 *7 (-1092 *3 *4 *5 *6)) (-4 *3 (-464))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-1086 *3 *4 *5))
+   (-5 *1 (-1128 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-114)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-1100 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-114)) (-5 *1 (-1009 *4 *5 *6 *7 *3)) (-4 *3 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-114)) (-5 *1 (-1136 *4 *5 *6 *7 *3)) (-4 *3 (-1100 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-114)) (-5 *1 (-1128 *4 *5 *6 *7 *3)) (-4 *3 (-1092 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5))
-   (-5 *2 (-1302)) (-5 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *7 (-1100 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-1086 *3 *4 *5))
+   (-5 *2 (-1294)) (-5 *1 (-1009 *3 *4 *5 *6 *7)) (-4 *7 (-1092 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5))
-   (-5 *2 (-1302)) (-5 *1 (-1136 *3 *4 *5 *6 *7)) (-4 *7 (-1100 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-1086 *3 *4 *5))
+   (-5 *2 (-1294)) (-5 *1 (-1128 *3 *4 *5 *6 *7)) (-4 *7 (-1092 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1188)) (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-1094 *4 *5 *6)) (-5 *2 (-1302)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1180)) (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-1086 *4 *5 *6)) (-5 *2 (-1294)) (-5 *1 (-1009 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1188)) (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-1094 *4 *5 *6)) (-5 *2 (-1302)) (-5 *1 (-1136 *4 *5 *6 *7 *8))
-   (-4 *8 (-1100 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1180)) (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-1086 *4 *5 *6)) (-5 *2 (-1294)) (-5 *1 (-1128 *4 *5 *6 *7 *8))
+   (-4 *8 (-1092 *4 *5 *6 *7))))) 
 (((*1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-1206)) (-5 *3 (-446)) (-4 *5 (-1130)) (-5 *1 (-1135 *5 *4))
+  (-12 (-5 *2 (-1198)) (-5 *3 (-446)) (-4 *5 (-1122)) (-5 *1 (-1127 *5 *4))
    (-4 *4 (-433 *5))))) 
-(((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1103))))
+(((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1095))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1133 *3 *4 *5 *6 *7)) (-4 *3 (-1130)) (-4 *4 (-1130))
-   (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130)) (-5 *2 (-114))))) 
+  (-12 (-4 *1 (-1125 *3 *4 *5 *6 *7)) (-4 *3 (-1122)) (-4 *4 (-1122))
+   (-4 *5 (-1122)) (-4 *6 (-1122)) (-4 *7 (-1122)) (-5 *2 (-114))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1133 *3 *4 *5 *6 *7)) (-4 *3 (-1130)) (-4 *4 (-1130))
-   (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130)) (-5 *2 (-114))))) 
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 (((*1 *2 *1)
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- ((*1 *1 *2) (-12 (-5 *2 (-709 (-973 (-558)))) (-4 *1 (-398))))
- ((*1 *1 *2) (-12 (-5 *2 (-709 (-973 (-391)))) (-4 *1 (-398))))
+   (-14 *3 (-661 (-1198))) (-14 *4 (-661 (-1198)))))
+ ((*1 *1 *2) (-12 (-5 *2 (-709 (-419 (-965 (-558))))) (-4 *1 (-398))))
+ ((*1 *1 *2) (-12 (-5 *2 (-709 (-419 (-965 (-391))))) (-4 *1 (-398))))
+ ((*1 *1 *2) (-12 (-5 *2 (-709 (-965 (-558)))) (-4 *1 (-398))))
+ ((*1 *1 *2) (-12 (-5 *2 (-709 (-965 (-391)))) (-4 *1 (-398))))
  ((*1 *1 *2) (-12 (-5 *2 (-709 (-326 (-558)))) (-4 *1 (-398))))
  ((*1 *1 *2) (-12 (-5 *2 (-709 (-326 (-391)))) (-4 *1 (-398))))
- ((*1 *1 *2) (-12 (-5 *2 (-419 (-973 (-558)))) (-4 *1 (-409))))
- ((*1 *1 *2) (-12 (-5 *2 (-419 (-973 (-391)))) (-4 *1 (-409))))
- ((*1 *1 *2) (-12 (-5 *2 (-973 (-558))) (-4 *1 (-409))))
- ((*1 *1 *2) (-12 (-5 *2 (-973 (-391))) (-4 *1 (-409))))
+ ((*1 *1 *2) (-12 (-5 *2 (-419 (-965 (-558)))) (-4 *1 (-409))))
+ ((*1 *1 *2) (-12 (-5 *2 (-419 (-965 (-391)))) (-4 *1 (-409))))
+ ((*1 *1 *2) (-12 (-5 *2 (-965 (-558))) (-4 *1 (-409))))
+ ((*1 *1 *2) (-12 (-5 *2 (-965 (-391))) (-4 *1 (-409))))
  ((*1 *1 *2) (-12 (-5 *2 (-326 (-558))) (-4 *1 (-409))))
  ((*1 *1 *2) (-12 (-5 *2 (-326 (-391))) (-4 *1 (-409))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 (-419 (-973 (-558))))) (-4 *1 (-453))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 (-419 (-973 (-391))))) (-4 *1 (-453))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 (-973 (-558)))) (-4 *1 (-453))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 (-973 (-391)))) (-4 *1 (-453))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 (-326 (-558)))) (-4 *1 (-453))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 (-326 (-391)))) (-4 *1 (-453))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1288 (-419 (-965 (-558))))) (-4 *1 (-453))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1288 (-419 (-965 (-391))))) (-4 *1 (-453))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1288 (-965 (-558)))) (-4 *1 (-453))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1288 (-965 (-391)))) (-4 *1 (-453))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1288 (-326 (-558)))) (-4 *1 (-453))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1288 (-326 (-391)))) (-4 *1 (-453))))
  ((*1 *2 *1)
   (-12
    (-5 *2
     (-3
      (|:| |nia|
-          (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-           (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+          (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+           (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
            (|:| |relerr| (-229))))
      (|:| |mdnia|
-          (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229)))))
+          (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229)))))
            (|:| |abserr| (-229)) (|:| |relerr| (-229))))))
    (-5 *1 (-789))))
  ((*1 *2 *1)
   (-12
    (-5 *2
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *1 (-830))))
@@ -6758,12 +6757,12 @@
    (-5 *2
     (-3
      (|:| |noa|
-          (-2 (|:| |fn| (-326 (-229))) (|:| -3943 (-661 (-229)))
-           (|:| |lb| (-661 (-863 (-229)))) (|:| |cf| (-661 (-326 (-229))))
-           (|:| |ub| (-661 (-863 (-229))))))
+          (-2 (|:| |fn| (-326 (-229))) (|:| -3866 (-661 (-229)))
+           (|:| |lb| (-661 (-855 (-229)))) (|:| |cf| (-661 (-326 (-229))))
+           (|:| |ub| (-661 (-855 (-229))))))
      (|:| |lsa|
-          (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3943 (-661 (-229)))))))
-   (-5 *1 (-862))))
+          (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3866 (-661 (-229)))))))
+   (-5 *1 (-854))))
  ((*1 *2 *1)
   (-12
    (-5 *2
@@ -6773,802 +6772,802 @@
            (-2 (|:| |start| (-229)) (|:| |finish| (-229)) (|:| |grid| (-791))
             (|:| |boundaryType| (-558)) (|:| |dStart| (-709 (-229)))
             (|:| |dFinish| (-709 (-229))))))
-     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1188))
+     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1180))
      (|:| |tol| (-229))))
-   (-5 *1 (-923))))
- ((*1 *1 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-1078))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-4 *1 (-1005 *3 *4 *5 *6))))
- ((*1 *2 *1) (-12 (-4 *1 (-1067 *2)) (-4 *2 (-1246))))
- ((*1 *1 *2)
-  (-4034
-   (-12 (-5 *2 (-973 *3))
-    (-12 (-3036 (-4 *3 (-38 (-419 (-558))))) (-3036 (-4 *3 (-38 (-558))))
-     (-4 *5 (-631 (-1206))))
-    (-4 *3 (-1078)) (-4 *1 (-1094 *3 *4 *5)) (-4 *4 (-815)) (-4 *5 (-869)))
-   (-12 (-5 *2 (-973 *3))
-    (-12 (-3036 (-4 *3 (-557))) (-3036 (-4 *3 (-38 (-419 (-558)))))
-     (-4 *3 (-38 (-558))) (-4 *5 (-631 (-1206))))
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-   (-12 (-5 *2 (-973 *3))
-    (-12 (-3036 (-4 *3 (-1020 (-558)))) (-4 *3 (-38 (-419 (-558))))
-     (-4 *5 (-631 (-1206))))
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- ((*1 *1 *2)
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-    (-4 *3 (-1078)) (-4 *4 (-815)) (-4 *5 (-869)))
-   (-12 (-5 *2 (-973 (-558))) (-4 *1 (-1094 *3 *4 *5))
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-    (-4 *4 (-815)) (-4 *5 (-869)))))
- ((*1 *1 *2)
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-   (-4 *3 (-38 (-419 (-558)))) (-4 *5 (-631 (-1206))) (-4 *3 (-1078))
-   (-4 *4 (-815)) (-4 *5 (-869))))) 
+   (-5 *1 (-915))))
+ ((*1 *1 *2)
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-1070))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-4 *1 (-997 *3 *4 *5 *6))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1059 *2)) (-4 *2 (-1238))))
+ ((*1 *1 *2)
+  (-3957
+   (-12 (-5 *2 (-965 *3))
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+   (-12 (-5 *2 (-965 *3))
+    (-12 (-2959 (-4 *3 (-557))) (-2959 (-4 *3 (-38 (-419 (-558)))))
+     (-4 *3 (-38 (-558))) (-4 *5 (-631 (-1198))))
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+   (-12 (-5 *2 (-965 *3))
+    (-12 (-2959 (-4 *3 (-1012 (-558)))) (-4 *3 (-38 (-419 (-558))))
+     (-4 *5 (-631 (-1198))))
+    (-4 *3 (-1070)) (-4 *1 (-1086 *3 *4 *5)) (-4 *4 (-815)) (-4 *5 (-861)))))
+ ((*1 *1 *2)
+  (-3957
+   (-12 (-5 *2 (-965 (-558))) (-4 *1 (-1086 *3 *4 *5))
+    (-12 (-2959 (-4 *3 (-38 (-419 (-558))))) (-4 *3 (-38 (-558)))
+     (-4 *5 (-631 (-1198))))
+    (-4 *3 (-1070)) (-4 *4 (-815)) (-4 *5 (-861)))
+   (-12 (-5 *2 (-965 (-558))) (-4 *1 (-1086 *3 *4 *5))
+    (-12 (-4 *3 (-38 (-419 (-558)))) (-4 *5 (-631 (-1198)))) (-4 *3 (-1070))
+    (-4 *4 (-815)) (-4 *5 (-861)))))
+ ((*1 *1 *2)
+  (-12 (-5 *2 (-965 (-419 (-558)))) (-4 *1 (-1086 *3 *4 *5))
+   (-4 *3 (-38 (-419 (-558)))) (-4 *5 (-631 (-1198))) (-4 *3 (-1070))
+   (-4 *4 (-815)) (-4 *5 (-861))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-569))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-569))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-569))))
  ((*1 *1 *1 *2)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-569))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-569))))
  ((*1 *1 *1 *2)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-569))))) 
 (((*1 *2 *1 *1)
   (-12
    (-5 *2
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-   (-5 *1 (-801 *3)) (-4 *3 (-569)) (-4 *3 (-1078))))
+    (-2 (|:| -3562 (-801 *3)) (|:| |coef1| (-801 *3)) (|:| |coef2| (-801 *3))))
+   (-5 *1 (-801 *3)) (-4 *3 (-569)) (-4 *3 (-1070))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *3 (-569)) (-4 *3 (-1078)) (-4 *4 (-815)) (-4 *5 (-869))
-   (-5 *2 (-2 (|:| -3639 *1) (|:| |coef1| *1) (|:| |coef2| *1)))
-   (-4 *1 (-1094 *3 *4 *5))))) 
+  (-12 (-4 *3 (-569)) (-4 *3 (-1070)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-5 *2 (-2 (|:| -3562 *1) (|:| |coef1| *1) (|:| |coef2| *1)))
+   (-4 *1 (-1086 *3 *4 *5))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-2 (|:| -3639 (-801 *3)) (|:| |coef1| (-801 *3))))
-   (-5 *1 (-801 *3)) (-4 *3 (-569)) (-4 *3 (-1078))))
+  (-12 (-5 *2 (-2 (|:| -3562 (-801 *3)) (|:| |coef1| (-801 *3))))
+   (-5 *1 (-801 *3)) (-4 *3 (-569)) (-4 *3 (-1070))))
  ((*1 *2 *1 *1)
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-   (-5 *2 (-2 (|:| -3639 *1) (|:| |coef1| *1))) (-4 *1 (-1094 *3 *4 *5))))) 
+  (-12 (-4 *3 (-569)) (-4 *3 (-1070)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-5 *2 (-2 (|:| -3562 *1) (|:| |coef1| *1))) (-4 *1 (-1086 *3 *4 *5))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-2 (|:| -3639 (-801 *3)) (|:| |coef2| (-801 *3))))
-   (-5 *1 (-801 *3)) (-4 *3 (-569)) (-4 *3 (-1078))))
+  (-12 (-5 *2 (-2 (|:| -3562 (-801 *3)) (|:| |coef2| (-801 *3))))
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  ((*1 *2 *1 *1)
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-   (-5 *2 (-2 (|:| -3639 *1) (|:| |coef2| *1))) (-4 *1 (-1094 *3 *4 *5))))) 
+  (-12 (-4 *3 (-569)) (-4 *3 (-1070)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-5 *2 (-2 (|:| -3562 *1) (|:| |coef2| *1))) (-4 *1 (-1086 *3 *4 *5))))) 
 (((*1 *2 *1 *1)
-  (-12 (-4 *3 (-569)) (-4 *3 (-1078)) (-4 *4 (-815)) (-4 *5 (-869))
-   (-5 *2 (-661 *1)) (-4 *1 (-1094 *3 *4 *5))))) 
+  (-12 (-4 *3 (-569)) (-4 *3 (-1070)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-5 *2 (-661 *1)) (-4 *1 (-1086 *3 *4 *5))))) 
 (((*1 *1 *1 *1 *2)
-  (-12 (-5 *2 (-791)) (-4 *1 (-1094 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-4 *3 (-569))))) 
+  (-12 (-5 *2 (-791)) (-4 *1 (-1086 *3 *4 *5)) (-4 *3 (-1070)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-4 *3 (-569))))) 
 (((*1 *1 *1 *1 *1 *2)
-  (-12 (-5 *2 (-791)) (-4 *1 (-1094 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-4 *3 (-569))))) 
+  (-12 (-5 *2 (-791)) (-4 *1 (-1086 *3 *4 *5)) (-4 *3 (-1070)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-4 *3 (-569))))) 
 (((*1 *1 *1 *1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-569))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-661 *1)) (-4 *1 (-464))))
  ((*1 *1 *1 *1) (-4 *1 (-464)))
- ((*1 *2 *3) (-12 (-5 *3 (-661 *2)) (-5 *1 (-498 *2)) (-4 *2 (-1272 (-558)))))
- ((*1 *2 *2 *2 *3) (-12 (-5 *3 (-558)) (-5 *1 (-716 *2)) (-4 *2 (-1272 *3))))
+ ((*1 *2 *3) (-12 (-5 *3 (-661 *2)) (-5 *1 (-498 *2)) (-4 *2 (-1264 (-558)))))
+ ((*1 *2 *2 *2 *3) (-12 (-5 *3 (-558)) (-5 *1 (-716 *2)) (-4 *2 (-1264 *3))))
  ((*1 *1 *1 *1) (-5 *1 (-791)))
  ((*1 *2 *2 *2)
-  (-12 (-4 *3 (-815)) (-4 *4 (-869)) (-4 *5 (-319)) (-5 *1 (-943 *3 *4 *5 *2))
-   (-4 *2 (-977 *5 *3 *4))))
+  (-12 (-4 *3 (-815)) (-4 *4 (-861)) (-4 *5 (-319)) (-5 *1 (-935 *3 *4 *5 *2))
+   (-4 *2 (-969 *5 *3 *4))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-977 *6 *4 *5)) (-5 *1 (-943 *4 *5 *6 *2))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-319))))
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-969 *6 *4 *5)) (-5 *1 (-935 *4 *5 *6 *2))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-319))))
  ((*1 *2 *2 *2)
-  (-12 (-5 *2 (-1200 *6)) (-4 *6 (-977 *5 *3 *4)) (-4 *3 (-815)) (-4 *4 (-869))
-   (-4 *5 (-319)) (-5 *1 (-943 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-1192 *6)) (-4 *6 (-969 *5 *3 *4)) (-4 *3 (-815)) (-4 *4 (-861))
+   (-4 *5 (-319)) (-5 *1 (-935 *3 *4 *5 *6))))
  ((*1 *2 *3)
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- ((*1 *1 *1 *1) (-5 *1 (-946)))
+  (-12 (-5 *3 (-661 (-1192 *7))) (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-319))
+   (-5 *2 (-1192 *7)) (-5 *1 (-935 *4 *5 *6 *7)) (-4 *7 (-969 *6 *4 *5))))
+ ((*1 *1 *1 *1) (-5 *1 (-938)))
  ((*1 *2 *2 *2)
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  ((*1 *2 *2 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
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    (-4 *2 (-464))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
    (-4 *2 (-464))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
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 (((*1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
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 (((*1 *1 *1)
-  (-12 (-4 *1 (-1094 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-815)) (-4 *4 (-869))
+  (-12 (-4 *1 (-1086 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-815)) (-4 *4 (-861))
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+(((*1 *1 *1 *2) (-12 (-5 *2 (-1198)) (-5 *1 (-1084))))) 
+(((*1 *1) (-5 *1 (-1084)))) 
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-  (-12 (-4 *1 (-1082 *3 *4 *5 *6 *7)) (-4 *5 (-1078)) (-4 *6 (-245 *4 *5))
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 (((*1 *2 *1)
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   (-12 (-5 *3 (-558)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-385 *2))
-   (-4 *5 (-385 *2)) (-4 *2 (-1246))))
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-  (-12 (-5 *3 (-558)) (-4 *1 (-1082 *4 *5 *2 *6 *7)) (-4 *6 (-245 *5 *2))
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+  (-12 (-5 *3 (-558)) (-4 *1 (-1074 *4 *5 *2 *6 *7)) (-4 *6 (-245 *5 *2))
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 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-558)) (-4 *1 (-57 *4 *2 *5)) (-4 *4 (-1246)) (-4 *5 (-385 *4))
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    (-4 *2 (-385 *4))))
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-  (-12 (-5 *3 (-558)) (-4 *1 (-1082 *4 *5 *6 *2 *7)) (-4 *6 (-1078))
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 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-558)) (-4 *1 (-57 *4 *5 *2)) (-4 *4 (-1246)) (-4 *5 (-385 *4))
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-  (-12 (-5 *3 (-558)) (-4 *1 (-1082 *4 *5 *6 *7 *2)) (-4 *6 (-1078))
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  ((*1 *1 *1)
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    (-4 *5 (-175))))
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   (-12 (-4 *4 (-376)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4)) (-5 *2 (-791))
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    (-5 *1 (-688 *5))))
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-  (-12 (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-385 *3))
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   (-12 (-4 *4 (-569)) (-4 *4 (-175)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))
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 (((*1 *2 *3)
   (-12 (-4 *4 (-376)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4)) (-5 *2 (-791))
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  ((*1 *2 *1)
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   (-12 (-4 *4 (-569)) (-4 *4 (-175)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))
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 (((*1 *2 *3)
-  (-12 (|has| *6 (-6 -4503)) (-4 *4 (-376)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))
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 (((*1 *2 *2 *3 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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+  (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-558))) (-5 *1 (-1068))))) 
 (((*1 *1 *1 *1) (-4 *1 (-145)))
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- ((*1 *1 *1 *1) (-5 *1 (-885)))
+ ((*1 *1 *1 *1) (-5 *1 (-877)))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 |RationalNumber|) (-5 *2 (-1 (-558))) (-5 *1 (-1076))
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 (((*1 *2 *3)
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 (((*1 *1 *2)
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    (-5 *1 (-331 *3 *4 *5))))
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-(((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1070))))) 
-(((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1070))))) 
-(((*1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-1070))))) 
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 (((*1 *2 *3 *4 *2)
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-   (-4 *2 (-13 (-433 *5) (-27) (-1232)))
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-   (-5 *1 (-573 *5 *2 *6)) (-4 *6 (-1130))))
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    (-4 *2
     (-13 (-376)
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 (((*1 *2 *1 *3)
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  ((*1 *2 *1)
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+(((*1 *2 *1 *2) (-12 (-5 *1 (-1047 *2)) (-4 *2 (-1238))))) 
 (((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-114))))
- ((*1 *1 *2 *2) (-12 (-5 *1 (-305 *2)) (-4 *2 (-1246))))
+ ((*1 *1 *2 *2) (-12 (-5 *1 (-305 *2)) (-4 *2 (-1238))))
  ((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-446))))
- ((*1 *1 *1 *1) (-5 *1 (-885)))
- ((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1055 *3)) (-4 *3 (-1246))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-1054 *3 *2)) (-4 *2 (-678 *3))))
+ ((*1 *1 *1 *1) (-5 *1 (-877)))
+ ((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1047 *3)) (-4 *3 (-1238))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-1046 *3 *2)) (-4 *2 (-678 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-376)) (-5 *2 (-2 (|:| -3761 *3) (|:| -2978 (-661 *5))))
-   (-5 *1 (-1054 *5 *3)) (-5 *4 (-661 *5)) (-4 *3 (-678 *5))))) 
+  (-12 (-4 *5 (-376)) (-5 *2 (-2 (|:| -3684 *3) (|:| -2909 (-661 *5))))
+   (-5 *1 (-1046 *5 *3)) (-5 *4 (-661 *5)) (-4 *3 (-678 *5))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1090 (-1053 *4) (-1200 (-1053 *4)))) (-5 *3 (-885))
-   (-5 *1 (-1053 *4)) (-4 *4 (-13 (-868) (-376) (-1049)))))) 
+  (-12 (-5 *2 (-1082 (-1045 *4) (-1192 (-1045 *4)))) (-5 *3 (-877))
+   (-5 *1 (-1045 *4)) (-4 *4 (-13 (-860) (-376) (-1041)))))) 
 (((*1 *2 *1)
-  (|partial| -12 (-5 *2 (-1090 (-1053 *3) (-1200 (-1053 *3))))
-   (-5 *1 (-1053 *3)) (-4 *3 (-13 (-868) (-376) (-1049)))))) 
+  (|partial| -12 (-5 *2 (-1082 (-1045 *3) (-1192 (-1045 *3))))
+   (-5 *1 (-1045 *3)) (-4 *3 (-13 (-860) (-376) (-1041)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-661 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558))))))
-   (-5 *1 (-1050 *3)) (-4 *3 (-1272 (-558)))))
+  (-12 (-5 *2 (-661 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558))))))
+   (-5 *1 (-1042 *3)) (-4 *3 (-1264 (-558)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *2 (-661 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558))))))
-   (-5 *1 (-1050 *3)) (-4 *3 (-1272 (-558)))
-   (-5 *4 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558)))))))
+  (-12 (-5 *2 (-661 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558))))))
+   (-5 *1 (-1042 *3)) (-4 *3 (-1264 (-558)))
+   (-5 *4 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558)))))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *2 (-661 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558))))))
-   (-5 *1 (-1050 *3)) (-4 *3 (-1272 (-558))) (-5 *4 (-419 (-558)))))
+  (-12 (-5 *2 (-661 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558))))))
+   (-5 *1 (-1042 *3)) (-4 *3 (-1264 (-558))) (-5 *4 (-419 (-558)))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *5 (-419 (-558))) (-5 *2 (-661 (-2 (|:| -3617 *5) (|:| -3616 *5))))
-   (-5 *1 (-1050 *3)) (-4 *3 (-1272 (-558)))
-   (-5 *4 (-2 (|:| -3617 *5) (|:| -3616 *5)))))
+  (-12 (-5 *5 (-419 (-558))) (-5 *2 (-661 (-2 (|:| -3540 *5) (|:| -3539 *5))))
+   (-5 *1 (-1042 *3)) (-4 *3 (-1264 (-558)))
+   (-5 *4 (-2 (|:| -3540 *5) (|:| -3539 *5)))))
  ((*1 *2 *3)
-  (-12 (-5 *2 (-661 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558))))))
-   (-5 *1 (-1051 *3)) (-4 *3 (-1272 (-419 (-558))))))
+  (-12 (-5 *2 (-661 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558))))))
+   (-5 *1 (-1043 *3)) (-4 *3 (-1264 (-419 (-558))))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *2 (-661 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558))))))
-   (-5 *1 (-1051 *3)) (-4 *3 (-1272 (-419 (-558))))
-   (-5 *4 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558)))))))
+  (-12 (-5 *2 (-661 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558))))))
+   (-5 *1 (-1043 *3)) (-4 *3 (-1264 (-419 (-558))))
+   (-5 *4 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558)))))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-419 (-558))) (-5 *2 (-661 (-2 (|:| -3617 *4) (|:| -3616 *4))))
-   (-5 *1 (-1051 *3)) (-4 *3 (-1272 *4))))
+  (-12 (-5 *4 (-419 (-558))) (-5 *2 (-661 (-2 (|:| -3540 *4) (|:| -3539 *4))))
+   (-5 *1 (-1043 *3)) (-4 *3 (-1264 *4))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *5 (-419 (-558))) (-5 *2 (-661 (-2 (|:| -3617 *5) (|:| -3616 *5))))
-   (-5 *1 (-1051 *3)) (-4 *3 (-1272 *5))
-   (-5 *4 (-2 (|:| -3617 *5) (|:| -3616 *5)))))) 
+  (-12 (-5 *5 (-419 (-558))) (-5 *2 (-661 (-2 (|:| -3540 *5) (|:| -3539 *5))))
+   (-5 *1 (-1043 *3)) (-4 *3 (-1264 *5))
+   (-5 *4 (-2 (|:| -3540 *5) (|:| -3539 *5)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558))))))
-   (-5 *2 (-661 (-419 (-558)))) (-5 *1 (-1050 *4)) (-4 *4 (-1272 (-558)))))) 
+  (-12 (-5 *3 (-661 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558))))))
+   (-5 *2 (-661 (-419 (-558)))) (-5 *1 (-1042 *4)) (-4 *4 (-1264 (-558)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558)))))
-   (-5 *2 (-419 (-558))) (-5 *1 (-1050 *4)) (-4 *4 (-1272 (-558)))))) 
+  (-12 (-5 *3 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558)))))
+   (-5 *2 (-419 (-558))) (-5 *1 (-1042 *4)) (-4 *4 (-1264 (-558)))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1296 *6)) (-5 *4 (-1296 (-558))) (-5 *5 (-558)) (-4 *6 (-1130))
-   (-5 *2 (-1 *6)) (-5 *1 (-1046 *6))))) 
+  (-12 (-5 *3 (-1288 *6)) (-5 *4 (-1288 (-558))) (-5 *5 (-558)) (-4 *6 (-1122))
+   (-5 *2 (-1 *6)) (-5 *1 (-1038 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-2 (|:| -3899 *4) (|:| -1662 (-558))))) (-4 *4 (-1130))
-   (-5 *2 (-1 *4)) (-5 *1 (-1046 *4))))) 
+  (-12 (-5 *3 (-661 (-2 (|:| -3822 *4) (|:| -1654 (-558))))) (-4 *4 (-1122))
+   (-5 *2 (-1 *4)) (-5 *1 (-1038 *4))))) 
 (((*1 *2 *3 *3 *3)
-  (|partial| -12 (-4 *4 (-13 (-376) (-149) (-1067 (-558)))) (-4 *5 (-1272 *4))
-   (-5 *2 (-661 (-419 *5))) (-5 *1 (-1045 *4 *5)) (-5 *3 (-419 *5))))) 
+  (|partial| -12 (-4 *4 (-13 (-376) (-149) (-1059 (-558)))) (-4 *5 (-1264 *4))
+   (-5 *2 (-661 (-419 *5))) (-5 *1 (-1037 *4 *5)) (-5 *3 (-419 *5))))) 
 (((*1 *2 *3 *3 *3 *4)
-  (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558))))
+  (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558))))
    (-5 *2
     (-2 (|:| |a| *6) (|:| |b| (-419 *6)) (|:| |h| *6) (|:| |c1| (-419 *6))
-     (|:| |c2| (-419 *6)) (|:| -3573 *6)))
-   (-5 *1 (-1045 *5 *6)) (-5 *3 (-419 *6))))) 
+     (|:| |c2| (-419 *6)) (|:| -3496 *6)))
+   (-5 *1 (-1037 *5 *6)) (-5 *3 (-419 *6))))) 
 (((*1 *2 *3 *3 *3 *4 *5)
-  (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1272 *6))
-   (-4 *6 (-13 (-376) (-149) (-1067 *4))) (-5 *4 (-558))
+  (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1264 *6))
+   (-4 *6 (-13 (-376) (-149) (-1059 *4))) (-5 *4 (-558))
    (-5 *2
     (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-114))))
-     (|:| -3761
+     (|:| -3684
           (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3)
            (|:| |beta| *3)))))
-   (-5 *1 (-1044 *6 *3))))) 
+   (-5 *1 (-1036 *6 *3))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-13 (-376) (-149) (-1067 (-558)))) (-4 *5 (-1272 *4))
+  (-12 (-4 *4 (-13 (-376) (-149) (-1059 (-558)))) (-4 *5 (-1264 *4))
    (-5 *2 (-2 (|:| |ans| (-419 *5)) (|:| |nosol| (-114))))
-   (-5 *1 (-1044 *4 *5)) (-5 *3 (-419 *5))))) 
+   (-5 *1 (-1036 *4 *5)) (-5 *3 (-419 *5))))) 
 (((*1 *2 *3 *3 *4)
-  (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558))))
+  (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558))))
    (-5 *2
-    (-2 (|:| |a| *6) (|:| |b| (-419 *6)) (|:| |c| (-419 *6)) (|:| -3573 *6)))
-   (-5 *1 (-1044 *5 *6)) (-5 *3 (-419 *6))))) 
+    (-2 (|:| |a| *6) (|:| |b| (-419 *6)) (|:| |c| (-419 *6)) (|:| -3496 *6)))
+   (-5 *1 (-1036 *5 *6)) (-5 *3 (-419 *6))))) 
 (((*1 *2 *3 *4 *4 *4 *5 *6 *7)
-  (|partial| -12 (-5 *5 (-1206))
+  (|partial| -12 (-5 *5 (-1198))
    (-5 *6
     (-1
      (-3
@@ -7576,12 +7575,12 @@
        (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *4) (|:| |logand| *4)))))
       "failed")
      *4 (-661 *4)))
-   (-5 *7 (-1 (-3 (-2 (|:| -2359 *4) (|:| |coeff| *4)) "failed") *4 *4))
-   (-4 *4 (-13 (-1232) (-27) (-433 *8)))
-   (-4 *8 (-13 (-464) (-149) (-1067 *3) (-658 *3))) (-5 *3 (-558))
-   (-5 *2 (-661 *4)) (-5 *1 (-1043 *8 *4))))) 
+   (-5 *7 (-1 (-3 (-2 (|:| -2351 *4) (|:| |coeff| *4)) "failed") *4 *4))
+   (-4 *4 (-13 (-1224) (-27) (-433 *8)))
+   (-4 *8 (-13 (-464) (-149) (-1059 *3) (-658 *3))) (-5 *3 (-558))
+   (-5 *2 (-661 *4)) (-5 *1 (-1035 *8 *4))))) 
 (((*1 *2 *3 *4 *4 *5 *6 *7)
-  (-12 (-5 *5 (-1206))
+  (-12 (-5 *5 (-1198))
    (-5 *6
     (-1
      (-3
@@ -7589,35 +7588,35 @@
        (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *4) (|:| |logand| *4)))))
       "failed")
      *4 (-661 *4)))
-   (-5 *7 (-1 (-3 (-2 (|:| -2359 *4) (|:| |coeff| *4)) "failed") *4 *4))
-   (-4 *4 (-13 (-1232) (-27) (-433 *8)))
-   (-4 *8 (-13 (-464) (-149) (-1067 *3) (-658 *3))) (-5 *3 (-558))
-   (-5 *2 (-2 (|:| |ans| *4) (|:| -3616 *4) (|:| |sol?| (-114))))
-   (-5 *1 (-1042 *8 *4))))) 
+   (-5 *7 (-1 (-3 (-2 (|:| -2351 *4) (|:| |coeff| *4)) "failed") *4 *4))
+   (-4 *4 (-13 (-1224) (-27) (-433 *8)))
+   (-4 *8 (-13 (-464) (-149) (-1059 *3) (-658 *3))) (-5 *3 (-558))
+   (-5 *2 (-2 (|:| |ans| *4) (|:| -3539 *4) (|:| |sol?| (-114))))
+   (-5 *1 (-1034 *8 *4))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-661 (-1206))) (-14 *3 (-661 (-1206)))
+  (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-661 (-1198))) (-14 *3 (-661 (-1198)))
    (-4 *4 (-401))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-892 *3)) (-5 *2 (-558))))
- ((*1 *1 *1) (-4 *1 (-1031))) ((*1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-1041))))
- ((*1 *1 *2) (-12 (-5 *2 (-419 (-558))) (-4 *1 (-1041))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-1041)) (-5 *2 (-946))))
- ((*1 *1 *1) (-4 *1 (-1041)))) 
-(((*1 *2 *1) (|partial| -12 (-4 *1 (-1041)) (-5 *2 (-885))))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-1200 *1)) (-4 *1 (-1041))))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-1200 *1)) (-4 *1 (-1041))))) 
-(((*1 *1 *1 *2) (-12 (-4 *1 (-1041)) (-5 *2 (-885))))) 
-(((*1 *1 *1 *2) (-12 (-4 *1 (-1041)) (-5 *2 (-885))))) 
-(((*1 *2 *1) (-12 (-4 *3 (-1246)) (-5 *2 (-661 *1)) (-4 *1 (-1039 *3))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-1039 *3)) (-4 *3 (-1246)) (-5 *2 (-661 *3))))) 
-(((*1 *2 *1 *1) (-12 (-4 *1 (-1039 *3)) (-4 *3 (-1246)) (-5 *2 (-558))))) 
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-884 *3)) (-5 *2 (-558))))
+ ((*1 *1 *1) (-4 *1 (-1023))) ((*1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-1033))))
+ ((*1 *1 *2) (-12 (-5 *2 (-419 (-558))) (-4 *1 (-1033))))
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-1033)) (-5 *2 (-938))))
+ ((*1 *1 *1) (-4 *1 (-1033)))) 
+(((*1 *2 *1) (|partial| -12 (-4 *1 (-1033)) (-5 *2 (-877))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-1192 *1)) (-4 *1 (-1033))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-1192 *1)) (-4 *1 (-1033))))) 
+(((*1 *1 *1 *2) (-12 (-4 *1 (-1033)) (-5 *2 (-877))))) 
+(((*1 *1 *1 *2) (-12 (-4 *1 (-1033)) (-5 *2 (-877))))) 
+(((*1 *2 *1) (-12 (-4 *3 (-1238)) (-5 *2 (-661 *1)) (-4 *1 (-1031 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-1031 *3)) (-4 *3 (-1238)) (-5 *2 (-661 *3))))) 
+(((*1 *2 *1 *1) (-12 (-4 *1 (-1031 *3)) (-4 *3 (-1238)) (-5 *2 (-558))))) 
 (((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1039 *3)) (-4 *3 (-1246)) (-4 *3 (-1130)) (-5 *2 (-114))))) 
+  (-12 (-4 *1 (-1031 *3)) (-4 *3 (-1238)) (-4 *3 (-1122)) (-5 *2 (-114))))) 
 (((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1039 *3)) (-4 *3 (-1246)) (-4 *3 (-1130)) (-5 *2 (-114))))) 
+  (-12 (-4 *1 (-1031 *3)) (-4 *3 (-1238)) (-4 *3 (-1122)) (-5 *2 (-114))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-661 *1)) (|has| *1 (-6 -4503)) (-4 *1 (-1039 *3))
-   (-4 *3 (-1246))))) 
-(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4503)) (-4 *1 (-1039 *2)) (-4 *2 (-1246))))) 
+  (-12 (-5 *2 (-661 *1)) (|has| *1 (-6 -4426)) (-4 *1 (-1031 *3))
+   (-4 *3 (-1238))))) 
+(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -4426)) (-4 *1 (-1031 *2)) (-4 *2 (-1238))))) 
 (((*1 *2 *1)
   (|partial| -12 (-4 *1 (-168 *3)) (-4 *3 (-175)) (-4 *3 (-557))
    (-5 *2 (-419 (-558)))))
@@ -7629,16 +7628,16 @@
   (|partial| -12 (-4 *1 (-818 *3)) (-4 *3 (-175)) (-4 *3 (-557))
    (-5 *2 (-419 (-558)))))
  ((*1 *2 *1)
-  (|partial| -12 (-5 *2 (-419 (-558))) (-5 *1 (-853 *3)) (-4 *3 (-557))
-   (-4 *3 (-1130))))
+  (|partial| -12 (-5 *2 (-419 (-558))) (-5 *1 (-845 *3)) (-4 *3 (-557))
+   (-4 *3 (-1122))))
  ((*1 *2 *1)
-  (|partial| -12 (-5 *2 (-419 (-558))) (-5 *1 (-863 *3)) (-4 *3 (-557))
-   (-4 *3 (-1130))))
+  (|partial| -12 (-5 *2 (-419 (-558))) (-5 *1 (-855 *3)) (-4 *3 (-557))
+   (-4 *3 (-1122))))
  ((*1 *2 *1)
-  (|partial| -12 (-4 *1 (-1027 *3)) (-4 *3 (-175)) (-4 *3 (-557))
+  (|partial| -12 (-4 *1 (-1019 *3)) (-4 *3 (-175)) (-4 *3 (-557))
    (-5 *2 (-419 (-558)))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *2 (-419 (-558))) (-5 *1 (-1037 *3)) (-4 *3 (-1067 *2))))) 
+  (|partial| -12 (-5 *2 (-419 (-558))) (-5 *1 (-1029 *3)) (-4 *3 (-1059 *2))))) 
 (((*1 *2 *1)
   (-12 (-4 *1 (-168 *3)) (-4 *3 (-175)) (-4 *3 (-557)) (-5 *2 (-114))))
  ((*1 *2 *1)
@@ -7647,13 +7646,13 @@
  ((*1 *2 *1)
   (-12 (-4 *1 (-818 *3)) (-4 *3 (-175)) (-4 *3 (-557)) (-5 *2 (-114))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-114)) (-5 *1 (-853 *3)) (-4 *3 (-557)) (-4 *3 (-1130))))
+  (-12 (-5 *2 (-114)) (-5 *1 (-845 *3)) (-4 *3 (-557)) (-4 *3 (-1122))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-114)) (-5 *1 (-863 *3)) (-4 *3 (-557)) (-4 *3 (-1130))))
+  (-12 (-5 *2 (-114)) (-5 *1 (-855 *3)) (-4 *3 (-557)) (-4 *3 (-1122))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1027 *3)) (-4 *3 (-175)) (-4 *3 (-557)) (-5 *2 (-114))))
+  (-12 (-4 *1 (-1019 *3)) (-4 *3 (-175)) (-4 *3 (-557)) (-5 *2 (-114))))
  ((*1 *2 *3)
-  (-12 (-5 *2 (-114)) (-5 *1 (-1037 *3)) (-4 *3 (-1067 (-419 (-558))))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-1029 *3)) (-4 *3 (-1059 (-419 (-558))))))) 
 (((*1 *2 *1)
   (-12 (-4 *1 (-168 *3)) (-4 *3 (-175)) (-4 *3 (-557)) (-5 *2 (-419 (-558)))))
  ((*1 *2 *1)
@@ -7662,1574 +7661,1574 @@
  ((*1 *2 *1)
   (-12 (-4 *1 (-818 *3)) (-4 *3 (-175)) (-4 *3 (-557)) (-5 *2 (-419 (-558)))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-419 (-558))) (-5 *1 (-853 *3)) (-4 *3 (-557)) (-4 *3 (-1130))))
+  (-12 (-5 *2 (-419 (-558))) (-5 *1 (-845 *3)) (-4 *3 (-557)) (-4 *3 (-1122))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-419 (-558))) (-5 *1 (-863 *3)) (-4 *3 (-557)) (-4 *3 (-1130))))
+  (-12 (-5 *2 (-419 (-558))) (-5 *1 (-855 *3)) (-4 *3 (-557)) (-4 *3 (-1122))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1027 *3)) (-4 *3 (-175)) (-4 *3 (-557)) (-5 *2 (-419 (-558)))))
- ((*1 *2 *3) (-12 (-5 *2 (-419 (-558))) (-5 *1 (-1037 *3)) (-4 *3 (-1067 *2))))) 
-(((*1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-1035))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-558)) (-5 *2 (-1302)) (-5 *1 (-1035))))) 
-(((*1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-1035))))
- ((*1 *2 *2) (-12 (-5 *2 (-558)) (-5 *1 (-1035))))) 
+  (-12 (-4 *1 (-1019 *3)) (-4 *3 (-175)) (-4 *3 (-557)) (-5 *2 (-419 (-558)))))
+ ((*1 *2 *3) (-12 (-5 *2 (-419 (-558))) (-5 *1 (-1029 *3)) (-4 *3 (-1059 *2))))) 
+(((*1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-1027))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-558)) (-5 *2 (-1294)) (-5 *1 (-1027))))) 
+(((*1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-1027))))
+ ((*1 *2 *2) (-12 (-5 *2 (-558)) (-5 *1 (-1027))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-558))) (-5 *4 (-558)) (-5 *2 (-51)) (-5 *1 (-1034))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-558))) (-5 *1 (-1033 *3)) (-14 *3 (-558))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1184 (-558))) (-5 *1 (-1033 *3)) (-14 *3 (-558))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-558))) (-5 *1 (-1033 *3)) (-14 *3 (-558))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-558))) (-5 *1 (-1033 *3)) (-14 *3 (-558))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 (-558))) (-5 *1 (-1033 *3)) (-14 *3 (-558))))) 
-(((*1 *1 *2 *2) (-12 (-5 *2 (-661 (-558))) (-5 *1 (-1033 *3)) (-14 *3 (-558))))) 
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+ ((*1 *2 *1) (-12 (-5 *2 (-159)) (-5 *1 (-888))))
+ ((*1 *2 *3) (-12 (-5 *3 (-962 *2)) (-5 *1 (-1003 *2)) (-4 *2 (-1070))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-159))))
- ((*1 *2 *3) (-12 (-5 *3 (-970 *2)) (-5 *1 (-1011 *2)) (-4 *2 (-1078))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-970 *2)) (-5 *1 (-1011 *2)) (-4 *2 (-1078))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-970 *2)) (-5 *1 (-1011 *2)) (-4 *2 (-1078))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-970 *2)) (-5 *1 (-1011 *2)) (-4 *2 (-1078))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-970 *2)) (-5 *1 (-1011 *2)) (-4 *2 (-1078))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-970 *2)) (-5 *1 (-1011 *2)) (-4 *2 (-1078))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-970 *2)) (-5 *1 (-1011 *2)) (-4 *2 (-1078))))) 
+ ((*1 *2 *3) (-12 (-5 *3 (-962 *2)) (-5 *1 (-1003 *2)) (-4 *2 (-1070))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-962 *2)) (-5 *1 (-1003 *2)) (-4 *2 (-1070))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-962 *2)) (-5 *1 (-1003 *2)) (-4 *2 (-1070))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-962 *2)) (-5 *1 (-1003 *2)) (-4 *2 (-1070))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-962 *2)) (-5 *1 (-1003 *2)) (-4 *2 (-1070))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-962 *2)) (-5 *1 (-1003 *2)) (-4 *2 (-1070))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-962 *2)) (-5 *1 (-1003 *2)) (-4 *2 (-1070))))) 
 (((*1 *2 *3 *4)
   (-12 (-4 *5 (-376))
-   (-5 *2 (-661 (-2 (|:| C (-709 *5)) (|:| |g| (-1296 *5)))))
-   (-5 *1 (-1007 *5)) (-5 *3 (-709 *5)) (-5 *4 (-1296 *5))))) 
-(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-558)) (-5 *3 (-946)) (-5 *1 (-719))))
+   (-5 *2 (-661 (-2 (|:| C (-709 *5)) (|:| |g| (-1288 *5))))) (-5 *1 (-999 *5))
+   (-5 *3 (-709 *5)) (-5 *4 (-1288 *5))))) 
+(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-558)) (-5 *3 (-938)) (-5 *1 (-719))))
  ((*1 *2 *2 *2 *3 *4)
   (-12 (-5 *2 (-709 *5)) (-5 *3 (-99 *5)) (-5 *4 (-1 *5 *5)) (-4 *5 (-376))
-   (-5 *1 (-1007 *5))))) 
+   (-5 *1 (-999 *5))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-977 *4 *5 *6)) (-4 *4 (-376)) (-4 *4 (-464))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *1 (-459 *4 *5 *6 *2))))
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-969 *4 *5 *6)) (-4 *4 (-376)) (-4 *4 (-464))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *1 (-459 *4 *5 *6 *2))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *4 (-99 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-376))
    (-5 *2 (-2 (|:| R (-709 *6)) (|:| A (-709 *6)) (|:| |Ainv| (-709 *6))))
-   (-5 *1 (-1007 *6)) (-5 *3 (-709 *6))))) 
+   (-5 *1 (-999 *6)) (-5 *3 (-709 *6))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-149)) (-4 *3 (-319))
-   (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-149)) (-4 *3 (-319))
+   (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-149)) (-4 *3 (-319))
-   (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-149)) (-4 *3 (-319))
+   (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-149)) (-4 *3 (-319))
-   (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-149)) (-4 *3 (-319))
+   (-4 *3 (-569)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-464)) (-4 *3 (-569))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-464)) (-4 *3 (-569))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-464)) (-4 *3 (-569))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-464)) (-4 *3 (-569))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-464)) (-4 *3 (-569))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-464)) (-4 *3 (-569))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-464)) (-4 *3 (-569))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-464)) (-4 *3 (-569))
+   (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-661 *7)) (-5 *3 (-114)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-464))
-   (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *1 (-1006 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-661 *7)) (-5 *3 (-114)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-464))
+   (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *1 (-998 *4 *5 *6 *7))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-464)) (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-5 *2 (-661 *3)) (-5 *1 (-1006 *4 *5 *6 *3)) (-4 *3 (-1094 *4 *5 *6))))) 
+  (-12 (-4 *4 (-464)) (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-5 *2 (-661 *3)) (-5 *1 (-998 *4 *5 *6 *3)) (-4 *3 (-1086 *4 *5 *6))))) 
 (((*1 *2 *2 *3 *4)
   (-12 (-5 *2 (-661 *8)) (-5 *3 (-1 (-114) *8 *8)) (-5 *4 (-1 *8 *8 *8))
-   (-4 *8 (-1094 *5 *6 *7)) (-4 *5 (-569)) (-4 *6 (-815)) (-4 *7 (-869))
-   (-5 *1 (-1006 *5 *6 *7 *8))))) 
+   (-4 *8 (-1086 *5 *6 *7)) (-4 *5 (-569)) (-4 *6 (-815)) (-4 *7 (-861))
+   (-5 *1 (-998 *5 *6 *7 *8))))) 
 (((*1 *2 *2 *3 *4 *5)
   (-12 (-5 *2 (-661 *9)) (-5 *3 (-1 (-114) *9)) (-5 *4 (-1 (-114) *9 *9))
-   (-5 *5 (-1 *9 *9 *9)) (-4 *9 (-1094 *6 *7 *8)) (-4 *6 (-569)) (-4 *7 (-815))
-   (-4 *8 (-869)) (-5 *1 (-1006 *6 *7 *8 *9))))) 
+   (-5 *5 (-1 *9 *9 *9)) (-4 *9 (-1086 *6 *7 *8)) (-4 *6 (-569)) (-4 *7 (-815))
+   (-4 *8 (-861)) (-5 *1 (-998 *6 *7 *8 *9))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-1094 *4 *5 *6))
-   (-5 *2 (-2 (|:| |bas| (-488 *4 *5 *6 *7)) (|:| -3821 (-661 *7))))
-   (-5 *1 (-1006 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
+  (|partial| -12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-1086 *4 *5 *6))
+   (-5 *2 (-2 (|:| |bas| (-488 *4 *5 *6 *7)) (|:| -3744 (-661 *7))))
+   (-5 *1 (-998 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-1094 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *1 (-1006 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-1086 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *1 (-998 *4 *5 *6 *2))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))
  ((*1 *2 *2 *2 *3)
-  (-12 (-5 *2 (-661 *7)) (-5 *3 (-114)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-569))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *1 (-1006 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-661 *7)) (-5 *3 (-114)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-569))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *1 (-998 *4 *5 *6 *7))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
    (-5 *2 (-2 (|:| |goodPols| (-661 *7)) (|:| |badPols| (-661 *7))))
-   (-5 *1 (-1006 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
+   (-5 *1 (-998 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-114))
-   (-5 *1 (-1006 *4 *5 *6 *3)) (-4 *3 (-1094 *4 *5 *6))))) 
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-114))
+   (-5 *1 (-998 *4 *5 *6 *3)) (-4 *3 (-1086 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
    (-5 *2 (-2 (|:| |goodPols| (-661 *7)) (|:| |badPols| (-661 *7))))
-   (-5 *1 (-1006 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
+   (-5 *1 (-998 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-661 (-326 (-229)))) (-5 *2 (-114)) (-5 *1 (-278))))
  ((*1 *2 *3) (-12 (-5 *3 (-326 (-229))) (-5 *2 (-114)) (-5 *1 (-278))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-114))
-   (-5 *1 (-1006 *4 *5 *6 *3)) (-4 *3 (-1094 *4 *5 *6))))) 
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-114))
+   (-5 *1 (-998 *4 *5 *6 *3)) (-4 *3 (-1086 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
    (-5 *2 (-2 (|:| |goodPols| (-661 *7)) (|:| |badPols| (-661 *7))))
-   (-5 *1 (-1006 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
+   (-5 *1 (-998 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-114))
-   (-5 *1 (-1006 *4 *5 *6 *3)) (-4 *3 (-1094 *4 *5 *6))))) 
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-114))
+   (-5 *1 (-998 *4 *5 *6 *3)) (-4 *3 (-1086 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-1094 *4 *5 *6))
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-1086 *4 *5 *6))
    (-5 *2 (-2 (|:| |goodPols| (-661 *7)) (|:| |badPols| (-661 *7))))
-   (-5 *1 (-1006 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
+   (-5 *1 (-998 *4 *5 *6 *7)) (-5 *3 (-661 *7))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-1 (-114) *8))) (-4 *8 (-1094 *5 *6 *7)) (-4 *5 (-569))
-   (-4 *6 (-815)) (-4 *7 (-869))
+  (-12 (-5 *3 (-661 (-1 (-114) *8))) (-4 *8 (-1086 *5 *6 *7)) (-4 *5 (-569))
+   (-4 *6 (-815)) (-4 *7 (-861))
    (-5 *2 (-2 (|:| |goodPols| (-661 *8)) (|:| |badPols| (-661 *8))))
-   (-5 *1 (-1006 *5 *6 *7 *8)) (-5 *4 (-661 *8))))) 
+   (-5 *1 (-998 *5 *6 *7 *8)) (-5 *4 (-661 *8))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-1 (-114) *8))) (-4 *8 (-1094 *5 *6 *7)) (-4 *5 (-569))
-   (-4 *6 (-815)) (-4 *7 (-869))
+  (-12 (-5 *3 (-661 (-1 (-114) *8))) (-4 *8 (-1086 *5 *6 *7)) (-4 *5 (-569))
+   (-4 *6 (-815)) (-4 *7 (-861))
    (-5 *2 (-2 (|:| |goodPols| (-661 *8)) (|:| |badPols| (-661 *8))))
-   (-5 *1 (-1006 *5 *6 *7 *8)) (-5 *4 (-661 *8))))) 
+   (-5 *1 (-998 *5 *6 *7 *8)) (-5 *4 (-661 *8))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 (-114) *8)) (-4 *8 (-1094 *5 *6 *7)) (-4 *5 (-569))
-   (-4 *6 (-815)) (-4 *7 (-869))
+  (-12 (-5 *3 (-1 (-114) *8)) (-4 *8 (-1086 *5 *6 *7)) (-4 *5 (-569))
+   (-4 *6 (-815)) (-4 *7 (-861))
    (-5 *2 (-2 (|:| |goodPols| (-661 *8)) (|:| |badPols| (-661 *8))))
-   (-5 *1 (-1006 *5 *6 *7 *8)) (-5 *4 (-661 *8))))) 
+   (-5 *1 (-998 *5 *6 *7 *8)) (-5 *4 (-661 *8))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1006 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-998 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 (-661 *8))) (-5 *3 (-661 *8)) (-4 *8 (-1094 *5 *6 *7))
-   (-4 *5 (-569)) (-4 *6 (-815)) (-4 *7 (-869)) (-5 *2 (-114))
-   (-5 *1 (-1006 *5 *6 *7 *8))))) 
+  (-12 (-5 *4 (-661 (-661 *8))) (-5 *3 (-661 *8)) (-4 *8 (-1086 *5 *6 *7))
+   (-4 *5 (-569)) (-4 *6 (-815)) (-4 *7 (-861)) (-5 *2 (-114))
+   (-5 *1 (-998 *5 *6 *7 *8))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-114)) (-5 *1 (-1006 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-114)) (-5 *1 (-998 *4 *5 *6 *7))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-661 *3))
-   (-5 *1 (-1006 *4 *5 *6 *3)) (-4 *3 (-1094 *4 *5 *6))))
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-661 *3))
+   (-5 *1 (-998 *4 *5 *6 *3)) (-4 *3 (-1086 *4 *5 *6))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-661 *3)) (-4 *3 (-1094 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *1 (-1006 *4 *5 *6 *3))))
+  (-12 (-5 *2 (-661 *3)) (-4 *3 (-1086 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *1 (-998 *4 *5 *6 *3))))
  ((*1 *2 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))
  ((*1 *2 *2 *2 *3)
   (-12 (-5 *3 (-1 (-661 *7) (-661 *7))) (-5 *2 (-661 *7))
-   (-4 *7 (-1094 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-5 *1 (-1006 *4 *5 *6 *7))))) 
+   (-4 *7 (-1086 *4 *5 *6)) (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-5 *1 (-998 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-661 *3))
-   (-5 *1 (-1006 *4 *5 *6 *3)) (-4 *3 (-1094 *4 *5 *6))))) 
+  (-12 (-4 *4 (-569)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-661 *3))
+   (-5 *1 (-998 *4 *5 *6 *3)) (-4 *3 (-1086 *4 *5 *6))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1094 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-1006 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-1086 *3 *4 *5)) (-4 *3 (-569)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-998 *3 *4 *5 *6))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1005 *3 *4 *5 *6)) (-4 *3 (-1078)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5)) (-5 *2 (-661 *5))))) 
+  (-12 (-4 *1 (-997 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-4 *6 (-1086 *3 *4 *5)) (-5 *2 (-661 *5))))) 
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 (((*1 *2 *3 *4)
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   (-12
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 (((*1 *2 *3)
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-   (-4 *3 (-977 *4 *6 *5))))) 
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 (((*1 *2 *3)
   (-12
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 (((*1 *2 *2 *3)
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 (((*1 *2 *3 *4)
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-     (-2 (|:| -3588 (-791))
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              (|:| |cols| (-661 (-558))))))
       (|:| |fgb| (-661 *8)))))
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 (((*1 *2 *3 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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-   (-4 *7 (-977 *4 *6 *5))))) 
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 (((*1 *2 *3)
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 (((*1 *2 *3 *4 *5 *6 *7)
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      (|:| |rgl|
           (-661
            (-2 (|:| |eqzro| (-661 *11)) (|:| |neqzro| (-661 *11))
-            (|:| |wcond| (-661 (-973 *8)))
+            (|:| |wcond| (-661 (-965 *8)))
             (|:| |bsoln|
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-                  (|:| -2230 (-661 (-1296 (-419 (-973 *8))))))))))
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      (|:| |rgsz| (-558))))
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 (((*1 *2 *3)
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     (-661
      (-2 (|:| |eqzro| (-661 *7)) (|:| |neqzro| (-661 *7))
-      (|:| |wcond| (-661 (-973 *4)))
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       (|:| |bsoln|
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-            (|:| -2230 (-661 (-1296 (-419 (-973 *4))))))))))
-   (-5 *1 (-951 *4 *5 *6 *7)) (-4 *7 (-977 *4 *6 *5))))) 
+           (-2 (|:| |partsol| (-1288 (-419 (-965 *4))))
+            (|:| -2222 (-661 (-1288 (-419 (-965 *4))))))))))
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 (((*1 *2 *3 *4)
   (-12
    (-5 *3
     (-661
      (-2 (|:| |eqzro| (-661 *8)) (|:| |neqzro| (-661 *8))
-      (|:| |wcond| (-661 (-973 *5)))
+      (|:| |wcond| (-661 (-965 *5)))
       (|:| |bsoln|
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-   (-4 *6 (-13 (-869) (-631 (-1206)))) (-4 *7 (-815)) (-5 *2 (-558))
-   (-5 *1 (-951 *5 *6 *7 *8))))) 
+           (-2 (|:| |partsol| (-1288 (-419 (-965 *5))))
+            (|:| -2222 (-661 (-1288 (-419 (-965 *5))))))))))
+   (-5 *4 (-1180)) (-4 *5 (-13 (-319) (-149))) (-4 *8 (-969 *5 *7 *6))
+   (-4 *6 (-13 (-861) (-631 (-1198)))) (-4 *7 (-815)) (-5 *2 (-558))
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 (((*1 *2 *3 *4)
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-   (-4 *6 (-13 (-869) (-631 (-1206)))) (-4 *7 (-815))
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    (-5 *2
     (-661
      (-2 (|:| |eqzro| (-661 *8)) (|:| |neqzro| (-661 *8))
-      (|:| |wcond| (-661 (-973 *5)))
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       (|:| |bsoln|
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-            (|:| -2230 (-661 (-1296 (-419 (-973 *5))))))))))
-   (-5 *1 (-951 *5 *6 *7 *8)) (-5 *4 (-661 *8))))
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     (-661
      (-2 (|:| |eqzro| (-661 *8)) (|:| |neqzro| (-661 *8))
-      (|:| |wcond| (-661 (-973 *5)))
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       (|:| |bsoln|
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-            (|:| -2230 (-661 (-1296 (-419 (-973 *5))))))))))
-   (-5 *1 (-951 *5 *6 *7 *8))))
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     (-661
      (-2 (|:| |eqzro| (-661 *7)) (|:| |neqzro| (-661 *7))
-      (|:| |wcond| (-661 (-973 *4)))
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       (|:| |bsoln|
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-            (|:| -2230 (-661 (-1296 (-419 (-973 *4))))))))))
-   (-5 *1 (-951 *4 *5 *6 *7))))
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  ((*1 *2 *3 *4 *5)
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+  (-12 (-5 *3 (-709 *9)) (-5 *5 (-938)) (-4 *9 (-969 *6 *8 *7))
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    (-5 *2
     (-661
      (-2 (|:| |eqzro| (-661 *9)) (|:| |neqzro| (-661 *9))
-      (|:| |wcond| (-661 (-973 *6)))
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       (|:| |bsoln|
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-   (-5 *1 (-951 *6 *7 *8 *9)) (-5 *4 (-661 *9))))
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-   (-4 *7 (-13 (-869) (-631 (-1206)))) (-4 *8 (-815))
+  (-12 (-5 *3 (-709 *9)) (-5 *4 (-661 (-1198))) (-5 *5 (-938))
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    (-5 *2
     (-661
      (-2 (|:| |eqzro| (-661 *9)) (|:| |neqzro| (-661 *9))
-      (|:| |wcond| (-661 (-973 *6)))
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       (|:| |bsoln|
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-            (|:| -2230 (-661 (-1296 (-419 (-973 *6))))))))))
-   (-5 *1 (-951 *6 *7 *8 *9))))
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  ((*1 *2 *3 *4)
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-   (-4 *5 (-13 (-319) (-149))) (-4 *6 (-13 (-869) (-631 (-1206))))
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    (-5 *2
     (-661
      (-2 (|:| |eqzro| (-661 *8)) (|:| |neqzro| (-661 *8))
-      (|:| |wcond| (-661 (-973 *5)))
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       (|:| |bsoln|
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-            (|:| -2230 (-661 (-1296 (-419 (-973 *5))))))))))
-   (-5 *1 (-951 *5 *6 *7 *8))))
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  ((*1 *2 *3 *4 *5)
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  ((*1 *2 *3 *4 *5)
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- ((*1 *2 *3 *4)
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-   (-4 *7 (-815)) (-5 *2 (-558)) (-5 *1 (-951 *5 *6 *7 *8))))
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+   (-4 *7 (-13 (-861) (-631 (-1198)))) (-4 *8 (-815)) (-5 *2 (-558))
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+ ((*1 *2 *3 *4)
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  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-709 *10)) (-5 *4 (-661 *10)) (-5 *5 (-946)) (-5 *6 (-1188))
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  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-709 *10)) (-5 *4 (-661 (-1206))) (-5 *5 (-946)) (-5 *6 (-1188))
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  ((*1 *2 *3 *4 *5)
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+  (-12 (-5 *3 (-709 *9)) (-5 *4 (-938)) (-5 *5 (-1180)) (-4 *9 (-969 *6 *8 *7))
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 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 *4)) (-4 *4 (-376)) (-4 *2 (-1272 *4))
-   (-5 *1 (-950 *4 *2))))) 
+  (-12 (-5 *3 (-661 *4)) (-4 *4 (-376)) (-4 *2 (-1264 *4))
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 (((*1 *2 *3)
-  (-12 (-4 *1 (-948)) (-5 *2 (-2 (|:| -4461 (-661 *1)) (|:| -2648 *1)))
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    (-5 *3 (-661 *1))))) 
 (((*1 *2 *3 *1)
-  (-12 (-4 *1 (-948)) (-5 *2 (-711 (-661 *1))) (-5 *3 (-661 *1))))) 
+  (-12 (-4 *1 (-940)) (-5 *2 (-711 (-661 *1))) (-5 *3 (-661 *1))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-661 (-973 *4))) (-5 *3 (-661 (-1206))) (-4 *4 (-464))
-   (-5 *1 (-945 *4))))) 
+  (-12 (-5 *2 (-661 (-965 *4))) (-5 *3 (-661 (-1198))) (-4 *4 (-464))
+   (-5 *1 (-937 *4))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-661 (-973 *4))) (-5 *3 (-661 (-1206))) (-4 *4 (-464))
-   (-5 *1 (-945 *4))))) 
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-(((*1 *2) (-12 (-5 *2 (-932 (-558))) (-5 *1 (-944))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-661 (-558))) (-5 *2 (-932 (-558))) (-5 *1 (-944))))
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-(((*1 *2 *3) (-12 (-5 *3 (-661 (-558))) (-5 *2 (-932 (-558))) (-5 *1 (-944))))
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+(((*1 *2 *3) (-12 (-5 *3 (-661 (-558))) (-5 *2 (-924 (-558))) (-5 *1 (-936))))
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 (((*1 *2 *2 *2)
-  (-12 (-4 *3 (-815)) (-4 *4 (-869)) (-4 *5 (-319)) (-5 *1 (-943 *3 *4 *5 *2))
-   (-4 *2 (-977 *5 *3 *4))))
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+   (-4 *2 (-969 *5 *3 *4))))
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-   (-4 *5 (-319)) (-5 *1 (-943 *3 *4 *5 *6))))
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+   (-4 *5 (-319)) (-5 *1 (-935 *3 *4 *5 *6))))
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-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-977 *6 *4 *5)) (-5 *1 (-943 *4 *5 *6 *2))
-   (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-319))))) 
-(((*1 *1 *2 *3) (-12 (-5 *3 (-417 *2)) (-4 *2 (-319)) (-5 *1 (-941 *2))))
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-969 *6 *4 *5)) (-5 *1 (-935 *4 *5 *6 *2))
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-   (-5 *2 (-51)) (-5 *1 (-942 *5))))
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+   (-5 *2 (-51)) (-5 *1 (-934 *5))))
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-(((*1 *2 *2)
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-(((*1 *2 *3)
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-   (-4 *3 (-1272 (-419 *4)))))) 
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+(((*1 *2 *3)
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 (((*1 *2 *3)
   (-12 (-5 *3 (-661 (-2 (|:| |den| (-558)) (|:| |gcdnum| (-558)))))
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-   (-4 *5 (-1272 (-419 *4)))))) 
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 (((*1 *2 *3)
-  (-12 (-4 *3 (-1272 (-419 (-558))))
-   (-5 *2 (-2 (|:| |den| (-558)) (|:| |gcdnum| (-558)))) (-5 *1 (-940 *3 *4))
-   (-4 *4 (-1272 (-419 *3)))))
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  ((*1 *2 *3)
-  (-12 (-4 *4 (-1272 (-419 *2))) (-5 *2 (-558)) (-5 *1 (-940 *4 *3))
-   (-4 *3 (-1272 (-419 *4)))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-558)) (-4 *4 (-1272 (-419 *3))) (-5 *2 (-946))
-   (-5 *1 (-940 *4 *5)) (-4 *5 (-1272 (-419 *4)))))) 
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 (((*1 *2 *3)
   (|partial| -12 (-5 *3 (-346 *5 *6 *7 *8)) (-4 *5 (-433 *4))
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-   (-5 *2 (-2 (|:| -4279 (-791)) (|:| -2622 *8)))
-   (-5 *1 (-938 *4 *5 *6 *7 *8))))
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+   (-4 *4 (-13 (-569) (-1059 (-558))))
+   (-5 *2 (-2 (|:| -4202 (-791)) (|:| -2614 *8)))
+   (-5 *1 (-930 *4 *5 *6 *7 *8))))
  ((*1 *2 *3)
   (|partial| -12 (-5 *3 (-346 (-419 (-558)) *4 *5 *6))
-   (-4 *4 (-1272 (-419 (-558)))) (-4 *5 (-1272 (-419 *4)))
+   (-4 *4 (-1264 (-419 (-558)))) (-4 *5 (-1264 (-419 *4)))
    (-4 *6 (-355 (-419 (-558)) *4 *5))
-   (-5 *2 (-2 (|:| -4279 (-791)) (|:| -2622 *6))) (-5 *1 (-939 *4 *5 *6))))) 
+   (-5 *2 (-2 (|:| -4202 (-791)) (|:| -2614 *6))) (-5 *1 (-931 *4 *5 *6))))) 
 (((*1 *2 *3)
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-   (-5 *1 (-938 *4 *5 *6 *7 *8))))
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+   (-4 *7 (-1264 (-419 *6))) (-4 *8 (-355 *5 *6 *7))
+   (-4 *4 (-13 (-569) (-1059 (-558)))) (-5 *2 (-114))
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+ ((*1 *2 *3) (-12 (-4 *1 (-929)) (-5 *2 (-417 (-1192 *1))) (-5 *3 (-1192 *1))))) 
+(((*1 *2 *3)
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+   (-4 *4 (-464)) (-4 *4 (-569)) (-4 *4 (-1122))))
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 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-661 (-1200 *5))) (-5 *3 (-1200 *5)) (-4 *5 (-168 *4))
+  (|partial| -12 (-5 *2 (-661 (-1192 *5))) (-5 *3 (-1192 *5)) (-4 *5 (-168 *4))
    (-4 *4 (-557)) (-5 *1 (-151 *4 *5))))
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-  (|partial| -12 (-5 *2 (-661 *3)) (-4 *3 (-1272 *5)) (-4 *5 (-1272 *4))
+  (|partial| -12 (-5 *2 (-661 *3)) (-4 *3 (-1264 *5)) (-4 *5 (-1264 *4))
    (-4 *4 (-363)) (-5 *1 (-371 *4 *5 *3))))
  ((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-661 (-1200 (-558)))) (-5 *3 (-1200 (-558)))
+  (|partial| -12 (-5 *2 (-661 (-1192 (-558)))) (-5 *3 (-1192 (-558)))
    (-5 *1 (-584))))
  ((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-661 (-1200 *1))) (-5 *3 (-1200 *1)) (-4 *1 (-937))))) 
+  (|partial| -12 (-5 *2 (-661 (-1192 *1))) (-5 *3 (-1192 *1)) (-4 *1 (-929))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-709 *1)) (-4 *1 (-363)) (-5 *2 (-1296 *1))))
+  (|partial| -12 (-5 *3 (-709 *1)) (-4 *1 (-363)) (-5 *2 (-1288 *1))))
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-   (-5 *2 (-1296 *1))))) 
+  (|partial| -12 (-5 *3 (-709 *1)) (-4 *1 (-147)) (-4 *1 (-929))
+   (-5 *2 (-1288 *1))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-711 *1)) (-4 *1 (-147))))
  ((*1 *1 *1) (-4 *1 (-363)))
- ((*1 *2 *1) (-12 (-5 *2 (-711 *1)) (-4 *1 (-147)) (-4 *1 (-937))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-711 *1)) (-4 *1 (-147)) (-4 *1 (-929))))) 
 (((*1 *2 *3 *4)
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-   (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-417 (-1200 *8))) (-5 *1 (-934 *5 *6 *7 *8))
-   (-5 *4 (-1200 *8))))
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+   (-4 *8 (-969 *5 *6 *7)) (-5 *2 (-417 (-1192 *8))) (-5 *1 (-926 *5 *6 *7 *8))
+   (-5 *4 (-1192 *8))))
  ((*1 *2 *3)
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-   (-5 *1 (-935 *4 *5)) (-5 *3 (-1200 *5))))) 
+  (-12 (-4 *4 (-929)) (-4 *5 (-1264 *4)) (-5 *2 (-417 (-1192 *5)))
+   (-5 *1 (-927 *4 *5)) (-5 *3 (-1192 *5))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-815)) (-4 *4 (-869)) (-4 *2 (-937)) (-5 *1 (-469 *3 *4 *2 *5))
-   (-4 *5 (-977 *2 *3 *4))))
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+   (-4 *5 (-969 *2 *3 *4))))
  ((*1 *2)
-  (-12 (-4 *3 (-815)) (-4 *4 (-869)) (-4 *2 (-937)) (-5 *1 (-934 *2 *3 *4 *5))
-   (-4 *5 (-977 *2 *3 *4))))
- ((*1 *2) (-12 (-4 *2 (-937)) (-5 *1 (-935 *2 *3)) (-4 *3 (-1272 *2))))) 
+  (-12 (-4 *3 (-815)) (-4 *4 (-861)) (-4 *2 (-929)) (-5 *1 (-926 *2 *3 *4 *5))
+   (-4 *5 (-969 *2 *3 *4))))
+ ((*1 *2) (-12 (-4 *2 (-929)) (-5 *1 (-927 *2 *3)) (-4 *3 (-1264 *2))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-937)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-417 (-1200 *7))) (-5 *1 (-934 *4 *5 *6 *7)) (-5 *3 (-1200 *7))))
+  (-12 (-4 *4 (-929)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-969 *4 *5 *6))
+   (-5 *2 (-417 (-1192 *7))) (-5 *1 (-926 *4 *5 *6 *7)) (-5 *3 (-1192 *7))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-937)) (-4 *5 (-1272 *4)) (-5 *2 (-417 (-1200 *5)))
-   (-5 *1 (-935 *4 *5)) (-5 *3 (-1200 *5))))) 
+  (-12 (-4 *4 (-929)) (-4 *5 (-1264 *4)) (-5 *2 (-417 (-1192 *5)))
+   (-5 *1 (-927 *4 *5)) (-5 *3 (-1192 *5))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-937)) (-4 *5 (-815)) (-4 *6 (-869)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-417 (-1200 *7))) (-5 *1 (-934 *4 *5 *6 *7)) (-5 *3 (-1200 *7))))
+  (-12 (-4 *4 (-929)) (-4 *5 (-815)) (-4 *6 (-861)) (-4 *7 (-969 *4 *5 *6))
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  ((*1 *2 *3)
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-   (-5 *1 (-935 *4 *5)) (-5 *3 (-1200 *5))))) 
+  (-12 (-4 *4 (-929)) (-4 *5 (-1264 *4)) (-5 *2 (-417 (-1192 *5)))
+   (-5 *1 (-927 *4 *5)) (-5 *3 (-1192 *5))))) 
 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-661 (-1200 *7))) (-5 *3 (-1200 *7))
-   (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-937)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-5 *1 (-934 *4 *5 *6 *7))))
+  (|partial| -12 (-5 *2 (-661 (-1192 *7))) (-5 *3 (-1192 *7))
+   (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-929)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-5 *1 (-926 *4 *5 *6 *7))))
  ((*1 *2 *2 *3)
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 (((*1 *2 *1)
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 (((*1 *2 *3 *1)
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 (((*1 *2 *3 *1)
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 (((*1 *2 *1 *3 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *1)
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 (((*1 *2 *1)
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 (((*1 *2 *3)
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  ((*1 *2 *3)
   (-12 (-5 *3 (-830))
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  ((*1 *2 *3 *4)
-  (-12 (-4 *1 (-860)) (-5 *3 (-1092))
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-     (|:| |ub| (-661 (-863 (-229))))))
-   (-5 *2 (-2 (|:| -3146 (-391)) (|:| |explanations| (-1188))))))
+    (-2 (|:| |fn| (-326 (-229))) (|:| -3866 (-661 (-229)))
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+     (|:| |ub| (-661 (-855 (-229))))))
+   (-5 *2 (-2 (|:| -3069 (-391)) (|:| |explanations| (-1180))))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-862))
+  (-12 (-5 *3 (-854))
    (-5 *2
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-     (|:| |explanations| (-661 (-1188)))))
-   (-5 *1 (-861))))
+    (-2 (|:| -3069 (-391)) (|:| -3970 (-1180))
+     (|:| |explanations| (-661 (-1180)))))
+   (-5 *1 (-853))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-862)) (-5 *4 (-1092))
+  (-12 (-5 *3 (-854)) (-5 *4 (-1084))
    (-5 *2
-    (-2 (|:| -3146 (-391)) (|:| -4047 (-1188))
-     (|:| |explanations| (-661 (-1188)))))
-   (-5 *1 (-861))))
+    (-2 (|:| -3069 (-391)) (|:| -3970 (-1180))
+     (|:| |explanations| (-661 (-1180)))))
+   (-5 *1 (-853))))
  ((*1 *2 *3 *4)
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+  (-12 (-4 *1 (-912)) (-5 *3 (-1084))
    (-5 *4
     (-2 (|:| |pde| (-661 (-326 (-229))))
      (|:| |constraints|
@@ -9237,27 +9236,27 @@
            (-2 (|:| |start| (-229)) (|:| |finish| (-229)) (|:| |grid| (-791))
             (|:| |boundaryType| (-558)) (|:| |dStart| (-709 (-229)))
             (|:| |dFinish| (-709 (-229))))))
-     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1188))
+     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1180))
      (|:| |tol| (-229))))
-   (-5 *2 (-2 (|:| -3146 (-391)) (|:| |explanations| (-1188))))))
+   (-5 *2 (-2 (|:| -3069 (-391)) (|:| |explanations| (-1180))))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-923))
+  (-12 (-5 *3 (-915))
    (-5 *2
-    (-2 (|:| -3146 (-391)) (|:| -4047 (-1188))
-     (|:| |explanations| (-661 (-1188)))))
-   (-5 *1 (-922))))
+    (-2 (|:| -3069 (-391)) (|:| -3970 (-1180))
+     (|:| |explanations| (-661 (-1180)))))
+   (-5 *1 (-914))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-923)) (-5 *4 (-1092))
+  (-12 (-5 *3 (-915)) (-5 *4 (-1084))
    (-5 *2
-    (-2 (|:| -3146 (-391)) (|:| -4047 (-1188))
-     (|:| |explanations| (-661 (-1188)))))
-   (-5 *1 (-922))))) 
+    (-2 (|:| -3069 (-391)) (|:| -3970 (-1180))
+     (|:| |explanations| (-661 (-1180)))))
+   (-5 *1 (-914))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-791)) (-4 *4 (-376)) (-5 *1 (-921 *2 *4)) (-4 *2 (-1272 *4))))) 
+  (-12 (-5 *3 (-791)) (-4 *4 (-376)) (-5 *1 (-913 *2 *4)) (-4 *2 (-1264 *4))))) 
 (((*1 *2 *2 *2)
-  (|partial| -12 (-4 *3 (-376)) (-5 *1 (-921 *2 *3)) (-4 *2 (-1272 *3))))) 
+  (|partial| -12 (-4 *3 (-376)) (-5 *1 (-913 *2 *3)) (-4 *2 (-1264 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *1 (-920))
+  (-12 (-4 *1 (-912))
    (-5 *3
     (-2 (|:| |pde| (-661 (-326 (-229))))
      (|:| |constraints|
@@ -9265,620 +9264,533 @@
            (-2 (|:| |start| (-229)) (|:| |finish| (-229)) (|:| |grid| (-791))
             (|:| |boundaryType| (-558)) (|:| |dStart| (-709 (-229)))
             (|:| |dFinish| (-709 (-229))))))
-     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1188))
+     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1180))
      (|:| |tol| (-229))))
-   (-5 *2 (-1064))))) 
+   (-5 *2 (-1056))))) 
 (((*1 *1) (-12 (-4 *1 (-477 *2 *3)) (-4 *2 (-175)) (-4 *3 (-23))))
  ((*1 *1) (-5 *1 (-547))) ((*1 *1) (-4 *1 (-742))) ((*1 *1) (-4 *1 (-746)))
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 (((*1 *2 *2 *2)
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1078)) (-5 *1 (-855 *3))))) 
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1070)) (-5 *1 (-847 *3))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-115)) (-4 *4 (-1078)) (-5 *1 (-734 *4 *2)) (-4 *2 (-668 *4))))
- ((*1 *2 *3 *2) (-12 (-5 *3 (-115)) (-5 *1 (-855 *2)) (-4 *2 (-1078))))) 
+  (-12 (-5 *3 (-115)) (-4 *4 (-1070)) (-5 *1 (-734 *4 *2)) (-4 *2 (-668 *4))))
+ ((*1 *2 *3 *2) (-12 (-5 *3 (-115)) (-5 *1 (-847 *2)) (-4 *2 (-1070))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *3 (-374 (-115))) (-4 *2 (-1078)) (-5 *1 (-734 *2 *4))
+  (-12 (-5 *3 (-374 (-115))) (-4 *2 (-1070)) (-5 *1 (-734 *2 *4))
    (-4 *4 (-668 *2))))
- ((*1 *1 *2 *3) (-12 (-5 *3 (-374 (-115))) (-5 *1 (-855 *2)) (-4 *2 (-1078))))) 
-(((*1 *2) (-12 (-5 *2 (-853 (-558))) (-5 *1 (-546))))
- ((*1 *1) (-12 (-5 *1 (-853 *2)) (-4 *2 (-1130))))) 
-(((*1 *2 *3 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-323)) (-5 *1 (-851))))) 
-(((*1 *2 *3 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-114)) (-5 *1 (-851))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-114)) (-5 *1 (-851))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-661 (-1188))) (-5 *1 (-851)) (-5 *3 (-1188))))) 
-(((*1 *2) (-12 (-5 *2 (-661 (-1188))) (-5 *1 (-851))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-51)) (-5 *1 (-851))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-51)) (-5 *1 (-851))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-845)) (-5 *2 (-51)) (-5 *1 (-851))))) 
-(((*1 *1 *2) (-12 (-4 *3 (-1078)) (-5 *1 (-850 *2 *3)) (-4 *2 (-728 *3))))) 
-(((*1 *2 *1) (-12 (-4 *2 (-728 *3)) (-5 *1 (-850 *2 *3)) (-4 *3 (-1078))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-843)) (-5 *2 (-1188))))
- ((*1 *2 *1 *3) (-12 (-4 *1 (-843)) (-5 *3 (-114)) (-5 *2 (-1188))))
- ((*1 *2 *3 *1) (-12 (-4 *1 (-843)) (-5 *3 (-845)) (-5 *2 (-1302))))
- ((*1 *2 *3 *1 *4)
-  (-12 (-4 *1 (-843)) (-5 *3 (-845)) (-5 *4 (-114)) (-5 *2 (-1302))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-326 *4)) (-4 *4 (-13 (-843) (-1078))) (-5 *2 (-1188))
-   (-5 *1 (-849 *4))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-326 *5)) (-5 *4 (-114)) (-4 *5 (-13 (-843) (-1078)))
-   (-5 *2 (-1188)) (-5 *1 (-849 *5))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-845)) (-5 *4 (-326 *5)) (-4 *5 (-13 (-843) (-1078)))
-   (-5 *2 (-1302)) (-5 *1 (-849 *5))))
- ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-845)) (-5 *4 (-326 *6)) (-5 *5 (-114))
-   (-4 *6 (-13 (-843) (-1078))) (-5 *2 (-1302)) (-5 *1 (-849 *6))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-848))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-848))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-848))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-848))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-848)) (-5 *1 (-847))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-1206))) (-5 *1 (-847))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-848)) (-5 *3 (-661 (-1206))) (-5 *1 (-847))))) 
-(((*1 *1) (-5 *1 (-846)))) 
-(((*1 *1) (-5 *1 (-846)))) 
-(((*1 *1) (-5 *1 (-846)))) 
-(((*1 *1) (-5 *1 (-846)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1206)) (-5 *1 (-845))))) 
-(((*1 *2 *1)
-  (-12 (-5 *2 (-2 (|:| |cd| (-1188)) (|:| -4047 (-1188)))) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1188)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1206)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-229)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-558)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1206)) (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-558)) (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-846)) (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-845))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-1188)) (-5 *3 (-846)) (-5 *1 (-845))))) 
-(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-1188)) (-5 *3 (-846)) (-5 *1 (-845))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1149)) (-5 *2 (-114)) (-5 *1 (-844))))) 
-(((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-1188)) (-5 *4 (-1149)) (-5 *2 (-114)) (-5 *1 (-844))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-844))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-844))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-844))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1149)) (-5 *1 (-844))))) 
-(((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-692 *3)) (-4 *3 (-869))))
- ((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-697 *3)) (-4 *3 (-869))))
- ((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-841 *3)) (-4 *3 (-869))))) 
+ ((*1 *1 *2 *3) (-12 (-5 *3 (-374 (-115))) (-5 *1 (-847 *2)) (-4 *2 (-1070))))) 
+(((*1 *2) (-12 (-5 *2 (-845 (-558))) (-5 *1 (-546))))
+ ((*1 *1) (-12 (-5 *1 (-845 *2)) (-4 *2 (-1122))))) 
+(((*1 *1 *2) (-12 (-4 *3 (-1070)) (-5 *1 (-843 *2 *3)) (-4 *2 (-728 *3))))) 
+(((*1 *2 *1) (-12 (-4 *2 (-728 *3)) (-5 *1 (-843 *2 *3)) (-4 *3 (-1070))))) 
+(((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-692 *3)) (-4 *3 (-861))))
+ ((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-697 *3)) (-4 *3 (-861))))
+ ((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-841 *3)) (-4 *3 (-861))))) 
 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *5 (-661 *4)) (-4 *4 (-376)) (-5 *2 (-1296 *4))
+  (|partial| -12 (-5 *5 (-661 *4)) (-4 *4 (-376)) (-5 *2 (-1288 *4))
    (-5 *1 (-836 *4 *3)) (-4 *3 (-678 *4))))) 
 (((*1 *2 *3)
   (-12 (-5 *3 (-661 *4)) (-4 *4 (-376)) (-5 *2 (-709 *4)) (-5 *1 (-836 *4 *5))
@@ -9887,191 +9799,191 @@
   (-12 (-5 *3 (-661 *5)) (-5 *4 (-791)) (-4 *5 (-376)) (-5 *2 (-709 *5))
    (-5 *1 (-836 *5 *6)) (-4 *6 (-678 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-973 *5))) (-5 *4 (-661 (-1206))) (-4 *5 (-569))
-   (-5 *2 (-661 (-661 (-305 (-419 (-973 *5)))))) (-5 *1 (-790 *5))))
+  (-12 (-5 *3 (-661 (-965 *5))) (-5 *4 (-661 (-1198))) (-4 *5 (-569))
+   (-5 *2 (-661 (-661 (-305 (-419 (-965 *5)))))) (-5 *1 (-790 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-973 *4))) (-4 *4 (-569))
-   (-5 *2 (-661 (-661 (-305 (-419 (-973 *4)))))) (-5 *1 (-790 *4))))
+  (-12 (-5 *3 (-661 (-965 *4))) (-4 *4 (-569))
+   (-5 *2 (-661 (-661 (-305 (-419 (-965 *4)))))) (-5 *1 (-790 *4))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-709 *7))
    (-5 *5
-    (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -2230 (-661 *6))) *7 *6))
+    (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -2222 (-661 *6))) *7 *6))
    (-4 *6 (-376)) (-4 *7 (-678 *6))
    (-5 *2
-    (-2 (|:| |particular| (-3 (-1296 *6) "failed"))
-     (|:| -2230 (-661 (-1296 *6)))))
-   (-5 *1 (-835 *6 *7)) (-5 *4 (-1296 *6))))) 
+    (-2 (|:| |particular| (-3 (-1288 *6) "failed"))
+     (|:| -2222 (-661 (-1288 *6)))))
+   (-5 *1 (-835 *6 *7)) (-5 *4 (-1288 *6))))) 
 (((*1 *2 *3 *4)
   (-12 (-4 *5 (-376))
    (-5 *2
     (-2 (|:| A (-709 *5))
      (|:| |eqs|
           (-661
-           (-2 (|:| C (-709 *5)) (|:| |g| (-1296 *5)) (|:| -3761 *6)
+           (-2 (|:| C (-709 *5)) (|:| |g| (-1288 *5)) (|:| -3684 *6)
             (|:| |rh| *5))))))
-   (-5 *1 (-835 *5 *6)) (-5 *3 (-709 *5)) (-5 *4 (-1296 *5))
+   (-5 *1 (-835 *5 *6)) (-5 *3 (-709 *5)) (-5 *4 (-1288 *5))
    (-4 *6 (-678 *5))))
  ((*1 *2 *3 *4)
   (-12 (-4 *5 (-376)) (-4 *6 (-678 *5))
-   (-5 *2 (-2 (|:| -1791 (-709 *6)) (|:| |vec| (-1296 *5))))
-   (-5 *1 (-835 *5 *6)) (-5 *3 (-709 *6)) (-5 *4 (-1296 *5))))) 
+   (-5 *2 (-2 (|:| -1783 (-709 *6)) (|:| |vec| (-1288 *5))))
+   (-5 *1 (-835 *5 *6)) (-5 *3 (-709 *6)) (-5 *4 (-1288 *5))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *3 (-675 (-419 *6))) (-5 *4 (-1 (-661 *5) *6))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-4 *6 (-1272 *5)) (-5 *2 (-661 (-419 *6))) (-5 *1 (-834 *5 *6))))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-4 *6 (-1264 *5)) (-5 *2 (-661 (-419 *6))) (-5 *1 (-834 *5 *6))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-675 (-419 *7))) (-5 *4 (-1 (-661 *6) *7))
    (-5 *5 (-1 (-417 *7) *7))
-   (-4 *6 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-4 *7 (-1272 *6)) (-5 *2 (-661 (-419 *7))) (-5 *1 (-834 *6 *7))))
+   (-4 *6 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-4 *7 (-1264 *6)) (-5 *2 (-661 (-419 *7))) (-5 *1 (-834 *6 *7))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-676 *6 (-419 *6))) (-5 *4 (-1 (-661 *5) *6))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-4 *6 (-1272 *5)) (-5 *2 (-661 (-419 *6))) (-5 *1 (-834 *5 *6))))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-4 *6 (-1264 *5)) (-5 *2 (-661 (-419 *6))) (-5 *1 (-834 *5 *6))))
  ((*1 *2 *3 *4 *5)
   (-12 (-5 *3 (-676 *7 (-419 *7))) (-5 *4 (-1 (-661 *6) *7))
    (-5 *5 (-1 (-417 *7) *7))
-   (-4 *6 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-4 *7 (-1272 *6)) (-5 *2 (-661 (-419 *7))) (-5 *1 (-834 *6 *7))))
+   (-4 *6 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-4 *7 (-1264 *6)) (-5 *2 (-661 (-419 *7))) (-5 *1 (-834 *6 *7))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-675 (-419 *5))) (-4 *5 (-1272 *4)) (-4 *4 (-27))
-   (-4 *4 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
+  (-12 (-5 *3 (-675 (-419 *5))) (-4 *5 (-1264 *4)) (-4 *4 (-27))
+   (-4 *4 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
    (-5 *2 (-661 (-419 *5))) (-5 *1 (-834 *4 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-675 (-419 *6))) (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1272 *5))
+  (-12 (-5 *3 (-675 (-419 *6))) (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1264 *5))
    (-4 *5 (-27))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
    (-5 *2 (-661 (-419 *6))) (-5 *1 (-834 *5 *6))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-676 *5 (-419 *5))) (-4 *5 (-1272 *4)) (-4 *4 (-27))
-   (-4 *4 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
+  (-12 (-5 *3 (-676 *5 (-419 *5))) (-4 *5 (-1264 *4)) (-4 *4 (-27))
+   (-4 *4 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
    (-5 *2 (-661 (-419 *5))) (-5 *1 (-834 *4 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-676 *6 (-419 *6))) (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1272 *5))
+  (-12 (-5 *3 (-676 *6 (-419 *6))) (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1264 *5))
    (-4 *5 (-27))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
    (-5 *2 (-661 (-419 *6))) (-5 *1 (-834 *5 *6))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *4 (-1 (-661 *5) *6))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-419 (-558))))) (-4 *6 (-1272 *5))
-   (-5 *2 (-661 (-2 (|:| |poly| *6) (|:| -3761 *3))))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *6 (-1264 *5))
+   (-5 *2 (-661 (-2 (|:| |poly| *6) (|:| -3684 *3))))
    (-5 *1 (-831 *5 *6 *3 *7)) (-4 *3 (-678 *6)) (-4 *7 (-678 (-419 *6)))))
  ((*1 *2 *3 *4)
   (-12 (-5 *4 (-1 (-661 *5) *6))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-4 *6 (-1272 *5))
-   (-5 *2 (-661 (-2 (|:| |poly| *6) (|:| -3761 (-676 *6 (-419 *6))))))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-4 *6 (-1264 *5))
+   (-5 *2 (-661 (-2 (|:| |poly| *6) (|:| -3684 (-676 *6 (-419 *6))))))
    (-5 *1 (-834 *5 *6)) (-5 *3 (-676 *6 (-419 *6)))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *4 (-1 (-661 *7) *7 (-1200 *7))) (-5 *5 (-1 (-417 *7) *7))
-   (-4 *7 (-1272 *6)) (-4 *6 (-13 (-376) (-149) (-1067 (-419 (-558)))))
-   (-5 *2 (-661 (-2 (|:| |frac| (-419 *7)) (|:| -3761 *3))))
+  (-12 (-5 *4 (-1 (-661 *7) *7 (-1192 *7))) (-5 *5 (-1 (-417 *7) *7))
+   (-4 *7 (-1264 *6)) (-4 *6 (-13 (-376) (-149) (-1059 (-419 (-558)))))
+   (-5 *2 (-661 (-2 (|:| |frac| (-419 *7)) (|:| -3684 *3))))
    (-5 *1 (-831 *6 *7 *3 *8)) (-4 *3 (-678 *7)) (-4 *8 (-678 (-419 *7)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-5 *2 (-661 (-2 (|:| |frac| (-419 *6)) (|:| -3761 (-676 *6 (-419 *6))))))
+  (-12 (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-5 *2 (-661 (-2 (|:| |frac| (-419 *6)) (|:| -3684 (-676 *6 (-419 *6))))))
    (-5 *1 (-834 *5 *6)) (-5 *3 (-676 *6 (-419 *6)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-376)) (-4 *7 (-1272 *5)) (-4 *4 (-744 *5 *7))
-   (-5 *2 (-2 (|:| -1791 (-709 *6)) (|:| |vec| (-1296 *5))))
+  (-12 (-4 *5 (-376)) (-4 *7 (-1264 *5)) (-4 *4 (-744 *5 *7))
+   (-5 *2 (-2 (|:| -1783 (-709 *6)) (|:| |vec| (-1288 *5))))
    (-5 *1 (-833 *5 *6 *7 *4 *3)) (-4 *6 (-678 *5)) (-4 *3 (-678 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-675 (-419 *2))) (-4 *2 (-1272 *4)) (-5 *1 (-832 *4 *2))
-   (-4 *4 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))))
+  (-12 (-5 *3 (-675 (-419 *2))) (-4 *2 (-1264 *4)) (-5 *1 (-832 *4 *2))
+   (-4 *4 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-676 *2 (-419 *2))) (-4 *2 (-1272 *4)) (-5 *1 (-832 *4 *2))
-   (-4 *4 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))))) 
+  (-12 (-5 *3 (-676 *2 (-419 *2))) (-4 *2 (-1264 *4)) (-5 *1 (-832 *4 *2))
+   (-4 *4 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-675 (-419 *6))) (-5 *4 (-419 *6)) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2230 (-661 *4))))
+  (-12 (-5 *3 (-675 (-419 *6))) (-5 *4 (-419 *6)) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2222 (-661 *4))))
    (-5 *1 (-832 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-675 (-419 *6))) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-5 *2 (-2 (|:| -2230 (-661 (-419 *6))) (|:| -1791 (-709 *5))))
+  (-12 (-5 *3 (-675 (-419 *6))) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-5 *2 (-2 (|:| -2222 (-661 (-419 *6))) (|:| -1783 (-709 *5))))
    (-5 *1 (-832 *5 *6)) (-5 *4 (-661 (-419 *6)))))
  ((*1 *2 *3 *4)
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-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2230 (-661 *4))))
+  (-12 (-5 *3 (-676 *6 (-419 *6))) (-5 *4 (-419 *6)) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2222 (-661 *4))))
    (-5 *1 (-832 *5 *6))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-676 *6 (-419 *6))) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-5 *2 (-2 (|:| -2230 (-661 (-419 *6))) (|:| -1791 (-709 *5))))
+  (-12 (-5 *3 (-676 *6 (-419 *6))) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-5 *2 (-2 (|:| -2222 (-661 (-419 *6))) (|:| -1783 (-709 *5))))
    (-5 *1 (-832 *5 *6)) (-5 *4 (-661 (-419 *6)))))) 
 (((*1 *2 *2 *3)
-  (-12 (-4 *4 (-13 (-376) (-149) (-1067 (-419 (-558))))) (-4 *3 (-1272 *4))
+  (-12 (-4 *4 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *3 (-1264 *4))
    (-5 *1 (-831 *4 *3 *2 *5)) (-4 *2 (-678 *3)) (-4 *5 (-678 (-419 *3)))))
  ((*1 *2 *2 *3)
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-   (-4 *5 (-1272 *4)) (-5 *1 (-831 *4 *5 *2 *6)) (-4 *2 (-678 *5))
+  (-12 (-5 *3 (-419 *5)) (-4 *4 (-13 (-376) (-149) (-1059 (-419 (-558)))))
+   (-4 *5 (-1264 *4)) (-5 *1 (-831 *4 *5 *2 *6)) (-4 *2 (-678 *5))
    (-4 *6 (-678 *3))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *4 (-1 (-661 *5) *6))
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-   (-5 *2 (-661 (-2 (|:| -4459 *5) (|:| -3761 *3)))) (-5 *1 (-831 *5 *6 *3 *7))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *6 (-1264 *5))
+   (-5 *2 (-661 (-2 (|:| -4382 *5) (|:| -3684 *3)))) (-5 *1 (-831 *5 *6 *3 *7))
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 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-376) (-149) (-1067 (-419 (-558))))) (-4 *5 (-1272 *4))
-   (-5 *2 (-661 (-2 (|:| |deg| (-791)) (|:| -3761 *5))))
+  (-12 (-4 *4 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *5 (-1264 *4))
+   (-5 *2 (-661 (-2 (|:| |deg| (-791)) (|:| -3684 *5))))
    (-5 *1 (-831 *4 *5 *3 *6)) (-4 *3 (-678 *5)) (-4 *6 (-678 (-419 *5)))))) 
 (((*1 *2 *3)
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-   (-4 *4 (-13 (-376) (-149) (-1067 (-419 (-558))))) (-4 *3 (-678 *2))
+  (-12 (-4 *2 (-1264 *4)) (-5 *1 (-831 *4 *2 *3 *5))
+   (-4 *4 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *3 (-678 *2))
    (-4 *5 (-678 (-419 *2)))))) 
 (((*1 *2 *3 *4)
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+  (-12 (-4 *2 (-1264 *4)) (-5 *1 (-829 *4 *2 *3 *5))
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    (-4 *5 (-678 (-419 *2)))))
  ((*1 *2 *3 *4)
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-   (-4 *4 (-13 (-376) (-149) (-1067 (-419 (-558))))) (-4 *5 (-678 *2))
+  (-12 (-4 *2 (-1264 *4)) (-5 *1 (-829 *4 *2 *5 *3))
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    (-4 *3 (-678 (-419 *2)))))) 
 (((*1 *2 *3)
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+  (-12 (-4 *4 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *5 (-1264 *4))
+   (-5 *2 (-661 (-2 (|:| -4203 *5) (|:| -3644 *5)))) (-5 *1 (-829 *4 *5 *3 *6))
    (-4 *3 (-678 *5)) (-4 *6 (-678 (-419 *5)))))
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-   (-5 *2 (-661 (-2 (|:| -4280 *4) (|:| -3721 *4)))) (-5 *1 (-829 *5 *4 *3 *6))
+  (-12 (-4 *5 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *4 (-1264 *5))
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+  (-12 (-4 *4 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *5 (-1264 *4))
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-   (-5 *2 (-661 (-2 (|:| -4280 *4) (|:| -3721 *4)))) (-5 *1 (-829 *5 *4 *6 *3))
+  (-12 (-4 *5 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *4 (-1264 *5))
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    (-4 *6 (-678 *4)) (-4 *3 (-678 (-419 *4)))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-419 *2)) (-4 *2 (-1272 *5))
-   (-5 *1 (-829 *5 *2 *3 *6)) (-4 *5 (-13 (-376) (-149) (-1067 (-419 (-558)))))
+  (|partial| -12 (-5 *4 (-419 *2)) (-4 *2 (-1264 *5))
+   (-5 *1 (-829 *5 *2 *3 *6)) (-4 *5 (-13 (-376) (-149) (-1059 (-419 (-558)))))
    (-4 *3 (-678 *2)) (-4 *6 (-678 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 (-419 *2))) (-4 *2 (-1272 *5)) (-5 *1 (-829 *5 *2 *3 *6))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-419 (-558))))) (-4 *3 (-678 *2))
+  (-12 (-5 *4 (-661 (-419 *2))) (-4 *2 (-1264 *5)) (-5 *1 (-829 *5 *2 *3 *6))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-419 (-558))))) (-4 *3 (-678 *2))
    (-4 *6 (-678 (-419 *2)))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *3 (-675 *4)) (-4 *4 (-355 *5 *6 *7))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-4 *6 (-1272 *5)) (-4 *7 (-1272 (-419 *6)))
-   (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2230 (-661 *4))))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-4 *6 (-1264 *5)) (-4 *7 (-1264 (-419 *6)))
+   (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2222 (-661 *4))))
    (-5 *1 (-828 *5 *6 *7 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-13 (-319) (-1067 (-558)) (-658 (-558)) (-149)))
+  (-12 (-5 *3 (-1198)) (-4 *4 (-13 (-319) (-1059 (-558)) (-658 (-558)) (-149)))
    (-5 *2 (-1 *5 *5)) (-5 *1 (-826 *4 *5))
-   (-4 *5 (-13 (-29 *4) (-1232) (-987)))))) 
+   (-4 *5 (-13 (-29 *4) (-1224) (-979)))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-13 (-319) (-1067 (-558)) (-658 (-558)) (-149)))
-   (-5 *1 (-826 *4 *2)) (-4 *2 (-13 (-29 *4) (-1232) (-987)))))) 
+  (-12 (-5 *3 (-1198)) (-4 *4 (-13 (-319) (-1059 (-558)) (-658 (-558)) (-149)))
+   (-5 *1 (-826 *4 *2)) (-4 *2 (-13 (-29 *4) (-1224) (-979)))))) 
 (((*1 *2 *3)
   (|partial| -12
    (-5 *3
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *2
@@ -10084,12 +9996,12 @@
    (-5 *2
     (-661
      (-2
-      (|:| -4367
+      (|:| -4290
            (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-            (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+            (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
             (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
             (|:| |abserr| (-229)) (|:| |relerr| (-229))))
-      (|:| -2294
+      (|:| -2286
            (-2 (|:| |stiffness| (-391)) (|:| |stability| (-391))
             (|:| |expense| (-391)) (|:| |accuracy| (-391))
             (|:| |intermediateResults| (-391)))))))
@@ -10098,274 +10010,274 @@
   (-12
    (-5 *2
     (-661
-     (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-      (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+     (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+      (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
       (|:| |relerr| (-229)))))
    (-5 *1 (-572))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-627 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130)) (-5 *2 (-661 *3))))
+  (-12 (-4 *1 (-627 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122)) (-5 *2 (-661 *3))))
  ((*1 *2 *1)
   (-12
    (-5 *2
     (-661
      (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-      (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+      (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
       (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
       (|:| |abserr| (-229)) (|:| |relerr| (-229)))))
    (-5 *1 (-825))))) 
-(((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-825))))) 
+(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-825))))) 
 (((*1 *1) (-5 *1 (-825)))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *5 (-1206)) (-4 *6 (-13 (-319) (-1067 (-558)) (-658 (-558)) (-149)))
-   (-4 *4 (-13 (-29 *6) (-1232) (-987)))
-   (-5 *2 (-2 (|:| |particular| *4) (|:| -2230 (-661 *4))))
+  (-12 (-5 *5 (-1198)) (-4 *6 (-13 (-319) (-1059 (-558)) (-658 (-558)) (-149)))
+   (-4 *4 (-13 (-29 *6) (-1224) (-979)))
+   (-5 *2 (-2 (|:| |particular| *4) (|:| -2222 (-661 *4))))
    (-5 *1 (-823 *6 *4 *3)) (-4 *3 (-678 *4))))) 
 (((*1 *2 *3)
   (-12 (-4 *1 (-822))
    (-5 *3
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
-   (-5 *2 (-1064))))) 
+   (-5 *2 (-1056))))) 
 (((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) (-12 (-4 *1 (-818 *2)) (-4 *2 (-175))))
- ((*1 *1 *2 *2) (-12 (-5 *2 (-1025 *3)) (-4 *3 (-175)) (-5 *1 (-820 *3))))) 
+ ((*1 *1 *2 *2) (-12 (-5 *2 (-1017 *3)) (-4 *3 (-175)) (-5 *1 (-820 *3))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-818 *2)) (-4 *2 (-175))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-818 *2)) (-4 *2 (-175))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-818 *2)) (-4 *2 (-175))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-818 *2)) (-4 *2 (-175))))) 
 (((*1 *1 *1) (-4 *1 (-250)))
  ((*1 *1 *1)
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+  (-12 (-4 *2 (-175)) (-5 *1 (-301 *2 *3 *4 *5 *6 *7)) (-4 *3 (-1264 *2))
    (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4)) (-14 *6 (-1 (-3 *4 "failed") *4 *4))
    (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4))))
  ((*1 *1 *1)
-  (-4034 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1246)))
-   (-12 (-5 *1 (-305 *2)) (-4 *2 (-485)) (-4 *2 (-1246)))))
+  (-3957 (-12 (-5 *1 (-305 *2)) (-4 *2 (-376)) (-4 *2 (-1238)))
+   (-12 (-5 *1 (-305 *2)) (-4 *2 (-485)) (-4 *2 (-1238)))))
  ((*1 *1 *1) (-4 *1 (-485)))
- ((*1 *2 *2) (-12 (-5 *2 (-1296 *3)) (-4 *3 (-363)) (-5 *1 (-540 *3))))
+ ((*1 *2 *2) (-12 (-5 *2 (-1288 *3)) (-4 *3 (-363)) (-5 *1 (-540 *3))))
  ((*1 *1 *1)
   (-12 (-5 *1 (-735 *2 *3 *4 *5 *6)) (-4 *2 (-175)) (-4 *3 (-23))
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
  ((*1 *1 *1) (-12 (-4 *1 (-818 *2)) (-4 *2 (-175)) (-4 *2 (-376))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1232)))))
+(((*1 *2 *1) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224)))))
  ((*1 *1 *1 *1) (-4 *1 (-815)))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
   (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391))
    (-5 *2
-    (-2 (|:| -3899 *4) (|:| -1747 *4) (|:| |totalpts| (-558))
+    (-2 (|:| -3822 *4) (|:| -1739 *4) (|:| |totalpts| (-558))
      (|:| |success| (-114))))
    (-5 *1 (-809)) (-5 *5 (-558))))) 
 (((*1 *2 *3 *4 *5 *5 *4 *6)
-  (-12 (-5 *4 (-558)) (-5 *6 (-1 (-1302) (-1296 *5) (-1296 *5) (-391)))
-   (-5 *3 (-1296 (-391))) (-5 *5 (-391)) (-5 *2 (-1302)) (-5 *1 (-808))))) 
+  (-12 (-5 *4 (-558)) (-5 *6 (-1 (-1294) (-1288 *5) (-1288 *5) (-391)))
+   (-5 *3 (-1288 (-391))) (-5 *5 (-391)) (-5 *2 (-1294)) (-5 *1 (-808))))) 
 (((*1 *2 *3 *4 *5 *6 *5 *3 *7)
   (-12 (-5 *4 (-558))
-   (-5 *6 (-2 (|:| |tryValue| (-391)) (|:| |did| (-391)) (|:| -1615 (-391))))
-   (-5 *7 (-1 (-1302) (-1296 *5) (-1296 *5) (-391))) (-5 *3 (-1296 (-391)))
-   (-5 *5 (-391)) (-5 *2 (-1302)) (-5 *1 (-808))))
+   (-5 *6 (-2 (|:| |tryValue| (-391)) (|:| |did| (-391)) (|:| -1607 (-391))))
+   (-5 *7 (-1 (-1294) (-1288 *5) (-1288 *5) (-391))) (-5 *3 (-1288 (-391)))
+   (-5 *5 (-391)) (-5 *2 (-1294)) (-5 *1 (-808))))
  ((*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3)
   (-12 (-5 *4 (-558))
-   (-5 *6 (-2 (|:| |tryValue| (-391)) (|:| |did| (-391)) (|:| -1615 (-391))))
-   (-5 *7 (-1 (-1302) (-1296 *5) (-1296 *5) (-391))) (-5 *3 (-1296 (-391)))
-   (-5 *5 (-391)) (-5 *2 (-1302)) (-5 *1 (-808))))) 
+   (-5 *6 (-2 (|:| |tryValue| (-391)) (|:| |did| (-391)) (|:| -1607 (-391))))
+   (-5 *7 (-1 (-1294) (-1288 *5) (-1288 *5) (-391))) (-5 *3 (-1288 (-391)))
+   (-5 *5 (-391)) (-5 *2 (-1294)) (-5 *1 (-808))))) 
 (((*1 *2 *3 *4 *5 *5 *5 *5 *4 *6)
-  (-12 (-5 *4 (-558)) (-5 *6 (-1 (-1302) (-1296 *5) (-1296 *5) (-391)))
-   (-5 *3 (-1296 (-391))) (-5 *5 (-391)) (-5 *2 (-1302)) (-5 *1 (-808))))) 
+  (-12 (-5 *4 (-558)) (-5 *6 (-1 (-1294) (-1288 *5) (-1288 *5) (-391)))
+   (-5 *3 (-1288 (-391))) (-5 *5 (-391)) (-5 *2 (-1294)) (-5 *1 (-808))))) 
 (((*1 *2 *3 *4 *5 *5 *6)
-  (-12 (-5 *4 (-558)) (-5 *6 (-1 (-1302) (-1296 *5) (-1296 *5) (-391)))
-   (-5 *3 (-1296 (-391))) (-5 *5 (-391)) (-5 *2 (-1302)) (-5 *1 (-808))))
+  (-12 (-5 *4 (-558)) (-5 *6 (-1 (-1294) (-1288 *5) (-1288 *5) (-391)))
+   (-5 *3 (-1288 (-391))) (-5 *5 (-391)) (-5 *2 (-1294)) (-5 *1 (-808))))
  ((*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3)
-  (-12 (-5 *4 (-558)) (-5 *6 (-1 (-1302) (-1296 *5) (-1296 *5) (-391)))
-   (-5 *3 (-1296 (-391))) (-5 *5 (-391)) (-5 *2 (-1302)) (-5 *1 (-808))))) 
+  (-12 (-5 *4 (-558)) (-5 *6 (-1 (-1294) (-1288 *5) (-1288 *5) (-391)))
+   (-5 *3 (-1288 (-391))) (-5 *5 (-391)) (-5 *2 (-1294)) (-5 *1 (-808))))) 
 (((*1 *2 *3 *2)
-  (-12 (-4 *1 (-807)) (-5 *2 (-1064))
+  (-12 (-4 *1 (-807)) (-5 *2 (-1056))
    (-5 *3
-    (-2 (|:| |fn| (-326 (-229))) (|:| -1646 (-661 (-1118 (-863 (-229)))))
+    (-2 (|:| |fn| (-326 (-229))) (|:| -1638 (-661 (-1110 (-855 (-229)))))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))))
  ((*1 *2 *3 *2)
-  (-12 (-4 *1 (-807)) (-5 *2 (-1064))
+  (-12 (-4 *1 (-807)) (-5 *2 (-1056))
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))))) 
-(((*1 *2 *3) (|partial| -12 (-5 *3 (-1188)) (-5 *2 (-391)) (-5 *1 (-806))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-391)) (-5 *1 (-806))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-946)) (-5 *1 (-806))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-946)) (-5 *2 (-1188)) (-5 *1 (-806))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-946)) (-5 *1 (-806))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-946)) (-5 *2 (-1188)) (-5 *1 (-806))))) 
-(((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-973 (-171 *4))) (-4 *4 (-175)) (-4 *4 (-631 (-391)))
+(((*1 *2 *3) (|partial| -12 (-5 *3 (-1180)) (-5 *2 (-391)) (-5 *1 (-806))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-391)) (-5 *1 (-806))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-938)) (-5 *1 (-806))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-938)) (-5 *2 (-1180)) (-5 *1 (-806))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-938)) (-5 *1 (-806))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-938)) (-5 *2 (-1180)) (-5 *1 (-806))))) 
+(((*1 *2 *3)
+  (|partial| -12 (-5 *3 (-965 (-171 *4))) (-4 *4 (-175)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-973 (-171 *5))) (-5 *4 (-946)) (-4 *5 (-175))
+  (|partial| -12 (-5 *3 (-965 (-171 *5))) (-5 *4 (-938)) (-4 *5 (-175))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-973 *4)) (-4 *4 (-1078)) (-4 *4 (-631 (-391)))
+  (|partial| -12 (-5 *3 (-965 *4)) (-4 *4 (-1070)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-973 *5)) (-5 *4 (-946)) (-4 *5 (-1078))
+  (|partial| -12 (-5 *3 (-965 *5)) (-5 *4 (-938)) (-4 *5 (-1070))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-419 (-973 *4))) (-4 *4 (-569)) (-4 *4 (-631 (-391)))
+  (|partial| -12 (-5 *3 (-419 (-965 *4))) (-4 *4 (-569)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-419 (-973 *5))) (-5 *4 (-946)) (-4 *5 (-569))
+  (|partial| -12 (-5 *3 (-419 (-965 *5))) (-5 *4 (-938)) (-4 *5 (-569))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-419 (-973 (-171 *4)))) (-4 *4 (-569))
+  (|partial| -12 (-5 *3 (-419 (-965 (-171 *4)))) (-4 *4 (-569))
    (-4 *4 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-419 (-973 (-171 *5)))) (-5 *4 (-946)) (-4 *5 (-569))
+  (|partial| -12 (-5 *3 (-419 (-965 (-171 *5)))) (-5 *4 (-938)) (-4 *5 (-569))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-326 *4)) (-4 *4 (-569)) (-4 *4 (-869))
+  (|partial| -12 (-5 *3 (-326 *4)) (-4 *4 (-569)) (-4 *4 (-861))
    (-4 *4 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-326 *5)) (-5 *4 (-946)) (-4 *5 (-569)) (-4 *5 (-869))
+  (|partial| -12 (-5 *3 (-326 *5)) (-5 *4 (-938)) (-4 *5 (-569)) (-4 *5 (-861))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-326 (-171 *4))) (-4 *4 (-569)) (-4 *4 (-869))
+  (|partial| -12 (-5 *3 (-326 (-171 *4))) (-4 *4 (-569)) (-4 *4 (-861))
    (-4 *4 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-326 (-171 *5))) (-5 *4 (-946)) (-4 *5 (-569))
-   (-4 *5 (-869)) (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391)))
+  (|partial| -12 (-5 *3 (-326 (-171 *5))) (-5 *4 (-938)) (-4 *5 (-569))
+   (-4 *5 (-861)) (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391)))
    (-5 *1 (-805 *5))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-973 *4)) (-4 *4 (-1078)) (-4 *4 (-631 *2))
+  (|partial| -12 (-5 *3 (-965 *4)) (-4 *4 (-1070)) (-4 *4 (-631 *2))
    (-5 *2 (-391)) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-973 *5)) (-5 *4 (-946)) (-4 *5 (-1078))
+  (|partial| -12 (-5 *3 (-965 *5)) (-5 *4 (-938)) (-4 *5 (-1070))
    (-4 *5 (-631 *2)) (-5 *2 (-391)) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-419 (-973 *4))) (-4 *4 (-569)) (-4 *4 (-631 *2))
+  (|partial| -12 (-5 *3 (-419 (-965 *4))) (-4 *4 (-569)) (-4 *4 (-631 *2))
    (-5 *2 (-391)) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-419 (-973 *5))) (-5 *4 (-946)) (-4 *5 (-569))
+  (|partial| -12 (-5 *3 (-419 (-965 *5))) (-5 *4 (-938)) (-4 *5 (-569))
    (-4 *5 (-631 *2)) (-5 *2 (-391)) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-326 *4)) (-4 *4 (-569)) (-4 *4 (-869))
+  (|partial| -12 (-5 *3 (-326 *4)) (-4 *4 (-569)) (-4 *4 (-861))
    (-4 *4 (-631 *2)) (-5 *2 (-391)) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-326 *5)) (-5 *4 (-946)) (-4 *5 (-569)) (-4 *5 (-869))
+  (|partial| -12 (-5 *3 (-326 *5)) (-5 *4 (-938)) (-4 *5 (-569)) (-4 *5 (-861))
    (-4 *5 (-631 *2)) (-5 *2 (-391)) (-5 *1 (-805 *5))))) 
 (((*1 *2 *3)
   (-12 (-5 *2 (-171 (-391))) (-5 *1 (-805 *3)) (-4 *3 (-631 (-391)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-946)) (-5 *2 (-171 (-391))) (-5 *1 (-805 *3))
+  (-12 (-5 *4 (-938)) (-5 *2 (-171 (-391))) (-5 *1 (-805 *3))
    (-4 *3 (-631 (-391)))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-171 *4)) (-4 *4 (-175)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-171 *5)) (-5 *4 (-946)) (-4 *5 (-175)) (-4 *5 (-631 (-391)))
+  (-12 (-5 *3 (-171 *5)) (-5 *4 (-938)) (-4 *5 (-175)) (-4 *5 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-973 (-171 *4))) (-4 *4 (-175)) (-4 *4 (-631 (-391)))
+  (-12 (-5 *3 (-965 (-171 *4))) (-4 *4 (-175)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-973 (-171 *5))) (-5 *4 (-946)) (-4 *5 (-175))
+  (-12 (-5 *3 (-965 (-171 *5))) (-5 *4 (-938)) (-4 *5 (-175))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-973 *4)) (-4 *4 (-1078)) (-4 *4 (-631 (-391)))
+  (-12 (-5 *3 (-965 *4)) (-4 *4 (-1070)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-973 *5)) (-5 *4 (-946)) (-4 *5 (-1078)) (-4 *5 (-631 (-391)))
+  (-12 (-5 *3 (-965 *5)) (-5 *4 (-938)) (-4 *5 (-1070)) (-4 *5 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-419 (-973 *4))) (-4 *4 (-569)) (-4 *4 (-631 (-391)))
+  (-12 (-5 *3 (-419 (-965 *4))) (-4 *4 (-569)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-973 *5))) (-5 *4 (-946)) (-4 *5 (-569))
+  (-12 (-5 *3 (-419 (-965 *5))) (-5 *4 (-938)) (-4 *5 (-569))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-419 (-973 (-171 *4)))) (-4 *4 (-569)) (-4 *4 (-631 (-391)))
+  (-12 (-5 *3 (-419 (-965 (-171 *4)))) (-4 *4 (-569)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-973 (-171 *5)))) (-5 *4 (-946)) (-4 *5 (-569))
+  (-12 (-5 *3 (-419 (-965 (-171 *5)))) (-5 *4 (-938)) (-4 *5 (-569))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-326 *4)) (-4 *4 (-569)) (-4 *4 (-869)) (-4 *4 (-631 (-391)))
+  (-12 (-5 *3 (-326 *4)) (-4 *4 (-569)) (-4 *4 (-861)) (-4 *4 (-631 (-391)))
    (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-326 *5)) (-5 *4 (-946)) (-4 *5 (-569)) (-4 *5 (-869))
+  (-12 (-5 *3 (-326 *5)) (-5 *4 (-938)) (-4 *5 (-569)) (-4 *5 (-861))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-326 (-171 *4))) (-4 *4 (-569)) (-4 *4 (-869))
+  (-12 (-5 *3 (-326 (-171 *4))) (-4 *4 (-569)) (-4 *4 (-861))
    (-4 *4 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-326 (-171 *5))) (-5 *4 (-946)) (-4 *5 (-569)) (-4 *5 (-869))
+  (-12 (-5 *3 (-326 (-171 *5))) (-5 *4 (-938)) (-4 *5 (-569)) (-4 *5 (-861))
    (-4 *5 (-631 (-391))) (-5 *2 (-171 (-391))) (-5 *1 (-805 *5))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-391)) (-5 *1 (-805 *3)) (-4 *3 (-631 *2))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-946)) (-5 *2 (-391)) (-5 *1 (-805 *3)) (-4 *3 (-631 *2))))
+  (-12 (-5 *4 (-938)) (-5 *2 (-391)) (-5 *1 (-805 *3)) (-4 *3 (-631 *2))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-973 *4)) (-4 *4 (-1078)) (-4 *4 (-631 *2)) (-5 *2 (-391))
+  (-12 (-5 *3 (-965 *4)) (-4 *4 (-1070)) (-4 *4 (-631 *2)) (-5 *2 (-391))
    (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-973 *5)) (-5 *4 (-946)) (-4 *5 (-1078)) (-4 *5 (-631 *2))
+  (-12 (-5 *3 (-965 *5)) (-5 *4 (-938)) (-4 *5 (-1070)) (-4 *5 (-631 *2))
    (-5 *2 (-391)) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-419 (-973 *4))) (-4 *4 (-569)) (-4 *4 (-631 *2)) (-5 *2 (-391))
+  (-12 (-5 *3 (-419 (-965 *4))) (-4 *4 (-569)) (-4 *4 (-631 *2)) (-5 *2 (-391))
    (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-973 *5))) (-5 *4 (-946)) (-4 *5 (-569)) (-4 *5 (-631 *2))
+  (-12 (-5 *3 (-419 (-965 *5))) (-5 *4 (-938)) (-4 *5 (-569)) (-4 *5 (-631 *2))
    (-5 *2 (-391)) (-5 *1 (-805 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-326 *4)) (-4 *4 (-569)) (-4 *4 (-869)) (-4 *4 (-631 *2))
+  (-12 (-5 *3 (-326 *4)) (-4 *4 (-569)) (-4 *4 (-861)) (-4 *4 (-631 *2))
    (-5 *2 (-391)) (-5 *1 (-805 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-326 *5)) (-5 *4 (-946)) (-4 *5 (-569)) (-4 *5 (-869))
+  (-12 (-5 *3 (-326 *5)) (-5 *4 (-938)) (-4 *5 (-569)) (-4 *5 (-861))
    (-4 *5 (-631 *2)) (-5 *2 (-391)) (-5 *1 (-805 *5))))) 
 (((*1 *2 *3 *2)
   (-12 (-5 *3 (-791)) (-5 *1 (-803 *2)) (-4 *2 (-38 (-419 (-558))))
@@ -10373,686 +10285,686 @@
 (((*1 *2 *3 *2)
   (-12 (-5 *3 (-791)) (-5 *1 (-803 *2)) (-4 *2 (-38 (-419 (-558))))
    (-4 *2 (-175))))) 
-(((*1 *1 *1 *1) (-12 (-5 *1 (-801 *2)) (-4 *2 (-1078))))) 
-(((*1 *1 *1 *1) (-12 (-5 *1 (-801 *2)) (-4 *2 (-1078))))) 
+(((*1 *1 *1 *1) (-12 (-5 *1 (-801 *2)) (-4 *2 (-1070))))) 
+(((*1 *1 *1 *1) (-12 (-5 *1 (-801 *2)) (-4 *2 (-1070))))) 
 (((*1 *2 *1 *1)
   (-12 (-5 *2 (-661 (-801 *3))) (-5 *1 (-801 *3)) (-4 *3 (-569))
-   (-4 *3 (-1078))))) 
+   (-4 *3 (-1070))))) 
 (((*1 *2 *1 *1)
   (-12
-   (-5 *2 (-2 (|:| -4263 *3) (|:| |coef1| (-801 *3)) (|:| |coef2| (-801 *3))))
-   (-5 *1 (-801 *3)) (-4 *3 (-569)) (-4 *3 (-1078))))) 
+   (-5 *2 (-2 (|:| -4186 *3) (|:| |coef1| (-801 *3)) (|:| |coef2| (-801 *3))))
+   (-5 *1 (-801 *3)) (-4 *3 (-569)) (-4 *3 (-1070))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-2 (|:| -4263 *3) (|:| |coef1| (-801 *3)))) (-5 *1 (-801 *3))
-   (-4 *3 (-569)) (-4 *3 (-1078))))) 
+  (-12 (-5 *2 (-2 (|:| -4186 *3) (|:| |coef1| (-801 *3)))) (-5 *1 (-801 *3))
+   (-4 *3 (-569)) (-4 *3 (-1070))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-2 (|:| -4263 *3) (|:| |coef2| (-801 *3)))) (-5 *1 (-801 *3))
-   (-4 *3 (-569)) (-4 *3 (-1078))))) 
+  (-12 (-5 *2 (-2 (|:| -4186 *3) (|:| |coef2| (-801 *3)))) (-5 *1 (-801 *3))
+   (-4 *3 (-569)) (-4 *3 (-1070))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *3 (-709 (-419 (-558))))
    (-5 *2
     (-661
      (-2 (|:| |outval| *4) (|:| |outmult| (-558))
       (|:| |outvect| (-661 (-709 *4))))))
-   (-5 *1 (-799 *4)) (-4 *4 (-13 (-376) (-868)))))) 
+   (-5 *1 (-799 *4)) (-4 *4 (-13 (-376) (-860)))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *3 (-709 (-419 (-558)))) (-5 *2 (-661 *4)) (-5 *1 (-799 *4))
-   (-4 *4 (-13 (-376) (-868)))))) 
+   (-4 *4 (-13 (-376) (-860)))))) 
 (((*1 *2 *3 *2) (-12 (-5 *3 (-709 *2)) (-4 *2 (-175)) (-5 *1 (-148 *2))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-175)) (-4 *2 (-1272 *4)) (-5 *1 (-180 *4 *2 *3))
+  (-12 (-4 *4 (-175)) (-4 *2 (-1264 *4)) (-5 *1 (-180 *4 *2 *3))
    (-4 *3 (-744 *4 *2))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-709 (-419 (-973 *5)))) (-5 *4 (-1206)) (-5 *2 (-973 *5))
+  (-12 (-5 *3 (-709 (-419 (-965 *5)))) (-5 *4 (-1198)) (-5 *2 (-965 *5))
    (-5 *1 (-304 *5)) (-4 *5 (-464))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-709 (-419 (-973 *4)))) (-5 *2 (-973 *4)) (-5 *1 (-304 *4))
+  (-12 (-5 *3 (-709 (-419 (-965 *4)))) (-5 *2 (-965 *4)) (-5 *1 (-304 *4))
    (-4 *4 (-464))))
- ((*1 *2 *1) (-12 (-4 *1 (-383 *3 *2)) (-4 *3 (-175)) (-4 *2 (-1272 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-383 *3 *2)) (-4 *3 (-175)) (-4 *2 (-1264 *3))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-709 (-171 (-419 (-558))))) (-5 *2 (-973 (-171 (-419 (-558)))))
-   (-5 *1 (-784 *4)) (-4 *4 (-13 (-376) (-868)))))
+  (-12 (-5 *3 (-709 (-171 (-419 (-558))))) (-5 *2 (-965 (-171 (-419 (-558)))))
+   (-5 *1 (-784 *4)) (-4 *4 (-13 (-376) (-860)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-709 (-171 (-419 (-558))))) (-5 *4 (-1206))
-   (-5 *2 (-973 (-171 (-419 (-558))))) (-5 *1 (-784 *5))
-   (-4 *5 (-13 (-376) (-868)))))
+  (-12 (-5 *3 (-709 (-171 (-419 (-558))))) (-5 *4 (-1198))
+   (-5 *2 (-965 (-171 (-419 (-558))))) (-5 *1 (-784 *5))
+   (-4 *5 (-13 (-376) (-860)))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-709 (-419 (-558)))) (-5 *2 (-973 (-419 (-558))))
-   (-5 *1 (-799 *4)) (-4 *4 (-13 (-376) (-868)))))
+  (-12 (-5 *3 (-709 (-419 (-558)))) (-5 *2 (-965 (-419 (-558))))
+   (-5 *1 (-799 *4)) (-4 *4 (-13 (-376) (-860)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-709 (-419 (-558)))) (-5 *4 (-1206))
-   (-5 *2 (-973 (-419 (-558)))) (-5 *1 (-799 *5)) (-4 *5 (-13 (-376) (-868)))))) 
+  (-12 (-5 *3 (-709 (-419 (-558)))) (-5 *4 (-1198))
+   (-5 *2 (-965 (-419 (-558)))) (-5 *1 (-799 *5)) (-4 *5 (-13 (-376) (-860)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-319)) (-5 *2 (-661 (-791)))
-   (-5 *1 (-798 *3 *4 *5 *6 *7)) (-4 *3 (-1272 *6)) (-4 *7 (-977 *6 *4 *5))))) 
+  (-12 (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-319)) (-5 *2 (-661 (-791)))
+   (-5 *1 (-798 *3 *4 *5 *6 *7)) (-4 *3 (-1264 *6)) (-4 *7 (-969 *6 *4 *5))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-4 *6 (-1272 *9)) (-4 *7 (-815)) (-4 *8 (-869)) (-4 *9 (-319))
-   (-4 *10 (-977 *9 *7 *8))
+  (-12 (-4 *6 (-1264 *9)) (-4 *7 (-815)) (-4 *8 (-861)) (-4 *9 (-319))
+   (-4 *10 (-969 *9 *7 *8))
    (-5 *2
-    (-2 (|:| |deter| (-661 (-1200 *10)))
-     (|:| |dterm| (-661 (-661 (-2 (|:| -3556 (-791)) (|:| |pcoef| *10)))))
+    (-2 (|:| |deter| (-661 (-1192 *10)))
+     (|:| |dterm| (-661 (-661 (-2 (|:| -3479 (-791)) (|:| |pcoef| *10)))))
      (|:| |nfacts| (-661 *6)) (|:| |nlead| (-661 *10))))
-   (-5 *1 (-798 *6 *7 *8 *9 *10)) (-5 *3 (-1200 *10)) (-5 *4 (-661 *6))
+   (-5 *1 (-798 *6 *7 *8 *9 *10)) (-5 *3 (-1192 *10)) (-5 *4 (-661 *6))
    (-5 *5 (-661 *10))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-363)) (-4 *5 (-341 *4)) (-4 *6 (-1272 *5)) (-5 *2 (-661 *3))
-   (-5 *1 (-797 *4 *5 *6 *3 *7)) (-4 *3 (-1272 *6)) (-14 *7 (-946))))) 
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 (((*1 *2 *3 *4)
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+  (-12 (-5 *3 (-419 *2)) (-5 *4 (-1 *2 *2)) (-4 *2 (-1264 *5))
    (-5 *1 (-747 *5 *2)) (-4 *5 (-376))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1272 *5)) (-4 *5 (-376))
-   (-5 *2 (-2 (|:| -3569 (-417 *3)) (|:| |special| (-417 *3))))
+  (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1264 *5)) (-4 *5 (-376))
+   (-5 *2 (-2 (|:| -3492 (-417 *3)) (|:| |special| (-417 *3))))
    (-5 *1 (-747 *5 *3))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-55))))
  ((*1 *2 *1)
-  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *2 (-114))
-   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-977 *3 *4 *5))))
+  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *2 (-114))
+   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-969 *3 *4 *5))))
  ((*1 *2 *1) (-12 (-4 *1 (-742)) (-5 *2 (-114))))
  ((*1 *2 *1) (-12 (-4 *1 (-746)) (-5 *2 (-114))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-791)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1078))
-   (-14 *4 (-661 (-1206)))))
+  (-12 (-5 *2 (-791)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1070))
+   (-14 *4 (-661 (-1198)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-791)) (-5 *1 (-227 *3 *4)) (-4 *3 (-13 (-1078) (-869)))
-   (-14 *4 (-661 (-1206)))))
+  (-12 (-5 *2 (-791)) (-5 *1 (-227 *3 *4)) (-4 *3 (-13 (-1070) (-861)))
+   (-14 *4 (-661 (-1198)))))
  ((*1 *1) (-12 (-4 *1 (-341 *2)) (-4 *2 (-381)) (-4 *2 (-376))))
  ((*1 *2 *1)
-  (|partial| -12 (-4 *1 (-349 *3 *4 *5 *2)) (-4 *3 (-376)) (-4 *4 (-1272 *3))
-   (-4 *5 (-1272 (-419 *4))) (-4 *2 (-355 *3 *4 *5))))
+  (|partial| -12 (-4 *1 (-349 *3 *4 *5 *2)) (-4 *3 (-376)) (-4 *4 (-1264 *3))
+   (-4 *5 (-1264 (-419 *4))) (-4 *2 (-355 *3 *4 *5))))
  ((*1 *1 *2)
   (-12 (-5 *2 (-791)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 *2) (-14 *4 *2)
    (-4 *5 (-175))))
- ((*1 *1) (-12 (-4 *2 (-175)) (-4 *1 (-744 *2 *3)) (-4 *3 (-1272 *2))))) 
+ ((*1 *1) (-12 (-4 *2 (-175)) (-4 *1 (-744 *2 *3)) (-4 *3 (-1264 *2))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1296 *1)) (-5 *4 (-1 *5 *5)) (-4 *5 (-376))
-   (-4 *1 (-744 *5 *6)) (-4 *5 (-175)) (-4 *6 (-1272 *5)) (-5 *2 (-709 *5))))) 
-(((*1 *1 *1 *2) (-12 (-4 *1 (-740)) (-5 *2 (-946))))
+  (-12 (-5 *3 (-1288 *1)) (-5 *4 (-1 *5 *5)) (-4 *5 (-376))
+   (-4 *1 (-744 *5 *6)) (-4 *5 (-175)) (-4 *6 (-1264 *5)) (-5 *2 (-709 *5))))) 
+(((*1 *1 *1 *2) (-12 (-4 *1 (-740)) (-5 *2 (-938))))
  ((*1 *1 *1 *2) (-12 (-4 *1 (-742)) (-5 *2 (-791))))) 
-(((*1 *1 *1 *2) (-12 (-4 *1 (-740)) (-5 *2 (-946))))
+(((*1 *1 *1 *2) (-12 (-4 *1 (-740)) (-5 *2 (-938))))
  ((*1 *1 *1 *2) (-12 (-4 *1 (-742)) (-5 *2 (-791))))) 
 (((*1 *1 *1) (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-175)) (-4 *2 (-569))))
  ((*1 *1 *1) (|partial| -4 *1 (-742)))) 
@@ -11061,7 +10973,7 @@
 (((*1 *1 *2 *2 *2 *2) (-12 (-5 *1 (-738 *2)) (-4 *2 (-376))))) 
 (((*1 *1 *1 *1)
   (|partial| -12 (-4 *2 (-175)) (-5 *1 (-301 *2 *3 *4 *5 *6 *7))
-   (-4 *3 (-1272 *2)) (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4))
+   (-4 *3 (-1264 *2)) (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4))
    (-14 *6 (-1 (-3 *4 "failed") *4 *4))
    (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4))))
  ((*1 *1 *1 *1)
@@ -11073,110 +10985,110 @@
    (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
    (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-1277 *3 *4 *5)) (-5 *1 (-331 *3 *4 *5)) (-4 *3 (-376))
-   (-14 *4 (-1206)) (-14 *5 *3)))
+  (-12 (-5 *2 (-1269 *3 *4 *5)) (-5 *1 (-331 *3 *4 *5)) (-4 *3 (-376))
+   (-14 *4 (-1198)) (-14 *5 *3)))
  ((*1 *2 *1) (-12 (-4 *1 (-416)) (-5 *2 (-558))))
  ((*1 *2 *1) (-12 (-5 *2 (-558)) (-5 *1 (-417 *3)) (-4 *3 (-569))))
  ((*1 *2 *1) (-12 (-5 *2 (-558)) (-5 *1 (-719))))
  ((*1 *2 *1)
-  (-12 (-4 *2 (-1130)) (-5 *1 (-733 *3 *2 *4)) (-4 *3 (-869))
+  (-12 (-4 *2 (-1122)) (-5 *1 (-733 *3 *2 *4)) (-4 *3 (-861))
    (-14 *4
-    (-1 (-114) (-2 (|:| -2639 *3) (|:| -2640 *2))
-     (-2 (|:| -2639 *3) (|:| -2640 *2))))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-946)) (-4 *1 (-381))))
+    (-1 (-114) (-2 (|:| -2631 *3) (|:| -2632 *2))
+     (-2 (|:| -2631 *3) (|:| -2632 *2))))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-938)) (-4 *1 (-381))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-946)) (-5 *2 (-1296 *4)) (-5 *1 (-540 *4)) (-4 *4 (-363))))
+  (-12 (-5 *3 (-938)) (-5 *2 (-1288 *4)) (-5 *1 (-540 *4)) (-4 *4 (-363))))
  ((*1 *2 *1)
-  (-12 (-4 *2 (-869)) (-5 *1 (-733 *2 *3 *4)) (-4 *3 (-1130))
+  (-12 (-4 *2 (-861)) (-5 *1 (-733 *2 *3 *4)) (-4 *3 (-1122))
    (-14 *4
-    (-1 (-114) (-2 (|:| -2639 *2) (|:| -2640 *3))
-     (-2 (|:| -2639 *2) (|:| -2640 *3))))))) 
-(((*1 *2 *2) (-12 (-4 *3 (-1078)) (-5 *1 (-732 *3 *2)) (-4 *2 (-1272 *3))))) 
+    (-1 (-114) (-2 (|:| -2631 *2) (|:| -2632 *3))
+     (-2 (|:| -2631 *2) (|:| -2632 *3))))))) 
+(((*1 *2 *2) (-12 (-4 *3 (-1070)) (-5 *1 (-732 *3 *2)) (-4 *2 (-1264 *3))))) 
 (((*1 *2 *1)
-  (-12 (-4 *3 (-1078)) (-5 *2 (-1296 *3)) (-5 *1 (-732 *3 *4))
-   (-4 *4 (-1272 *3))))) 
+  (-12 (-4 *3 (-1070)) (-5 *2 (-1288 *3)) (-5 *1 (-732 *3 *4))
+   (-4 *4 (-1264 *3))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-1296 *3)) (-4 *3 (-1078)) (-5 *1 (-732 *3 *4))
-   (-4 *4 (-1272 *3))))) 
+  (-12 (-5 *2 (-1288 *3)) (-4 *3 (-1070)) (-5 *1 (-732 *3 *4))
+   (-4 *4 (-1264 *3))))) 
 (((*1 *2 *1)
-  (-12 (-4 *3 (-1078)) (-5 *2 (-1296 *3)) (-5 *1 (-732 *3 *4))
-   (-4 *4 (-1272 *3))))) 
+  (-12 (-4 *3 (-1070)) (-5 *2 (-1288 *3)) (-5 *1 (-732 *3 *4))
+   (-4 *4 (-1264 *3))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-1078)) (-5 *2 (-985 (-732 *3 *4))) (-5 *1 (-732 *3 *4))
-   (-4 *4 (-1272 *3))))) 
+  (-12 (-4 *3 (-1070)) (-5 *2 (-977 (-732 *3 *4))) (-5 *1 (-732 *3 *4))
+   (-4 *4 (-1264 *3))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-1078)) (-5 *2 (-985 (-732 *3 *4))) (-5 *1 (-732 *3 *4))
-   (-4 *4 (-1272 *3))))) 
+  (-12 (-4 *3 (-1070)) (-5 *2 (-977 (-732 *3 *4))) (-5 *1 (-732 *3 *4))
+   (-4 *4 (-1264 *3))))) 
 (((*1 *1 *1)
-  (-12 (-4 *2 (-363)) (-4 *2 (-1078)) (-5 *1 (-732 *2 *3)) (-4 *3 (-1272 *2))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-885)) (-5 *2 (-1188)) (-5 *1 (-730))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-885)) (-5 *2 (-1188)) (-5 *1 (-730))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-885)) (-5 *2 (-1188)) (-5 *1 (-730))))) 
+  (-12 (-4 *2 (-363)) (-4 *2 (-1070)) (-5 *1 (-732 *2 *3)) (-4 *3 (-1264 *2))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-877)) (-5 *2 (-1180)) (-5 *1 (-730))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-877)) (-5 *2 (-1180)) (-5 *1 (-730))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-877)) (-5 *2 (-1180)) (-5 *1 (-730))))) 
 (((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10)
-  (|partial| -12 (-5 *2 (-661 (-1200 *13))) (-5 *3 (-1200 *13))
+  (|partial| -12 (-5 *2 (-661 (-1192 *13))) (-5 *3 (-1192 *13))
    (-5 *4 (-661 *12)) (-5 *5 (-661 *10)) (-5 *6 (-661 *13))
-   (-5 *7 (-661 (-661 (-2 (|:| -3556 (-791)) (|:| |pcoef| *13)))))
-   (-5 *8 (-661 (-791))) (-5 *9 (-1296 (-661 (-1200 *10)))) (-4 *12 (-869))
-   (-4 *10 (-319)) (-4 *13 (-977 *10 *11 *12)) (-4 *11 (-815))
+   (-5 *7 (-661 (-661 (-2 (|:| -3479 (-791)) (|:| |pcoef| *13)))))
+   (-5 *8 (-661 (-791))) (-5 *9 (-1288 (-661 (-1192 *10)))) (-4 *12 (-861))
+   (-4 *10 (-319)) (-4 *13 (-969 *10 *11 *12)) (-4 *11 (-815))
    (-5 *1 (-727 *11 *12 *10 *13))))) 
 (((*1 *2 *3 *4 *5 *6 *7 *8 *9)
-  (|partial| -12 (-5 *4 (-661 *11)) (-5 *5 (-661 (-1200 *9))) (-5 *6 (-661 *9))
-   (-5 *7 (-661 *12)) (-5 *8 (-661 (-791))) (-4 *11 (-869)) (-4 *9 (-319))
-   (-4 *12 (-977 *9 *10 *11)) (-4 *10 (-815)) (-5 *2 (-661 (-1200 *12)))
-   (-5 *1 (-727 *10 *11 *9 *12)) (-5 *3 (-1200 *12))))) 
+  (|partial| -12 (-5 *4 (-661 *11)) (-5 *5 (-661 (-1192 *9))) (-5 *6 (-661 *9))
+   (-5 *7 (-661 *12)) (-5 *8 (-661 (-791))) (-4 *11 (-861)) (-4 *9 (-319))
+   (-4 *12 (-969 *9 *10 *11)) (-4 *10 (-815)) (-5 *2 (-661 (-1192 *12)))
+   (-5 *1 (-727 *10 *11 *9 *12)) (-5 *3 (-1192 *12))))) 
 (((*1 *2 *3 *4 *5 *6 *2 *7 *8)
-  (|partial| -12 (-5 *2 (-661 (-1200 *11))) (-5 *3 (-1200 *11))
+  (|partial| -12 (-5 *2 (-661 (-1192 *11))) (-5 *3 (-1192 *11))
    (-5 *4 (-661 *10)) (-5 *5 (-661 *8)) (-5 *6 (-661 (-791)))
-   (-5 *7 (-1296 (-661 (-1200 *8)))) (-4 *10 (-869)) (-4 *8 (-319))
-   (-4 *11 (-977 *8 *9 *10)) (-4 *9 (-815)) (-5 *1 (-727 *9 *10 *8 *11))))) 
+   (-5 *7 (-1288 (-661 (-1192 *8)))) (-4 *10 (-861)) (-4 *8 (-319))
+   (-4 *11 (-969 *8 *9 *10)) (-4 *9 (-815)) (-5 *1 (-727 *9 *10 *8 *11))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1206)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-722 *3 *5 *6 *7))
-   (-4 *3 (-631 (-547))) (-4 *5 (-1246)) (-4 *6 (-1246)) (-4 *7 (-1246))))
+  (-12 (-5 *4 (-1198)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-722 *3 *5 *6 *7))
+   (-4 *3 (-631 (-547))) (-4 *5 (-1238)) (-4 *6 (-1238)) (-4 *7 (-1238))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1206)) (-5 *2 (-1 *6 *5)) (-5 *1 (-726 *3 *5 *6))
-   (-4 *3 (-631 (-547))) (-4 *5 (-1246)) (-4 *6 (-1246))))) 
+  (-12 (-5 *4 (-1198)) (-5 *2 (-1 *6 *5)) (-5 *1 (-726 *3 *5 *6))
+   (-4 *3 (-631 (-547))) (-4 *5 (-1238)) (-4 *6 (-1238))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1206)) (-5 *2 (-1 *6 *5)) (-5 *1 (-726 *4 *5 *6))
-   (-4 *4 (-631 (-547))) (-4 *5 (-1246)) (-4 *6 (-1246))))) 
+  (-12 (-5 *3 (-1198)) (-5 *2 (-1 *6 *5)) (-5 *1 (-726 *4 *5 *6))
+   (-4 *4 (-631 (-547))) (-4 *5 (-1238)) (-4 *6 (-1238))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-725 *3 *4))
-   (-4 *3 (-1246)) (-4 *4 (-1246))))) 
-(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-661 (-1206))) (-5 *3 (-1206)) (-5 *1 (-547))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-1206)) (-5 *1 (-724 *3)) (-4 *3 (-631 (-547)))))
+   (-4 *3 (-1238)) (-4 *4 (-1238))))) 
+(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-661 (-1198))) (-5 *3 (-1198)) (-5 *1 (-547))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1198)) (-5 *1 (-724 *3)) (-4 *3 (-631 (-547)))))
  ((*1 *2 *3 *2 *2)
-  (-12 (-5 *2 (-1206)) (-5 *1 (-724 *3)) (-4 *3 (-631 (-547)))))
+  (-12 (-5 *2 (-1198)) (-5 *1 (-724 *3)) (-4 *3 (-631 (-547)))))
  ((*1 *2 *3 *2 *2 *2)
-  (-12 (-5 *2 (-1206)) (-5 *1 (-724 *3)) (-4 *3 (-631 (-547)))))
+  (-12 (-5 *2 (-1198)) (-5 *1 (-724 *3)) (-4 *3 (-631 (-547)))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *4 (-661 (-1206))) (-5 *2 (-1206)) (-5 *1 (-724 *3))
+  (-12 (-5 *4 (-661 (-1198))) (-5 *2 (-1198)) (-5 *1 (-724 *3))
    (-4 *3 (-631 (-547)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1206)) (-5 *2 (-1 (-229) (-229))) (-5 *1 (-723 *3))
+  (-12 (-5 *4 (-1198)) (-5 *2 (-1 (-229) (-229))) (-5 *1 (-723 *3))
    (-4 *3 (-631 (-547)))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1206)) (-5 *2 (-1 (-229) (-229) (-229))) (-5 *1 (-723 *3))
+  (-12 (-5 *4 (-1198)) (-5 *2 (-1 (-229) (-229) (-229))) (-5 *1 (-723 *3))
    (-4 *3 (-631 (-547)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1206)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-722 *4 *5 *6 *7))
-   (-4 *4 (-631 (-547))) (-4 *5 (-1246)) (-4 *6 (-1246)) (-4 *7 (-1246))))) 
-(((*1 *2) (-12 (-5 *2 (-946)) (-5 *1 (-721))))
- ((*1 *2 *2) (-12 (-5 *2 (-946)) (-5 *1 (-721))))) 
+  (-12 (-5 *3 (-1198)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-722 *4 *5 *6 *7))
+   (-4 *4 (-631 (-547))) (-4 *5 (-1238)) (-4 *6 (-1238)) (-4 *7 (-1238))))) 
+(((*1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-721))))
+ ((*1 *2 *2) (-12 (-5 *2 (-938)) (-5 *1 (-721))))) 
 (((*1 *2 *3 *3)
   (-12 (-4 *3 (-319)) (-4 *3 (-175)) (-4 *4 (-385 *3)) (-4 *5 (-385 *3))
-   (-5 *2 (-2 (|:| -2192 *3) (|:| -3380 *3))) (-5 *1 (-708 *3 *4 *5 *6))
+   (-5 *2 (-2 (|:| -2184 *3) (|:| -3303 *3))) (-5 *1 (-708 *3 *4 *5 *6))
    (-4 *6 (-706 *3 *4 *5))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-2 (|:| -2192 *3) (|:| -3380 *3))) (-5 *1 (-720 *3))
+  (-12 (-5 *2 (-2 (|:| -2184 *3) (|:| -3303 *3))) (-5 *1 (-720 *3))
    (-4 *3 (-319))))) 
 (((*1 *2 *2 *3 *3) (-12 (-5 *2 (-709 *3)) (-4 *3 (-319)) (-5 *1 (-720 *3))))) 
 (((*1 *2 *2 *3) (-12 (-5 *2 (-709 *3)) (-4 *3 (-319)) (-5 *1 (-720 *3))))) 
 (((*1 *2 *2) (-12 (-5 *2 (-709 *3)) (-4 *3 (-319)) (-5 *1 (-720 *3))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-416)) (-5 *2 (-558))))
  ((*1 *2 *1) (-12 (-5 *2 (-558)) (-5 *1 (-719))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-946)) (|has| *1 (-6 -4493)) (-4 *1 (-416))))
- ((*1 *2) (-12 (-4 *1 (-416)) (-5 *2 (-946))))
- ((*1 *2 *2) (-12 (-5 *2 (-946)) (-5 *1 (-719))))
- ((*1 *2) (-12 (-5 *2 (-946)) (-5 *1 (-719))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-938)) (|has| *1 (-6 -4416)) (-4 *1 (-416))))
+ ((*1 *2) (-12 (-4 *1 (-416)) (-5 *2 (-938))))
+ ((*1 *2 *2) (-12 (-5 *2 (-938)) (-5 *1 (-719))))
+ ((*1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-719))))) 
 (((*1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-719))))
  ((*1 *2 *2) (-12 (-5 *2 (-558)) (-5 *1 (-719))))) 
 (((*1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-719))))
@@ -11184,85 +11096,85 @@
 (((*1 *2 *3 *3 *3 *4)
   (-12 (-5 *3 (-1 (-229) (-229) (-229)))
    (-5 *4 (-1 (-229) (-229) (-229) (-229)))
-   (-5 *2 (-1 (-970 (-229)) (-229) (-229))) (-5 *1 (-717))))) 
+   (-5 *2 (-1 (-962 (-229)) (-229) (-229))) (-5 *1 (-717))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *6)
-  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1118 (-229)))
-   (-5 *6 (-661 (-270))) (-5 *2 (-1162 (-229))) (-5 *1 (-717))))) 
+  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1110 (-229)))
+   (-5 *6 (-661 (-270))) (-5 *2 (-1154 (-229))) (-5 *1 (-717))))) 
 (((*1 *2 *3 *4 *5 *5 *6)
   (-12 (-5 *3 (-1 (-229) (-229) (-229)))
    (-5 *4 (-3 (-1 (-229) (-229) (-229) (-229)) "undefined"))
-   (-5 *5 (-1118 (-229))) (-5 *6 (-661 (-270))) (-5 *2 (-1162 (-229)))
+   (-5 *5 (-1110 (-229))) (-5 *6 (-661 (-270))) (-5 *2 (-1154 (-229)))
    (-5 *1 (-717))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *5 *6)
   (-12 (-5 *3 (-1 (-229) (-229) (-229)))
    (-5 *4 (-3 (-1 (-229) (-229) (-229) (-229)) "undefined"))
-   (-5 *5 (-1118 (-229))) (-5 *6 (-661 (-270))) (-5 *2 (-1162 (-229)))
+   (-5 *5 (-1110 (-229))) (-5 *6 (-661 (-270))) (-5 *2 (-1154 (-229)))
    (-5 *1 (-717))))
  ((*1 *2 *3 *4 *4 *5)
-  (-12 (-5 *3 (-1 (-970 (-229)) (-229) (-229))) (-5 *4 (-1118 (-229)))
-   (-5 *5 (-661 (-270))) (-5 *2 (-1162 (-229))) (-5 *1 (-717))))
+  (-12 (-5 *3 (-1 (-962 (-229)) (-229) (-229))) (-5 *4 (-1110 (-229)))
+   (-5 *5 (-661 (-270))) (-5 *2 (-1154 (-229))) (-5 *1 (-717))))
  ((*1 *2 *2 *3 *4 *4 *5)
-  (-12 (-5 *2 (-1162 (-229))) (-5 *3 (-1 (-970 (-229)) (-229) (-229)))
-   (-5 *4 (-1118 (-229))) (-5 *5 (-661 (-270))) (-5 *1 (-717))))) 
+  (-12 (-5 *2 (-1154 (-229))) (-5 *3 (-1 (-962 (-229)) (-229) (-229)))
+   (-5 *4 (-1110 (-229))) (-5 *5 (-661 (-270))) (-5 *1 (-717))))) 
 (((*1 *2 *2 *3 *2)
-  (-12 (-5 *3 (-791)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) (-4 *2 (-1272 *4))))
+  (-12 (-5 *3 (-791)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) (-4 *2 (-1264 *4))))
  ((*1 *2 *2 *3 *2 *3)
-  (-12 (-5 *3 (-558)) (-5 *1 (-716 *2)) (-4 *2 (-1272 *3))))) 
+  (-12 (-5 *3 (-558)) (-5 *1 (-716 *2)) (-4 *2 (-1264 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-2 (|:| |deg| (-791)) (|:| -3051 *5)))) (-4 *5 (-1272 *4))
+  (-12 (-5 *3 (-661 (-2 (|:| |deg| (-791)) (|:| -2974 *5)))) (-4 *5 (-1264 *4))
    (-4 *4 (-363)) (-5 *2 (-661 *5)) (-5 *1 (-220 *4 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-2 (|:| -4239 *5) (|:| -4455 (-558))))) (-5 *4 (-558))
-   (-4 *5 (-1272 *4)) (-5 *2 (-661 *5)) (-5 *1 (-716 *5))))) 
+  (-12 (-5 *3 (-661 (-2 (|:| -4162 *5) (|:| -4378 (-558))))) (-5 *4 (-558))
+   (-4 *5 (-1264 *4)) (-5 *2 (-661 *5)) (-5 *1 (-716 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-558)) (-5 *2 (-661 (-2 (|:| -4239 *3) (|:| -4455 *4))))
-   (-5 *1 (-716 *3)) (-4 *3 (-1272 *4))))) 
-(((*1 *2 *2 *3) (-12 (-5 *3 (-558)) (-5 *1 (-716 *2)) (-4 *2 (-1272 *3))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-294 *2)) (-4 *2 (-1246)) (-4 *2 (-1130))))
- ((*1 *1 *1) (-12 (-4 *1 (-715 *2)) (-4 *2 (-1130))))) 
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 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1296 (-326 (-229)))) (-5 *4 (-661 (-1206)))
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 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *5 (-791)) (-4 *6 (-1130)) (-4 *3 (-925 *6)) (-5 *2 (-709 *3))
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 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-1130)) (-4 *3 (-925 *5)) (-5 *2 (-709 *3))
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 (((*1 *2 *2 *3)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4)
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+(((*1 *2 *2 *2) (-12 (-5 *2 (-709 *3)) (-4 *3 (-1070)) (-5 *1 (-710 *3))))
+ ((*1 *2 *2 *2 *2) (-12 (-5 *2 (-709 *3)) (-4 *3 (-1070)) (-5 *1 (-710 *3))))) 
+(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-709 *3)) (-4 *3 (-1070)) (-5 *1 (-710 *3))))) 
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 (((*1 *2 *2)
   (|partial| -12 (-4 *3 (-569)) (-4 *3 (-175)) (-4 *4 (-385 *3))
    (-4 *5 (-385 *3)) (-5 *1 (-708 *3 *4 *5 *2)) (-4 *2 (-706 *3 *4 *5))))) 
@@ -11279,346 +11191,346 @@
   (-12 (-5 *3 (-558)) (-4 *4 (-175)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))
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 (((*1 *1 *1)
-  (-12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-385 *2))
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    (-4 *4 (-385 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-385 *2))
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    (-4 *4 (-385 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1078)) (-4 *3 (-385 *2))
+  (-12 (-4 *1 (-706 *2 *3 *4)) (-4 *2 (-1070)) (-4 *3 (-385 *2))
    (-4 *4 (-385 *2))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-558)) (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-385 *3))
+  (-12 (-5 *2 (-558)) (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1070)) (-4 *4 (-385 *3))
    (-4 *5 (-385 *3))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-558)) (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-385 *3))
+  (-12 (-5 *2 (-558)) (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1070)) (-4 *4 (-385 *3))
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-  (-12 (-5 *2 (-558)) (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-385 *3))
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    (-4 *5 (-385 *3))))) 
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-  (-12 (-5 *2 (-558)) (-4 *1 (-706 *3 *4 *5)) (-4 *3 (-1078)) (-4 *4 (-385 *3))
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3)
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 (((*1 *2 *3 *4)
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-    (-2 (|:| |particular| (-3 (-1296 (-419 *8)) "failed"))
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 (((*1 *1 *1) (-4 *1 (-682)))) 
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 (((*1 *2 *3)
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      "failed"))
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      #3="failed"))
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      #3#))
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 (((*1 *1 *2) (-12 (-5 *2 (-402)) (-5 *1 (-649))))) 
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 (((*1 *2 *2 *3)
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   (-12 (-5 *3 (-661 *6)) (-5 *4 (-661 (-255 *5 *6))) (-4 *6 (-464))
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-  (-12 (-5 *3 (-661 (-493 *4 *5))) (-14 *4 (-661 (-1206))) (-4 *5 (-464))
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 (((*1 *2 *3)
-  (-12 (-14 *4 (-661 (-1206))) (-4 *5 (-464))
+  (-12 (-14 *4 (-661 (-1198))) (-4 *5 (-464))
    (-5 *2 (-2 (|:| |glbase| (-661 (-255 *4 *5))) (|:| |glval| (-661 (-558)))))
    (-5 *1 (-648 *4 *5)) (-5 *3 (-661 (-255 *4 *5)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-493 *4 *5))) (-14 *4 (-661 (-1206))) (-4 *5 (-464))
+  (-12 (-5 *3 (-661 (-493 *4 *5))) (-14 *4 (-661 (-1198))) (-4 *5 (-464))
    (-5 *2 (-2 (|:| |gblist| (-661 (-255 *4 *5))) (|:| |gvlist| (-661 (-558)))))
    (-5 *1 (-648 *4 *5))))) 
 (((*1 *2 *2)
   (-12 (-4 *3 (-569)) (-5 *1 (-646 *3 *2))
-   (-4 *2 (-13 (-433 *3) (-1031) (-1232)))))
+   (-4 *2 (-13 (-433 *3) (-1023) (-1224)))))
  ((*1 *1 *1) (-4 *1 (-647)))) 
 (((*1 *2 *2)
   (-12 (-4 *3 (-569)) (-5 *1 (-646 *3 *2))
-   (-4 *2 (-13 (-433 *3) (-1031) (-1232)))))
+   (-4 *2 (-13 (-433 *3) (-1023) (-1224)))))
  ((*1 *1 *1) (-4 *1 (-647)))) 
 (((*1 *2 *2)
   (-12 (-4 *3 (-569)) (-5 *1 (-646 *3 *2))
-   (-4 *2 (-13 (-433 *3) (-1031) (-1232)))))
+   (-4 *2 (-13 (-433 *3) (-1023) (-1224)))))
  ((*1 *1 *1) (-4 *1 (-647)))) 
 (((*1 *2 *2)
   (-12 (-4 *3 (-569)) (-5 *1 (-646 *3 *2))
-   (-4 *2 (-13 (-433 *3) (-1031) (-1232)))))
+   (-4 *2 (-13 (-433 *3) (-1023) (-1224)))))
  ((*1 *1 *1) (-4 *1 (-647)))) 
 (((*1 *2 *2)
   (-12 (-4 *3 (-569)) (-5 *1 (-646 *3 *2))
-   (-4 *2 (-13 (-433 *3) (-1031) (-1232)))))
+   (-4 *2 (-13 (-433 *3) (-1023) (-1224)))))
  ((*1 *1 *1) (-4 *1 (-647)))) 
 (((*1 *2 *2)
   (-12 (-4 *3 (-569)) (-5 *1 (-646 *3 *2))
-   (-4 *2 (-13 (-433 *3) (-1031) (-1232)))))
+   (-4 *2 (-13 (-433 *3) (-1023) (-1224)))))
  ((*1 *1 *1) (-4 *1 (-647)))) 
 (((*1 *2 *3)
   (-12 (-5 *3 (-115)) (-4 *4 (-569)) (-5 *2 (-114)) (-5 *1 (-32 *4 *5))
@@ -11628,120 +11540,120 @@
    (-4 *5 (-433 *4))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-115)) (-4 *4 (-569)) (-5 *2 (-114)) (-5 *1 (-287 *4 *5))
-   (-4 *5 (-13 (-433 *4) (-1031)))))
+   (-4 *5 (-13 (-433 *4) (-1023)))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-115)) (-5 *2 (-114)) (-5 *1 (-309 *4)) (-4 *4 (-310))))
  ((*1 *2 *3) (-12 (-4 *1 (-310)) (-5 *3 (-115)) (-5 *2 (-114))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-115)) (-4 *5 (-1130)) (-5 *2 (-114)) (-5 *1 (-432 *4 *5))
+  (-12 (-5 *3 (-115)) (-4 *5 (-1122)) (-5 *2 (-114)) (-5 *1 (-432 *4 *5))
    (-4 *4 (-433 *5))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-115)) (-4 *4 (-569)) (-5 *2 (-114)) (-5 *1 (-443 *4 *5))
    (-4 *5 (-433 *4))))
  ((*1 *2 *3)
   (-12 (-5 *3 (-115)) (-4 *4 (-569)) (-5 *2 (-114)) (-5 *1 (-646 *4 *5))
-   (-4 *5 (-13 (-433 *4) (-1031) (-1232)))))) 
+   (-4 *5 (-13 (-433 *4) (-1023) (-1224)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-800 *5 (-886 *6)))) (-5 *4 (-114)) (-4 *5 (-464))
-   (-14 *6 (-661 (-1206)))
-   (-5 *2 (-661 (-1175 *5 (-543 (-886 *6)) (-886 *6) (-800 *5 (-886 *6)))))
+  (-12 (-5 *3 (-661 (-800 *5 (-878 *6)))) (-5 *4 (-114)) (-4 *5 (-464))
+   (-14 *6 (-661 (-1198)))
+   (-5 *2 (-661 (-1167 *5 (-543 (-878 *6)) (-878 *6) (-800 *5 (-878 *6)))))
    (-5 *1 (-645 *5 *6))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-800 *5 (-886 *6)))) (-5 *4 (-114)) (-4 *5 (-464))
-   (-14 *6 (-661 (-1206))) (-5 *2 (-661 (-1075 *5 *6))) (-5 *1 (-645 *5 *6))))) 
+  (-12 (-5 *3 (-661 (-800 *5 (-878 *6)))) (-5 *4 (-114)) (-4 *5 (-464))
+   (-14 *6 (-661 (-1198))) (-5 *2 (-661 (-1067 *5 *6))) (-5 *1 (-645 *5 *6))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 (-973 *3))) (-4 *3 (-464)) (-5 *1 (-373 *3 *4))
-   (-14 *4 (-661 (-1206)))))
+  (-12 (-5 *2 (-661 (-965 *3))) (-4 *3 (-464)) (-5 *1 (-373 *3 *4))
+   (-14 *4 (-661 (-1198)))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-464)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-459 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-464)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-459 *3 *4 *5 *6))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-661 *7)) (-5 *3 (-1188)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-464))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *1 (-459 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-661 *7)) (-5 *3 (-1180)) (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-464))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *1 (-459 *4 *5 *6 *7))))
  ((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-661 *7)) (-5 *3 (-1188)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-464))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *1 (-459 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-661 *7)) (-5 *3 (-1180)) (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-464))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *1 (-459 *4 *5 *6 *7))))
  ((*1 *1 *1)
-  (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-869)) (-5 *1 (-516 *2 *3 *4 *5))
-   (-4 *5 (-977 *2 *3 *4))))
+  (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-861)) (-5 *1 (-516 *2 *3 *4 *5))
+   (-4 *5 (-969 *2 *3 *4))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-661 (-800 *3 (-886 *4)))) (-4 *3 (-464))
-   (-14 *4 (-661 (-1206))) (-5 *1 (-645 *3 *4))))) 
+  (-12 (-5 *2 (-661 (-800 *3 (-878 *4)))) (-4 *3 (-464))
+   (-14 *4 (-661 (-1198))) (-5 *1 (-645 *3 *4))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-661 (-973 *3))) (-4 *3 (-464)) (-5 *1 (-373 *3 *4))
-   (-14 *4 (-661 (-1206)))))
+  (|partial| -12 (-5 *2 (-661 (-965 *3))) (-4 *3 (-464)) (-5 *1 (-373 *3 *4))
+   (-14 *4 (-661 (-1198)))))
  ((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-661 (-800 *3 (-886 *4)))) (-4 *3 (-464))
-   (-14 *4 (-661 (-1206))) (-5 *1 (-645 *3 *4))))) 
+  (|partial| -12 (-5 *2 (-661 (-800 *3 (-878 *4)))) (-4 *3 (-464))
+   (-14 *4 (-661 (-1198))) (-5 *1 (-645 *3 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-973 *4))) (-4 *4 (-464)) (-5 *2 (-114))
-   (-5 *1 (-373 *4 *5)) (-14 *5 (-661 (-1206)))))
+  (-12 (-5 *3 (-661 (-965 *4))) (-4 *4 (-464)) (-5 *2 (-114))
+   (-5 *1 (-373 *4 *5)) (-14 *5 (-661 (-1198)))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-800 *4 (-886 *5)))) (-4 *4 (-464))
-   (-14 *5 (-661 (-1206))) (-5 *2 (-114)) (-5 *1 (-645 *4 *5))))) 
+  (-12 (-5 *3 (-661 (-800 *4 (-878 *5)))) (-4 *4 (-464))
+   (-14 *5 (-661 (-1198))) (-5 *2 (-114)) (-5 *1 (-645 *4 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 *4)) (-4 *4 (-869)) (-5 *2 (-661 (-684 *4 *5)))
+  (-12 (-5 *3 (-661 *4)) (-4 *4 (-861)) (-5 *2 (-661 (-684 *4 *5)))
    (-5 *1 (-644 *4 *5 *6)) (-4 *5 (-13 (-175) (-737 (-419 (-558)))))
-   (-14 *6 (-946))))) 
+   (-14 *6 (-938))))) 
 (((*1 *2 *1)
   (-12 (-5 *2 (-661 (-2 (|:| |k| (-692 *3)) (|:| |c| *4))))
-   (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-869))
-   (-4 *4 (-13 (-175) (-737 (-419 (-558))))) (-14 *5 (-946))))) 
+   (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-861))
+   (-4 *4 (-13 (-175) (-737 (-419 (-558))))) (-14 *5 (-938))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-661 (-305 *4))) (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-869))
-   (-4 *4 (-13 (-175) (-737 (-419 (-558))))) (-14 *5 (-946))))) 
+  (-12 (-5 *2 (-661 (-305 *4))) (-5 *1 (-644 *3 *4 *5)) (-4 *3 (-861))
+   (-4 *4 (-13 (-175) (-737 (-419 (-558))))) (-14 *5 (-938))))) 
 (((*1 *2 *3 *4 *5 *6 *7 *6)
   (|partial| -12
    (-5 *5
     (-2 (|:| |contp| *3)
-     (|:| -1995 (-661 (-2 (|:| |irr| *10) (|:| -2634 (-558)))))))
-   (-5 *6 (-661 *3)) (-5 *7 (-661 *8)) (-4 *8 (-869)) (-4 *3 (-319))
-   (-4 *10 (-977 *3 *9 *8)) (-4 *9 (-815))
+     (|:| -1987 (-661 (-2 (|:| |irr| *10) (|:| -2626 (-558)))))))
+   (-5 *6 (-661 *3)) (-5 *7 (-661 *8)) (-4 *8 (-861)) (-4 *3 (-319))
+   (-4 *10 (-969 *3 *9 *8)) (-4 *9 (-815))
    (-5 *2
     (-2 (|:| |polfac| (-661 *10)) (|:| |correct| *3)
-     (|:| |corrfact| (-661 (-1200 *3)))))
-   (-5 *1 (-642 *8 *9 *3 *10)) (-5 *4 (-661 (-1200 *3)))))) 
+     (|:| |corrfact| (-661 (-1192 *3)))))
+   (-5 *1 (-642 *8 *9 *3 *10)) (-5 *4 (-661 (-1192 *3)))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *4 (-791)) (-5 *5 (-661 *3)) (-4 *3 (-319)) (-4 *6 (-869))
+  (-12 (-5 *4 (-791)) (-5 *5 (-661 *3)) (-4 *3 (-319)) (-4 *6 (-861))
    (-4 *7 (-815)) (-5 *2 (-114)) (-5 *1 (-642 *6 *7 *3 *8))
-   (-4 *8 (-977 *3 *7 *6))))) 
+   (-4 *8 (-969 *3 *7 *6))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-869)) (-4 *6 (-1094 *3 *4 *5))
-   (-5 *1 (-641 *3 *4 *5 *6 *7 *2)) (-4 *7 (-1100 *3 *4 *5 *6))
-   (-4 *2 (-1138 *3 *4 *5 *6))))) 
-(((*1 *2 *1) (-12 (-4 *2 (-569)) (-5 *1 (-640 *2 *3)) (-4 *3 (-1272 *2))))) 
+  (-12 (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-861)) (-4 *6 (-1086 *3 *4 *5))
+   (-5 *1 (-641 *3 *4 *5 *6 *7 *2)) (-4 *7 (-1092 *3 *4 *5 *6))
+   (-4 *2 (-1130 *3 *4 *5 *6))))) 
+(((*1 *2 *1) (-12 (-4 *2 (-569)) (-5 *1 (-640 *2 *3)) (-4 *3 (-1264 *2))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-13 (-319) (-149) (-1067 (-558)) (-658 (-558))))
-   (-5 *1 (-639 *4 *2)) (-4 *2 (-13 (-1232) (-987) (-29 *4)))))) 
+  (-12 (-5 *3 (-1198)) (-4 *4 (-13 (-319) (-149) (-1059 (-558)) (-658 (-558))))
+   (-5 *1 (-639 *4 *2)) (-4 *2 (-13 (-1224) (-979) (-29 *4)))))) 
 (((*1 *1) (-5 *1 (-634)))) 
 (((*1 *2 *3 *3 *3)
   (|partial| -12
-   (-4 *4 (-13 (-149) (-27) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-4 *5 (-1272 *4)) (-5 *2 (-1200 (-419 *5))) (-5 *1 (-632 *4 *5))
+   (-4 *4 (-13 (-149) (-27) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-4 *5 (-1264 *4)) (-5 *2 (-1192 (-419 *5))) (-5 *1 (-632 *4 *5))
    (-5 *3 (-419 *5))))
  ((*1 *2 *3 *3 *3 *4)
-  (|partial| -12 (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-149) (-27) (-1067 (-558)) (-1067 (-419 (-558)))))
-   (-5 *2 (-1200 (-419 *6))) (-5 *1 (-632 *5 *6)) (-5 *3 (-419 *6))))) 
+  (|partial| -12 (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-149) (-27) (-1059 (-558)) (-1059 (-419 (-558)))))
+   (-5 *2 (-1192 (-419 *6))) (-5 *1 (-632 *5 *6)) (-5 *3 (-419 *6))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-628 *4)) (-4 *4 (-1130)) (-4 *2 (-1130))
+  (|partial| -12 (-5 *3 (-628 *4)) (-4 *4 (-1122)) (-4 *2 (-1122))
    (-5 *1 (-629 *2 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-628 *4)) (-5 *1 (-629 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)) (-4 *2 (-1232))))
- ((*1 *2 *1) (-12 (-5 *1 (-343 *2)) (-4 *2 (-869))))
- ((*1 *2 *1) (-12 (-5 *2 (-661 *3)) (-5 *1 (-628 *3)) (-4 *3 (-1130))))) 
+  (-12 (-5 *2 (-628 *4)) (-5 *1 (-629 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175)) (-4 *2 (-1224))))
+ ((*1 *2 *1) (-12 (-5 *1 (-343 *2)) (-4 *2 (-861))))
+ ((*1 *2 *1) (-12 (-5 *2 (-661 *3)) (-5 *1 (-628 *3)) (-4 *3 (-1122))))) 
 (((*1 *1 *2 *3) (-12 (-5 *2 (-115)) (-5 *3 (-661 *1)) (-4 *1 (-310))))
  ((*1 *1 *2 *1) (-12 (-4 *1 (-310)) (-5 *2 (-115))))
- ((*1 *1 *2) (-12 (-5 *2 (-1206)) (-5 *1 (-628 *3)) (-4 *3 (-1130))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1198)) (-5 *1 (-628 *3)) (-4 *3 (-1122))))
  ((*1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-115)) (-5 *3 (-661 *5)) (-5 *4 (-791)) (-4 *5 (-1130))
+  (-12 (-5 *2 (-115)) (-5 *3 (-661 *5)) (-5 *4 (-791)) (-4 *5 (-1122))
    (-5 *1 (-628 *5))))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-1206)) (-5 *1 (-628 *3)) (-4 *3 (-1130))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-1198)) (-5 *1 (-628 *3)) (-4 *3 (-1122))))) 
 (((*1 *2 *3 *1)
-  (-12 (-4 *1 (-627 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130)) (-5 *2 (-114))))) 
+  (-12 (-4 *1 (-627 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122)) (-5 *2 (-114))))) 
 (((*1 *2 *3 *1)
-  (|partial| -12 (-4 *1 (-627 *3 *2)) (-4 *3 (-1130)) (-4 *2 (-1130))))) 
+  (|partial| -12 (-4 *1 (-627 *3 *2)) (-4 *3 (-1122)) (-4 *2 (-1122))))) 
 (((*1 *1) (-5 *1 (-620))) ((*1 *1) (-5 *1 (-622))) ((*1 *1) (-5 *1 (-623)))) 
 (((*1 *1) (-5 *1 (-622))) ((*1 *1) (-5 *1 (-623)))) 
 (((*1 *1) (-5 *1 (-622))) ((*1 *1) (-5 *1 (-623)))) 
@@ -11766,18 +11678,18 @@
 (((*1 *1) (-5 *1 (-621)))) 
 (((*1 *1) (-5 *1 (-620)))) 
 (((*1 *1) (-5 *1 (-620)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-985 (-187 (-141)))) (-5 *1 (-345))))
- ((*1 *2 *1) (-12 (-5 *2 (-661 (-1247))) (-5 *1 (-617))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-977 (-187 (-141)))) (-5 *1 (-345))))
+ ((*1 *2 *1) (-12 (-5 *2 (-661 (-1239))) (-5 *1 (-617))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
     (-661
      (-2
-      (|:| -4367
-           (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-            (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+      (|:| -4290
+           (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+            (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
             (|:| |relerr| (-229))))
-      (|:| -2294
+      (|:| -2286
            (-2
             (|:| |endPointContinuity|
                  (-3 (|:| |continuous| "Continuous at the end points")
@@ -11790,10 +11702,10 @@
                   (|:| |notEvaluated|
                        "End point continuity not yet evaluated")))
             (|:| |singularitiesStream|
-                 (-3 (|:| |str| (-1184 (-229)))
+                 (-3 (|:| |str| (-1176 (-229)))
                   (|:| |notEvaluated|
                        "Internal singularities not yet evaluated")))
-            (|:| -1646
+            (|:| -1638
                  (-3 (|:| |finite| "The range is finite")
                   (|:| |lowerInfinite| "The bottom of range is infinite")
                   (|:| |upperInfinite| "The top of range is infinite")
@@ -11802,152 +11714,152 @@
                   (|:| |notEvaluated| "Range not yet evaluated"))))))))
    (-5 *1 (-572))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1246)) (-5 *2 (-661 *4))))) 
+  (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1238)) (-5 *2 (-661 *4))))) 
 (((*1 *2 *3 *1)
-  (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1246)) (-5 *2 (-114))))) 
+  (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1238)) (-5 *2 (-114))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1246)) (-5 *2 (-661 *3))))) 
+  (-12 (-4 *1 (-616 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1238)) (-5 *2 (-661 *3))))) 
 (((*1 *2 *3 *1)
-  (-12 (|has| *1 (-6 -4502)) (-4 *1 (-616 *4 *3)) (-4 *4 (-1130))
-   (-4 *3 (-1246)) (-4 *3 (-1130)) (-5 *2 (-114))))) 
+  (-12 (|has| *1 (-6 -4425)) (-4 *1 (-616 *4 *3)) (-4 *4 (-1122))
+   (-4 *3 (-1238)) (-4 *3 (-1122)) (-5 *2 (-114))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-616 *2 *3)) (-4 *3 (-1246)) (-4 *2 (-1130)) (-4 *2 (-869))))) 
+  (-12 (-4 *1 (-616 *2 *3)) (-4 *3 (-1238)) (-4 *2 (-1122)) (-4 *2 (-861))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-616 *2 *3)) (-4 *3 (-1246)) (-4 *2 (-1130)) (-4 *2 (-869))))) 
+  (-12 (-4 *1 (-616 *2 *3)) (-4 *3 (-1238)) (-4 *2 (-1122)) (-4 *2 (-861))))) 
 (((*1 *1 *1 *2)
-  (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1246)) (-4 *3 (-385 *2))
+  (-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1238)) (-4 *3 (-385 *2))
    (-4 *4 (-385 *2))))
  ((*1 *1 *1 *2)
-  (-12 (|has| *1 (-6 -4503)) (-4 *1 (-616 *3 *2)) (-4 *3 (-1130))
-   (-4 *2 (-1246))))) 
+  (-12 (|has| *1 (-6 -4426)) (-4 *1 (-616 *3 *2)) (-4 *3 (-1122))
+   (-4 *2 (-1238))))) 
 (((*1 *2 *1 *3 *3)
-  (-12 (|has| *1 (-6 -4503)) (-4 *1 (-616 *3 *4)) (-4 *3 (-1130))
-   (-4 *4 (-1246)) (-5 *2 (-1302))))) 
+  (-12 (|has| *1 (-6 -4426)) (-4 *1 (-616 *3 *4)) (-4 *3 (-1122))
+   (-4 *4 (-1238)) (-5 *2 (-1294))))) 
 (((*1 *2 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-628 *2))) (-5 *4 (-661 (-1206)))
-   (-4 *2 (-13 (-433 (-171 *5)) (-1031) (-1232))) (-4 *5 (-569))
-   (-5 *1 (-612 *5 *6 *2)) (-4 *6 (-13 (-433 *5) (-1031) (-1232)))))) 
+  (-12 (-5 *3 (-661 (-628 *2))) (-5 *4 (-661 (-1198)))
+   (-4 *2 (-13 (-433 (-171 *5)) (-1023) (-1224))) (-4 *5 (-569))
+   (-5 *1 (-612 *5 *6 *2)) (-4 *6 (-13 (-433 *5) (-1023) (-1224)))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-569)) (-5 *2 (-171 *5)) (-5 *1 (-612 *4 *5 *3))
-   (-4 *5 (-13 (-433 *4) (-1031) (-1232)))
-   (-4 *3 (-13 (-433 (-171 *4)) (-1031) (-1232)))))) 
+   (-4 *5 (-13 (-433 *4) (-1023) (-1224)))
+   (-4 *3 (-13 (-433 (-171 *4)) (-1023) (-1224)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *2 (-13 (-433 (-171 *4)) (-1031) (-1232)))
-   (-5 *1 (-612 *4 *3 *2)) (-4 *3 (-13 (-433 *4) (-1031) (-1232)))))) 
+  (-12 (-4 *4 (-569)) (-4 *2 (-13 (-433 (-171 *4)) (-1023) (-1224)))
+   (-5 *1 (-612 *4 *3 *2)) (-4 *3 (-13 (-433 *4) (-1023) (-1224)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-4 *2 (-13 (-433 *4) (-1031) (-1232)))
-   (-5 *1 (-612 *4 *2 *3)) (-4 *3 (-13 (-433 (-171 *4)) (-1031) (-1232)))))) 
+  (-12 (-4 *4 (-569)) (-4 *2 (-13 (-433 *4) (-1023) (-1224)))
+   (-5 *1 (-612 *4 *2 *3)) (-4 *3 (-13 (-433 (-171 *4)) (-1023) (-1224)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-171 *5)) (-4 *5 (-13 (-433 *4) (-1031) (-1232))) (-4 *4 (-569))
-   (-4 *2 (-13 (-433 (-171 *4)) (-1031) (-1232))) (-5 *1 (-612 *4 *5 *2))))) 
+  (-12 (-5 *3 (-171 *5)) (-4 *5 (-13 (-433 *4) (-1023) (-1224))) (-4 *4 (-569))
+   (-4 *2 (-13 (-433 (-171 *4)) (-1023) (-1224))) (-5 *1 (-612 *4 *5 *2))))) 
 (((*1 *1) (-5 *1 (-609)))) 
 (((*1 *1) (-5 *1 (-609)))) 
 (((*1 *1) (-5 *1 (-609)))) 
 (((*1 *1) (-5 *1 (-609)))) 
 (((*1 *1 *1 *2) (-12 (-5 *2 (-661 (-609))) (-5 *1 (-609))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1055 (-863 (-558))))
-   (-5 *3 (-1184 (-2 (|:| |k| (-558)) (|:| |c| *4)))) (-4 *4 (-1078))
+  (-12 (-5 *2 (-1047 (-855 (-558))))
+   (-5 *3 (-1176 (-2 (|:| |k| (-558)) (|:| |c| *4)))) (-4 *4 (-1070))
    (-5 *1 (-607 *4))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-1055 (-863 (-558)))) (-5 *1 (-607 *3)) (-4 *3 (-1078))))) 
+  (-12 (-5 *2 (-1047 (-855 (-558)))) (-5 *1 (-607 *3)) (-4 *3 (-1070))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-1184 (-2 (|:| |k| (-558)) (|:| |c| *3)))) (-5 *1 (-607 *3))
-   (-4 *3 (-1078))))) 
+  (-12 (-5 *2 (-1176 (-2 (|:| |k| (-558)) (|:| |c| *3)))) (-5 *1 (-607 *3))
+   (-4 *3 (-1070))))) 
 (((*1 *1 *1 *1 *2)
-  (|partial| -12 (-5 *2 (-114)) (-5 *1 (-607 *3)) (-4 *3 (-1078))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-607 *2)) (-4 *2 (-1078))))) 
-(((*1 *1 *1 *1) (-12 (-5 *1 (-607 *2)) (-4 *2 (-1078))))) 
+  (|partial| -12 (-5 *2 (-114)) (-5 *1 (-607 *3)) (-4 *3 (-1070))))) 
+(((*1 *1 *1) (-12 (-5 *1 (-607 *2)) (-4 *2 (-1070))))) 
+(((*1 *1 *1 *1) (-12 (-5 *1 (-607 *2)) (-4 *2 (-1070))))) 
 (((*1 *2 *3 *4 *5 *6 *7)
-  (-12 (-5 *3 (-1184 (-2 (|:| |k| (-558)) (|:| |c| *6))))
-   (-5 *4 (-1055 (-863 (-558)))) (-5 *5 (-1206)) (-5 *7 (-419 (-558)))
-   (-4 *6 (-1078)) (-5 *2 (-885)) (-5 *1 (-607 *6))))) 
+  (-12 (-5 *3 (-1176 (-2 (|:| |k| (-558)) (|:| |c| *6))))
+   (-5 *4 (-1047 (-855 (-558)))) (-5 *5 (-1198)) (-5 *7 (-419 (-558)))
+   (-4 *6 (-1070)) (-5 *2 (-877)) (-5 *1 (-607 *6))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1 *2)
   (-12 (-5 *2 (-419 (-558))) (-5 *1 (-607 *3)) (-4 *3 (-38 *2))
-   (-4 *3 (-1078))))) 
+   (-4 *3 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1078))))) 
+  (-12 (-5 *1 (-607 *2)) (-4 *2 (-38 (-419 (-558)))) (-4 *2 (-1070))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1138 *5 *6 *7 *8))
-   (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) (-4 *7 (-869))
-   (-4 *8 (-1094 *5 *6 *7)) (-5 *2 (-114)) (-5 *1 (-603 *5 *6 *7 *8 *3))))) 
+  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1130 *5 *6 *7 *8))
+   (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) (-4 *7 (-861))
+   (-4 *8 (-1086 *5 *6 *7)) (-5 *2 (-114)) (-5 *1 (-603 *5 *6 *7 *8 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-946))) (-5 *4 (-929 (-558))) (-5 *2 (-709 (-558)))
+  (-12 (-5 *3 (-661 (-938))) (-5 *4 (-921 (-558))) (-5 *2 (-709 (-558)))
    (-5 *1 (-602))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-946))) (-5 *2 (-661 (-709 (-558)))) (-5 *1 (-602))))
+  (-12 (-5 *3 (-661 (-938))) (-5 *2 (-661 (-709 (-558)))) (-5 *1 (-602))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-946))) (-5 *4 (-661 (-929 (-558))))
+  (-12 (-5 *3 (-661 (-938))) (-5 *4 (-661 (-921 (-558))))
    (-5 *2 (-661 (-709 (-558)))) (-5 *1 (-602))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-661 (-946))) (-5 *2 (-791)) (-5 *1 (-602))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-661 (-938))) (-5 *2 (-791)) (-5 *1 (-602))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-13 (-319) (-149) (-1067 (-558)) (-658 (-558))))
-   (-5 *1 (-440 *4 *2)) (-4 *2 (-13 (-1232) (-29 *4)))))
+  (-12 (-5 *3 (-1198)) (-4 *4 (-13 (-319) (-149) (-1059 (-558)) (-658 (-558))))
+   (-5 *1 (-440 *4 *2)) (-4 *2 (-13 (-1224) (-29 *4)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-973 *5))) (-5 *4 (-1206)) (-4 *5 (-149))
-   (-4 *5 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *2 (-326 *5))
+  (-12 (-5 *3 (-419 (-965 *5))) (-5 *4 (-1198)) (-4 *5 (-149))
+   (-4 *5 (-13 (-464) (-1059 (-558)) (-658 (-558)))) (-5 *2 (-326 *5))
    (-5 *1 (-601 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-595 *2)) (-4 *2 (-13 (-29 *4) (-1232))) (-5 *1 (-597 *4 *2))
-   (-4 *4 (-13 (-464) (-1067 (-558)) (-658 (-558))))))
+  (-12 (-5 *3 (-595 *2)) (-4 *2 (-13 (-29 *4) (-1224))) (-5 *1 (-597 *4 *2))
+   (-4 *4 (-13 (-464) (-1059 (-558)) (-658 (-558))))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-595 (-419 (-973 *4))))
-   (-4 *4 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *2 (-326 *4))
+  (-12 (-5 *3 (-595 (-419 (-965 *4))))
+   (-4 *4 (-13 (-464) (-1059 (-558)) (-658 (-558)))) (-5 *2 (-326 *4))
    (-5 *1 (-601 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-946)) (-5 *2 (-1200 *4)) (-5 *1 (-600 *4)) (-4 *4 (-363))))) 
+  (-12 (-5 *3 (-938)) (-5 *2 (-1192 *4)) (-5 *1 (-600 *4)) (-4 *4 (-363))))) 
 (((*1 *2 *2) (-12 (-5 *1 (-599 *2)) (-4 *2 (-557))))) 
 (((*1 *2 *2) (|partial| -12 (-5 *1 (-599 *2)) (-4 *2 (-557))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-114)) (-5 *1 (-599 *3)) (-4 *3 (-557))))) 
@@ -11955,7 +11867,7 @@
 (((*1 *2 *2 *3)
   (|partial| -12 (-5 *3 (-791)) (-5 *1 (-599 *2)) (-4 *2 (-557))))
  ((*1 *2 *3)
-  (-12 (-5 *2 (-2 (|:| -3172 *3) (|:| -2640 (-791)))) (-5 *1 (-599 *3))
+  (-12 (-5 *2 (-2 (|:| -3095 *3) (|:| -2632 (-791)))) (-5 *1 (-599 *3))
    (-4 *3 (-557))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *4 (-791)) (-5 *2 (-114)) (-5 *1 (-599 *3)) (-4 *3 (-557))))) 
@@ -11966,8 +11878,8 @@
   (-12
    (-5 *3
     (-661
-     (-2 (|:| |scalar| (-419 (-558))) (|:| |coeff| (-1200 *2))
-      (|:| |logand| (-1200 *2)))))
+     (-2 (|:| |scalar| (-419 (-558))) (|:| |coeff| (-1192 *2))
+      (|:| |logand| (-1192 *2)))))
    (-5 *4 (-661 (-2 (|:| |integrand| *2) (|:| |intvar| *2)))) (-4 *2 (-376))
    (-5 *1 (-595 *2))))) 
 (((*1 *2 *1) (-12 (-5 *1 (-595 *2)) (-4 *2 (-376))))) 
@@ -11975,15 +11887,15 @@
   (-12
    (-5 *2
     (-661
-     (-2 (|:| |scalar| (-419 (-558))) (|:| |coeff| (-1200 *3))
-      (|:| |logand| (-1200 *3)))))
+     (-2 (|:| |scalar| (-419 (-558))) (|:| |coeff| (-1192 *3))
+      (|:| |logand| (-1192 *3)))))
    (-5 *1 (-595 *3)) (-4 *3 (-376))))) 
 (((*1 *2 *1)
   (-12 (-5 *2 (-661 (-2 (|:| |integrand| *3) (|:| |intvar| *3))))
    (-5 *1 (-595 *3)) (-4 *3 (-376))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-595 *3)) (-4 *3 (-376))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-594))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-591))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-594))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-591))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-216 4 (-130))) (-5 *1 (-591))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-503)) (-5 *2 (-711 (-591))) (-5 *1 (-591))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-711 (-1 (-547) (-661 (-547))))) (-5 *1 (-115))))
@@ -11991,17 +11903,17 @@
  ((*1 *1) (-5 *1 (-590)))) 
 (((*1 *1) (-5 *1 (-590)))) 
 (((*1 *1) (-5 *1 (-590)))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-589))))
+(((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-589))))
  ((*1 *1 *2) (-12 (-5 *2 (-402)) (-5 *1 (-589))))) 
 (((*1 *2 *2 *3 *3)
-  (|partial| -12 (-5 *3 (-1206))
-   (-4 *4 (-13 (-319) (-149) (-1067 (-558)) (-658 (-558))))
-   (-5 *1 (-587 *4 *2)) (-4 *2 (-13 (-1232) (-987) (-1168) (-29 *4)))))) 
+  (|partial| -12 (-5 *3 (-1198))
+   (-4 *4 (-13 (-319) (-149) (-1059 (-558)) (-658 (-558))))
+   (-5 *1 (-587 *4 *2)) (-4 *2 (-13 (-1224) (-979) (-1160) (-29 *4)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1272 *5)) (-4 *5 (-376))
+  (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1264 *5)) (-4 *5 (-376))
    (-5 *2 (-2 (|:| |answer| *3) (|:| |polypart| *3))) (-5 *1 (-586 *5 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1272 *5)) (-4 *5 (-376))
+  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5)) (-4 *5 (-376))
    (-5 *2
     (-2 (|:| |ir| (-595 (-419 *6))) (|:| |specpart| (-419 *6))
      (|:| |polypart| *6)))
@@ -12009,28 +11921,28 @@
 (((*1 *2 *2 *3)
   (|partial| -12 (-5 *2 (-640 *4 *5))
    (-5 *3
-    (-1 (-2 (|:| |ans| *4) (|:| -3616 *4) (|:| |sol?| (-114))) (-558) *4))
-   (-4 *4 (-376)) (-4 *5 (-1272 *4)) (-5 *1 (-586 *4 *5))))) 
+    (-1 (-2 (|:| |ans| *4) (|:| -3539 *4) (|:| |sol?| (-114))) (-558) *4))
+   (-4 *4 (-376)) (-4 *5 (-1264 *4)) (-5 *1 (-586 *4 *5))))) 
 (((*1 *2 *2 *3 *4)
   (|partial| -12
-   (-5 *3 (-1 (-3 (-2 (|:| -2359 *4) (|:| |coeff| *4)) "failed") *4))
-   (-4 *4 (-376)) (-5 *1 (-586 *4 *2)) (-4 *2 (-1272 *4))))) 
+   (-5 *3 (-1 (-3 (-2 (|:| -2351 *4) (|:| |coeff| *4)) "failed") *4))
+   (-4 *4 (-376)) (-5 *1 (-586 *4 *2)) (-4 *2 (-1264 *4))))) 
 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *4 (-1 *7 *7)) (-5 *5 (-661 (-419 *7))) (-4 *7 (-1272 *6))
+  (|partial| -12 (-5 *4 (-1 *7 *7)) (-5 *5 (-661 (-419 *7))) (-4 *7 (-1264 *6))
    (-5 *3 (-419 *7)) (-4 *6 (-376))
    (-5 *2
     (-2 (|:| |mainpart| *3)
      (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
    (-5 *1 (-586 *6 *7))))) 
 (((*1 *2 *3 *4 *3)
-  (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1272 *5)) (-4 *5 (-376))
-   (-5 *2 (-2 (|:| -2359 (-419 *6)) (|:| |coeff| (-419 *6))))
+  (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5)) (-4 *5 (-376))
+   (-5 *2 (-2 (|:| -2351 (-419 *6)) (|:| |coeff| (-419 *6))))
    (-5 *1 (-586 *5 *6)) (-5 *3 (-419 *6))))) 
 (((*1 *2 *3 *4 *5 *6)
   (|partial| -12 (-5 *4 (-1 *8 *8))
    (-5 *5
-    (-1 (-2 (|:| |ans| *7) (|:| -3616 *7) (|:| |sol?| (-114))) (-558) *7))
-   (-5 *6 (-661 (-419 *8))) (-4 *7 (-376)) (-4 *8 (-1272 *7)) (-5 *3 (-419 *8))
+    (-1 (-2 (|:| |ans| *7) (|:| -3539 *7) (|:| |sol?| (-114))) (-558) *7))
+   (-5 *6 (-661 (-419 *8))) (-4 *7 (-376)) (-4 *8 (-1264 *7)) (-5 *3 (-419 *8))
    (-5 *2
     (-2
      (|:| |answer|
@@ -12040,8 +11952,8 @@
    (-5 *1 (-586 *7 *8))))) 
 (((*1 *2 *3 *4 *5 *6)
   (|partial| -12 (-5 *4 (-1 *8 *8))
-   (-5 *5 (-1 (-3 (-2 (|:| -2359 *7) (|:| |coeff| *7)) "failed") *7))
-   (-5 *6 (-661 (-419 *8))) (-4 *7 (-376)) (-4 *8 (-1272 *7)) (-5 *3 (-419 *8))
+   (-5 *5 (-1 (-3 (-2 (|:| -2351 *7) (|:| |coeff| *7)) "failed") *7))
+   (-5 *6 (-661 (-419 *8))) (-4 *7 (-376)) (-4 *8 (-1264 *7)) (-5 *3 (-419 *8))
    (-5 *2
     (-2
      (|:| |answer|
@@ -12052,154 +11964,154 @@
 (((*1 *2 *3 *4 *5 *3)
   (-12 (-5 *4 (-1 *7 *7))
    (-5 *5
-    (-1 (-2 (|:| |ans| *6) (|:| -3616 *6) (|:| |sol?| (-114))) (-558) *6))
-   (-4 *6 (-376)) (-4 *7 (-1272 *6))
+    (-1 (-2 (|:| |ans| *6) (|:| -3539 *6) (|:| |sol?| (-114))) (-558) *6))
+   (-4 *6 (-376)) (-4 *7 (-1264 *6))
    (-5 *2
     (-3 (-2 (|:| |answer| (-419 *7)) (|:| |a0| *6))
-     (-2 (|:| -2359 (-419 *7)) (|:| |coeff| (-419 *7))) "failed"))
+     (-2 (|:| -2351 (-419 *7)) (|:| |coeff| (-419 *7))) "failed"))
    (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) 
 (((*1 *2 *3 *4 *5 *3)
   (-12 (-5 *4 (-1 *7 *7))
-   (-5 *5 (-1 (-3 (-2 (|:| -2359 *6) (|:| |coeff| *6)) "failed") *6))
-   (-4 *6 (-376)) (-4 *7 (-1272 *6))
+   (-5 *5 (-1 (-3 (-2 (|:| -2351 *6) (|:| |coeff| *6)) "failed") *6))
+   (-4 *6 (-376)) (-4 *7 (-1264 *6))
    (-5 *2
     (-3 (-2 (|:| |answer| (-419 *7)) (|:| |a0| *6))
-     (-2 (|:| -2359 (-419 *7)) (|:| |coeff| (-419 *7))) "failed"))
+     (-2 (|:| -2351 (-419 *7)) (|:| |coeff| (-419 *7))) "failed"))
    (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) 
 (((*1 *2 *3 *4 *5)
   (-12 (-5 *4 (-1 *7 *7)) (-5 *5 (-1 (-3 (-661 *6) "failed") (-558) *6 *6))
-   (-4 *6 (-376)) (-4 *7 (-1272 *6))
+   (-4 *6 (-376)) (-4 *7 (-1264 *6))
    (-5 *2 (-2 (|:| |answer| (-595 (-419 *7))) (|:| |a0| *6)))
    (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) 
 (((*1 *2 *3 *4 *5)
   (-12 (-5 *4 (-1 *7 *7))
    (-5 *5
-    (-1 (-2 (|:| |ans| *6) (|:| -3616 *6) (|:| |sol?| (-114))) (-558) *6))
-   (-4 *6 (-376)) (-4 *7 (-1272 *6))
+    (-1 (-2 (|:| |ans| *6) (|:| -3539 *6) (|:| |sol?| (-114))) (-558) *6))
+   (-4 *6 (-376)) (-4 *7 (-1264 *6))
    (-5 *2 (-2 (|:| |answer| (-595 (-419 *7))) (|:| |a0| *6)))
    (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) 
 (((*1 *2 *3 *4 *5)
   (-12 (-5 *4 (-1 *7 *7))
-   (-5 *5 (-1 (-3 (-2 (|:| -2359 *6) (|:| |coeff| *6)) "failed") *6))
-   (-4 *6 (-376)) (-4 *7 (-1272 *6))
+   (-5 *5 (-1 (-3 (-2 (|:| -2351 *6) (|:| |coeff| *6)) "failed") *6))
+   (-4 *6 (-376)) (-4 *7 (-1264 *6))
    (-5 *2 (-2 (|:| |answer| (-595 (-419 *7))) (|:| |a0| *6)))
    (-5 *1 (-586 *6 *7)) (-5 *3 (-419 *7))))) 
 (((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *5 (-1 (-595 *3) *3 (-1206)))
+  (-12 (-5 *5 (-1 (-595 *3) *3 (-1198)))
    (-5 *6
-    (-1 (-3 (-2 (|:| |special| *3) (|:| |integrand| *3)) "failed") *3 (-1206)))
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-   (-5 *4 (-1206)) (-4 *7 (-631 (-913 (-558)))) (-4 *7 (-464))
-   (-4 *7 (-909 (-558))) (-4 *7 (-1130)) (-5 *2 (-595 *3))
+    (-1 (-3 (-2 (|:| |special| *3) (|:| |integrand| *3)) "failed") *3 (-1198)))
+   (-4 *3 (-296)) (-4 *3 (-647)) (-4 *3 (-1059 *4)) (-4 *3 (-433 *7))
+   (-5 *4 (-1198)) (-4 *7 (-631 (-905 (-558)))) (-4 *7 (-464))
+   (-4 *7 (-901 (-558))) (-4 *7 (-1122)) (-5 *2 (-595 *3))
    (-5 *1 (-585 *7 *3))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-464)) (-4 *4 (-1130)) (-5 *1 (-585 *4 *2))
+  (-12 (-5 *3 (-1198)) (-4 *4 (-464)) (-4 *4 (-1122)) (-5 *1 (-585 *4 *2))
    (-4 *2 (-296)) (-4 *2 (-433 *4))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-569)) (-4 *4 (-1130)) (-5 *1 (-585 *4 *2))
+  (-12 (-5 *3 (-1198)) (-4 *4 (-569)) (-4 *4 (-1122)) (-5 *1 (-585 *4 *2))
    (-4 *2 (-433 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 *6)) (-5 *4 (-1206)) (-4 *6 (-433 *5)) (-4 *5 (-1130))
+  (-12 (-5 *3 (-661 *6)) (-5 *4 (-1198)) (-4 *6 (-433 *5)) (-4 *5 (-1122))
    (-5 *2 (-661 (-628 *6))) (-5 *1 (-585 *5 *6))))) 
 (((*1 *2 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-628 *6))) (-5 *4 (-1206)) (-5 *2 (-628 *6))
-   (-4 *6 (-433 *5)) (-4 *5 (-1130)) (-5 *1 (-585 *5 *6))))) 
+  (-12 (-5 *3 (-661 (-628 *6))) (-5 *4 (-1198)) (-5 *2 (-628 *6))
+   (-4 *6 (-433 *5)) (-4 *5 (-1122)) (-5 *1 (-585 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-628 *5))) (-4 *4 (-1130)) (-5 *2 (-628 *5))
+  (-12 (-5 *3 (-661 (-628 *5))) (-4 *4 (-1122)) (-5 *2 (-628 *5))
    (-5 *1 (-585 *4 *5)) (-4 *5 (-433 *4))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-661 (-628 *5))) (-5 *3 (-1206)) (-4 *5 (-433 *4))
-   (-4 *4 (-1130)) (-5 *1 (-585 *4 *5))))) 
+  (-12 (-5 *2 (-661 (-628 *5))) (-5 *3 (-1198)) (-4 *5 (-433 *4))
+   (-4 *4 (-1122)) (-5 *1 (-585 *4 *5))))) 
 (((*1 *2 *3 *4 *3)
-  (|partial| -12 (-5 *4 (-1206)) (-4 *5 (-13 (-569) (-1067 (-558)) (-149)))
-   (-5 *2 (-2 (|:| -2359 (-419 (-973 *5))) (|:| |coeff| (-419 (-973 *5)))))
-   (-5 *1 (-582 *5)) (-5 *3 (-419 (-973 *5)))))) 
+  (|partial| -12 (-5 *4 (-1198)) (-4 *5 (-13 (-569) (-1059 (-558)) (-149)))
+   (-5 *2 (-2 (|:| -2351 (-419 (-965 *5))) (|:| |coeff| (-419 (-965 *5)))))
+   (-5 *1 (-582 *5)) (-5 *3 (-419 (-965 *5)))))) 
 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *4 (-1206)) (-5 *5 (-661 (-419 (-973 *6))))
-   (-5 *3 (-419 (-973 *6))) (-4 *6 (-13 (-569) (-1067 (-558)) (-149)))
+  (|partial| -12 (-5 *4 (-1198)) (-5 *5 (-661 (-419 (-965 *6))))
+   (-5 *3 (-419 (-965 *6))) (-4 *6 (-13 (-569) (-1059 (-558)) (-149)))
    (-5 *2
     (-2 (|:| |mainpart| *3)
      (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
    (-5 *1 (-582 *6))))) 
 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-419 (-973 *4))) (-5 *3 (-1206))
-   (-4 *4 (-13 (-569) (-1067 (-558)) (-149))) (-5 *1 (-582 *4))))) 
+  (|partial| -12 (-5 *2 (-419 (-965 *4))) (-5 *3 (-1198))
+   (-4 *4 (-13 (-569) (-1059 (-558)) (-149))) (-5 *1 (-582 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1206)) (-4 *5 (-13 (-319) (-149) (-1067 (-558)) (-658 (-558))))
-   (-5 *2 (-595 *3)) (-5 *1 (-440 *5 *3)) (-4 *3 (-13 (-1232) (-29 *5)))))
+  (-12 (-5 *4 (-1198)) (-4 *5 (-13 (-319) (-149) (-1059 (-558)) (-658 (-558))))
+   (-5 *2 (-595 *3)) (-5 *1 (-440 *5 *3)) (-4 *3 (-13 (-1224) (-29 *5)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1206)) (-4 *5 (-13 (-569) (-1067 (-558)) (-149)))
-   (-5 *2 (-595 (-419 (-973 *5)))) (-5 *1 (-582 *5)) (-5 *3 (-419 (-973 *5)))))) 
+  (-12 (-5 *4 (-1198)) (-4 *5 (-13 (-569) (-1059 (-558)) (-149)))
+   (-5 *2 (-595 (-419 (-965 *5)))) (-5 *1 (-582 *5)) (-5 *3 (-419 (-965 *5)))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *2 (-558)) (-5 *1 (-581 *3)) (-4 *3 (-1067 *2))))) 
+  (|partial| -12 (-5 *2 (-558)) (-5 *1 (-581 *3)) (-4 *3 (-1059 *2))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-661 (-419 *6))) (-5 *3 (-419 *6)) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-376) (-149) (-1067 (-558))))
+  (|partial| -12 (-5 *4 (-661 (-419 *6))) (-5 *3 (-419 *6)) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-376) (-149) (-1059 (-558))))
    (-5 *2
     (-2 (|:| |mainpart| *3)
      (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
    (-5 *1 (-580 *5 *6))))) 
 (((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-13 (-376) (-149) (-1067 (-558)))) (-4 *5 (-1272 *4))
-   (-5 *2 (-2 (|:| -2359 (-419 *5)) (|:| |coeff| (-419 *5))))
+  (|partial| -12 (-4 *4 (-13 (-376) (-149) (-1059 (-558)))) (-4 *5 (-1264 *4))
+   (-5 *2 (-2 (|:| -2351 (-419 *5)) (|:| |coeff| (-419 *5))))
    (-5 *1 (-580 *4 *5)) (-5 *3 (-419 *5))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-419 *4)) (-4 *4 (-1272 *3))
-   (-4 *3 (-13 (-376) (-149) (-1067 (-558)))) (-5 *1 (-580 *3 *4))))) 
+  (|partial| -12 (-5 *2 (-419 *4)) (-4 *4 (-1264 *3))
+   (-4 *3 (-13 (-376) (-149) (-1059 (-558)))) (-5 *1 (-580 *3 *4))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1206)) (-4 *5 (-631 (-913 (-558))))
-   (-4 *5 (-909 (-558))) (-4 *5 (-13 (-1067 (-558)) (-464) (-658 (-558))))
+  (|partial| -12 (-5 *4 (-1198)) (-4 *5 (-631 (-905 (-558))))
+   (-4 *5 (-901 (-558))) (-4 *5 (-13 (-1059 (-558)) (-464) (-658 (-558))))
    (-5 *2 (-2 (|:| |special| *3) (|:| |integrand| *3))) (-5 *1 (-579 *5 *3))
-   (-4 *3 (-647)) (-4 *3 (-13 (-27) (-1232) (-433 *5)))))
+   (-4 *3 (-647)) (-4 *3 (-13 (-27) (-1224) (-433 *5)))))
  ((*1 *2 *2 *3 *4 *4)
-  (|partial| -12 (-5 *3 (-1206)) (-5 *4 (-863 *2)) (-4 *2 (-1168))
-   (-4 *2 (-13 (-27) (-1232) (-433 *5))) (-4 *5 (-631 (-913 (-558))))
-   (-4 *5 (-909 (-558))) (-4 *5 (-13 (-1067 (-558)) (-464) (-658 (-558))))
+  (|partial| -12 (-5 *3 (-1198)) (-5 *4 (-855 *2)) (-4 *2 (-1160))
+   (-4 *2 (-13 (-27) (-1224) (-433 *5))) (-4 *5 (-631 (-905 (-558))))
+   (-4 *5 (-901 (-558))) (-4 *5 (-13 (-1059 (-558)) (-464) (-658 (-558))))
    (-5 *1 (-579 *5 *2))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1206)) (-4 *5 (-631 (-913 (-558))))
-   (-4 *5 (-909 (-558))) (-4 *5 (-13 (-1067 (-558)) (-464) (-658 (-558))))
+  (|partial| -12 (-5 *4 (-1198)) (-4 *5 (-631 (-905 (-558))))
+   (-4 *5 (-901 (-558))) (-4 *5 (-13 (-1059 (-558)) (-464) (-658 (-558))))
    (-5 *2 (-2 (|:| |special| *3) (|:| |integrand| *3))) (-5 *1 (-579 *5 *3))
-   (-4 *3 (-647)) (-4 *3 (-13 (-27) (-1232) (-433 *5)))))) 
+   (-4 *3 (-647)) (-4 *3 (-13 (-27) (-1224) (-433 *5)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1206)) (-4 *5 (-13 (-1067 (-558)) (-464) (-658 (-558))))
-   (-5 *2 (-2 (|:| -2565 *3) (|:| |nconst| *3))) (-5 *1 (-579 *5 *3))
-   (-4 *3 (-13 (-27) (-1232) (-433 *5)))))) 
+  (-12 (-5 *4 (-1198)) (-4 *5 (-13 (-1059 (-558)) (-464) (-658 (-558))))
+   (-5 *2 (-2 (|:| -2557 *3) (|:| |nconst| *3))) (-5 *1 (-579 *5 *3))
+   (-4 *3 (-13 (-27) (-1224) (-433 *5)))))) 
 (((*1 *2 *3 *4 *5 *5 *6)
-  (-12 (-5 *5 (-628 *4)) (-5 *6 (-1206)) (-4 *4 (-13 (-433 *7) (-27) (-1232)))
-   (-4 *7 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2230 (-661 *4))))
-   (-5 *1 (-578 *7 *4 *3)) (-4 *3 (-678 *4)) (-4 *3 (-1130))))) 
+  (-12 (-5 *5 (-628 *4)) (-5 *6 (-1198)) (-4 *4 (-13 (-433 *7) (-27) (-1224)))
+   (-4 *7 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2222 (-661 *4))))
+   (-5 *1 (-578 *7 *4 *3)) (-4 *3 (-678 *4)) (-4 *3 (-1122))))) 
 (((*1 *2 *2 *2 *2 *3 *3 *4)
-  (|partial| -12 (-5 *3 (-628 *2)) (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1206)))
-   (-4 *2 (-13 (-433 *5) (-27) (-1232)))
-   (-4 *5 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *1 (-578 *5 *2 *6)) (-4 *6 (-1130))))) 
+  (|partial| -12 (-5 *3 (-628 *2)) (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1198)))
+   (-4 *2 (-13 (-433 *5) (-27) (-1224)))
+   (-4 *5 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *1 (-578 *5 *2 *6)) (-4 *6 (-1122))))) 
 (((*1 *2 *3 *4 *4 *5)
   (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-661 *3))
-   (-4 *3 (-13 (-433 *6) (-27) (-1232)))
-   (-4 *6 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
+   (-4 *3 (-13 (-433 *6) (-27) (-1224)))
+   (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
    (-5 *2
     (-2 (|:| |mainpart| *3)
      (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
-   (-5 *1 (-578 *6 *3 *7)) (-4 *7 (-1130))))) 
+   (-5 *1 (-578 *6 *3 *7)) (-4 *7 (-1122))))) 
 (((*1 *2 *3 *4 *4 *3)
-  (|partial| -12 (-5 *4 (-628 *3)) (-4 *3 (-13 (-433 *5) (-27) (-1232)))
-   (-4 *5 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *2 (-2 (|:| -2359 *3) (|:| |coeff| *3))) (-5 *1 (-578 *5 *3 *6))
-   (-4 *6 (-1130))))) 
+  (|partial| -12 (-5 *4 (-628 *3)) (-4 *3 (-13 (-433 *5) (-27) (-1224)))
+   (-4 *5 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *2 (-2 (|:| -2351 *3) (|:| |coeff| *3))) (-5 *1 (-578 *5 *3 *6))
+   (-4 *6 (-1122))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-628 *3)) (-4 *3 (-13 (-433 *5) (-27) (-1232)))
-   (-4 *5 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558)))) (-5 *2 (-595 *3))
-   (-5 *1 (-578 *5 *3 *6)) (-4 *6 (-1130))))) 
+  (-12 (-5 *4 (-628 *3)) (-4 *3 (-13 (-433 *5) (-27) (-1224)))
+   (-4 *5 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558)))) (-5 *2 (-595 *3))
+   (-5 *1 (-578 *5 *3 *6)) (-4 *6 (-1122))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1272 *5)) (-4 *5 (-376))
-   (-4 *7 (-1272 (-419 *6))) (-5 *2 (-2 (|:| |answer| *3) (|:| -2358 *3)))
+  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5)) (-4 *5 (-376))
+   (-4 *7 (-1264 (-419 *6))) (-5 *2 (-2 (|:| |answer| *3) (|:| -2350 *3)))
    (-5 *1 (-575 *5 *6 *7 *3)) (-4 *3 (-355 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1272 *5)) (-4 *5 (-376))
+  (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1264 *5)) (-4 *5 (-376))
    (-5 *2
-    (-2 (|:| |answer| (-419 *6)) (|:| -2358 (-419 *6))
+    (-2 (|:| |answer| (-419 *6)) (|:| -2350 (-419 *6))
      (|:| |specpart| (-419 *6)) (|:| |polypart| *6)))
    (-5 *1 (-576 *5 *6)) (-5 *3 (-419 *6))))) 
 (((*1 *2 *2 *3) (-12 (-5 *2 (-558)) (-5 *3 (-791)) (-5 *1 (-574))))) 
@@ -12219,79 +12131,79 @@
   (-12 (-5 *3 (-661 *8))
    (-5 *4
     (-661
-     (-2 (|:| -2230 (-709 *7)) (|:| |basisDen| *7)
+     (-2 (|:| -2222 (-709 *7)) (|:| |basisDen| *7)
       (|:| |basisInv| (-709 *7)))))
-   (-5 *5 (-791)) (-4 *8 (-1272 *7)) (-4 *7 (-1272 *6)) (-4 *6 (-363))
+   (-5 *5 (-791)) (-4 *8 (-1264 *7)) (-4 *7 (-1264 *6)) (-4 *6 (-363))
    (-5 *2
-    (-2 (|:| -2230 (-709 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-709 *7))))
+    (-2 (|:| -2222 (-709 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-709 *7))))
    (-5 *1 (-510 *6 *7 *8))))
  ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-558)) (-5 *1 (-574))))) 
 (((*1 *2 *3 *4 *5 *5 *4 *6)
-  (-12 (-5 *5 (-628 *4)) (-5 *6 (-1200 *4))
-   (-4 *4 (-13 (-433 *7) (-27) (-1232)))
-   (-4 *7 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2230 (-661 *4))))
-   (-5 *1 (-573 *7 *4 *3)) (-4 *3 (-678 *4)) (-4 *3 (-1130))))
+  (-12 (-5 *5 (-628 *4)) (-5 *6 (-1192 *4))
+   (-4 *4 (-13 (-433 *7) (-27) (-1224)))
+   (-4 *7 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2222 (-661 *4))))
+   (-5 *1 (-573 *7 *4 *3)) (-4 *3 (-678 *4)) (-4 *3 (-1122))))
  ((*1 *2 *3 *4 *5 *5 *5 *4 *6)
-  (-12 (-5 *5 (-628 *4)) (-5 *6 (-419 (-1200 *4)))
-   (-4 *4 (-13 (-433 *7) (-27) (-1232)))
-   (-4 *7 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2230 (-661 *4))))
-   (-5 *1 (-573 *7 *4 *3)) (-4 *3 (-678 *4)) (-4 *3 (-1130))))) 
+  (-12 (-5 *5 (-628 *4)) (-5 *6 (-419 (-1192 *4)))
+   (-4 *4 (-13 (-433 *7) (-27) (-1224)))
+   (-4 *7 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2222 (-661 *4))))
+   (-5 *1 (-573 *7 *4 *3)) (-4 *3 (-678 *4)) (-4 *3 (-1122))))) 
 (((*1 *2 *2 *2 *3 *3 *4 *2 *5)
   (|partial| -12 (-5 *3 (-628 *2))
-   (-5 *4 (-1 (-3 *2 #1="failed") *2 *2 (-1206))) (-5 *5 (-1200 *2))
-   (-4 *2 (-13 (-433 *6) (-27) (-1232)))
-   (-4 *6 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *1 (-573 *6 *2 *7)) (-4 *7 (-1130))))
+   (-5 *4 (-1 (-3 *2 #1="failed") *2 *2 (-1198))) (-5 *5 (-1192 *2))
+   (-4 *2 (-13 (-433 *6) (-27) (-1224)))
+   (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *1 (-573 *6 *2 *7)) (-4 *7 (-1122))))
  ((*1 *2 *2 *2 *3 *3 *4 *3 *2 *5)
-  (|partial| -12 (-5 *3 (-628 *2)) (-5 *4 (-1 (-3 *2 #1#) *2 *2 (-1206)))
-   (-5 *5 (-419 (-1200 *2))) (-4 *2 (-13 (-433 *6) (-27) (-1232)))
-   (-4 *6 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *1 (-573 *6 *2 *7)) (-4 *7 (-1130))))) 
+  (|partial| -12 (-5 *3 (-628 *2)) (-5 *4 (-1 (-3 *2 #1#) *2 *2 (-1198)))
+   (-5 *5 (-419 (-1192 *2))) (-4 *2 (-13 (-433 *6) (-27) (-1224)))
+   (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *1 (-573 *6 *2 *7)) (-4 *7 (-1122))))) 
 (((*1 *2 *3 *4 *4 *5 *3 *6)
-  (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-661 *3)) (-5 *6 (-1200 *3))
-   (-4 *3 (-13 (-433 *7) (-27) (-1232)))
-   (-4 *7 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
+  (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-661 *3)) (-5 *6 (-1192 *3))
+   (-4 *3 (-13 (-433 *7) (-27) (-1224)))
+   (-4 *7 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
    (-5 *2
     (-2 (|:| |mainpart| *3)
      (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
-   (-5 *1 (-573 *7 *3 *8)) (-4 *8 (-1130))))
+   (-5 *1 (-573 *7 *3 *8)) (-4 *8 (-1122))))
  ((*1 *2 *3 *4 *4 *5 *4 *3 *6)
-  (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-661 *3)) (-5 *6 (-419 (-1200 *3)))
-   (-4 *3 (-13 (-433 *7) (-27) (-1232)))
-   (-4 *7 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
+  (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-661 *3)) (-5 *6 (-419 (-1192 *3)))
+   (-4 *3 (-13 (-433 *7) (-27) (-1224)))
+   (-4 *7 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
    (-5 *2
     (-2 (|:| |mainpart| *3)
      (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
-   (-5 *1 (-573 *7 *3 *8)) (-4 *8 (-1130))))) 
+   (-5 *1 (-573 *7 *3 *8)) (-4 *8 (-1122))))) 
 (((*1 *2 *3 *4 *4 *3 *3 *5)
-  (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-1200 *3))
-   (-4 *3 (-13 (-433 *6) (-27) (-1232)))
-   (-4 *6 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *2 (-2 (|:| -2359 *3) (|:| |coeff| *3))) (-5 *1 (-573 *6 *3 *7))
-   (-4 *7 (-1130))))
+  (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-1192 *3))
+   (-4 *3 (-13 (-433 *6) (-27) (-1224)))
+   (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *2 (-2 (|:| -2351 *3) (|:| |coeff| *3))) (-5 *1 (-573 *6 *3 *7))
+   (-4 *7 (-1122))))
  ((*1 *2 *3 *4 *4 *3 *4 *3 *5)
-  (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-419 (-1200 *3)))
-   (-4 *3 (-13 (-433 *6) (-27) (-1232)))
-   (-4 *6 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558))))
-   (-5 *2 (-2 (|:| -2359 *3) (|:| |coeff| *3))) (-5 *1 (-573 *6 *3 *7))
-   (-4 *7 (-1130))))) 
+  (|partial| -12 (-5 *4 (-628 *3)) (-5 *5 (-419 (-1192 *3)))
+   (-4 *3 (-13 (-433 *6) (-27) (-1224)))
+   (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558))))
+   (-5 *2 (-2 (|:| -2351 *3) (|:| |coeff| *3))) (-5 *1 (-573 *6 *3 *7))
+   (-4 *7 (-1122))))) 
 (((*1 *2 *3 *4 *4 *3 *5)
-  (-12 (-5 *4 (-628 *3)) (-5 *5 (-1200 *3))
-   (-4 *3 (-13 (-433 *6) (-27) (-1232)))
-   (-4 *6 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558)))) (-5 *2 (-595 *3))
-   (-5 *1 (-573 *6 *3 *7)) (-4 *7 (-1130))))
+  (-12 (-5 *4 (-628 *3)) (-5 *5 (-1192 *3))
+   (-4 *3 (-13 (-433 *6) (-27) (-1224)))
+   (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558)))) (-5 *2 (-595 *3))
+   (-5 *1 (-573 *6 *3 *7)) (-4 *7 (-1122))))
  ((*1 *2 *3 *4 *4 *4 *3 *5)
-  (-12 (-5 *4 (-628 *3)) (-5 *5 (-419 (-1200 *3)))
-   (-4 *3 (-13 (-433 *6) (-27) (-1232)))
-   (-4 *6 (-13 (-464) (-1067 (-558)) (-149) (-658 (-558)))) (-5 *2 (-595 *3))
-   (-5 *1 (-573 *6 *3 *7)) (-4 *7 (-1130))))) 
+  (-12 (-5 *4 (-628 *3)) (-5 *5 (-419 (-1192 *3)))
+   (-4 *3 (-13 (-433 *6) (-27) (-1224)))
+   (-4 *6 (-13 (-464) (-1059 (-558)) (-149) (-658 (-558)))) (-5 *2 (-595 *3))
+   (-5 *1 (-573 *6 *3 *7)) (-4 *7 (-1122))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *2
     (-2
@@ -12304,9 +12216,9 @@
            (|:| |bothSingular| "There are singularities at both end points")
            (|:| |notEvaluated| "End point continuity not yet evaluated")))
      (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1184 (-229)))
+          (-3 (|:| |str| (-1176 (-229)))
            (|:| |notEvaluated| "Internal singularities not yet evaluated")))
-     (|:| -1646
+     (|:| -1638
           (-3 (|:| |finite| "The range is finite")
            (|:| |lowerInfinite| "The bottom of range is infinite")
            (|:| |upperInfinite| "The top of range is infinite")
@@ -12316,8 +12228,8 @@
 (((*1 *2 *3)
   (|partial| -12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *2
     (-2
@@ -12330,9 +12242,9 @@
            (|:| |bothSingular| "There are singularities at both end points")
            (|:| |notEvaluated| "End point continuity not yet evaluated")))
      (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1184 (-229)))
+          (-3 (|:| |str| (-1176 (-229)))
            (|:| |notEvaluated| "Internal singularities not yet evaluated")))
-     (|:| -1646
+     (|:| -1638
           (-3 (|:| |finite| "The range is finite")
            (|:| |lowerInfinite| "The bottom of range is infinite")
            (|:| |upperInfinite| "The top of range is infinite")
@@ -12344,11 +12256,11 @@
    (-5 *2
     (-661
      (-2
-      (|:| -4367
-           (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-            (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+      (|:| -4290
+           (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+            (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
             (|:| |relerr| (-229))))
-      (|:| -2294
+      (|:| -2286
            (-2
             (|:| |endPointContinuity|
                  (-3 (|:| |continuous| "Continuous at the end points")
@@ -12361,10 +12273,10 @@
                   (|:| |notEvaluated|
                        "End point continuity not yet evaluated")))
             (|:| |singularitiesStream|
-                 (-3 (|:| |str| (-1184 (-229)))
+                 (-3 (|:| |str| (-1176 (-229)))
                   (|:| |notEvaluated|
                        "Internal singularities not yet evaluated")))
-            (|:| -1646
+            (|:| -1638
                  (-3 (|:| |finite| "The range is finite")
                   (|:| |lowerInfinite| "The bottom of range is infinite")
                   (|:| |upperInfinite| "The top of range is infinite")
@@ -12372,68 +12284,68 @@
                        "Both top and bottom points are infinite")
                   (|:| |notEvaluated| "Range not yet evaluated"))))))))
    (-5 *1 (-572))))) 
-(((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-572))))) 
+(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-572))))) 
 (((*1 *1) (-5 *1 (-572)))) 
 (((*1 *2 *2) (|partial| -12 (-5 *1 (-571 *2)) (-4 *2 (-557))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-417 *3)) (-5 *1 (-571 *3)) (-4 *3 (-557))))) 
 (((*1 *2 *3 *4 *5 *6)
-  (|partial| -12 (-5 *4 (-1206)) (-5 *6 (-661 (-628 *3))) (-5 *5 (-628 *3))
-   (-4 *3 (-13 (-27) (-1232) (-433 *7)))
-   (-4 *7 (-13 (-464) (-149) (-1067 (-558)) (-658 (-558))))
-   (-5 *2 (-2 (|:| -2359 *3) (|:| |coeff| *3))) (-5 *1 (-570 *7 *3))))) 
+  (|partial| -12 (-5 *4 (-1198)) (-5 *6 (-661 (-628 *3))) (-5 *5 (-628 *3))
+   (-4 *3 (-13 (-27) (-1224) (-433 *7)))
+   (-4 *7 (-13 (-464) (-149) (-1059 (-558)) (-658 (-558))))
+   (-5 *2 (-2 (|:| -2351 *3) (|:| |coeff| *3))) (-5 *1 (-570 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1206)) (-4 *5 (-13 (-464) (-149) (-1067 (-558)) (-658 (-558))))
+  (-12 (-5 *4 (-1198)) (-4 *5 (-13 (-464) (-149) (-1059 (-558)) (-658 (-558))))
    (-5 *2 (-595 *3)) (-5 *1 (-570 *5 *3))
-   (-4 *3 (-13 (-27) (-1232) (-433 *5)))))) 
+   (-4 *3 (-13 (-27) (-1224) (-433 *5)))))) 
 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *3 (-1206))
-   (-4 *4 (-13 (-464) (-149) (-1067 (-558)) (-658 (-558))))
-   (-5 *1 (-570 *4 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *4)))))) 
+  (|partial| -12 (-5 *3 (-1198))
+   (-4 *4 (-13 (-464) (-149) (-1059 (-558)) (-658 (-558))))
+   (-5 *1 (-570 *4 *2)) (-4 *2 (-13 (-27) (-1224) (-433 *4)))))) 
 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *4 (-1206)) (-5 *5 (-661 *3))
-   (-4 *3 (-13 (-27) (-1232) (-433 *6)))
-   (-4 *6 (-13 (-464) (-149) (-1067 (-558)) (-658 (-558))))
+  (|partial| -12 (-5 *4 (-1198)) (-5 *5 (-661 *3))
+   (-4 *3 (-13 (-27) (-1224) (-433 *6)))
+   (-4 *6 (-13 (-464) (-149) (-1059 (-558)) (-658 (-558))))
    (-5 *2
     (-2 (|:| |mainpart| *3)
      (|:| |limitedlogs| (-661 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
    (-5 *1 (-570 *6 *3))))) 
 (((*1 *2 *3 *4 *3)
-  (|partial| -12 (-5 *4 (-1206))
-   (-4 *5 (-13 (-464) (-149) (-1067 (-558)) (-658 (-558))))
-   (-5 *2 (-2 (|:| -2359 *3) (|:| |coeff| *3))) (-5 *1 (-570 *5 *3))
-   (-4 *3 (-13 (-27) (-1232) (-433 *5)))))) 
+  (|partial| -12 (-5 *4 (-1198))
+   (-4 *5 (-13 (-464) (-149) (-1059 (-558)) (-658 (-558))))
+   (-5 *2 (-2 (|:| -2351 *3) (|:| |coeff| *3))) (-5 *1 (-570 *5 *3))
+   (-4 *3 (-13 (-27) (-1224) (-433 *5)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-2 (|:| -1988 *1) (|:| -4489 *1) (|:| |associate| *1)))
+  (-12 (-5 *2 (-2 (|:| -1980 *1) (|:| -4412 *1) (|:| |associate| *1)))
    (-4 *1 (-569))))) 
 (((*1 *1 *1) (-4 *1 (-569)))) 
 (((*1 *2 *1 *1) (-12 (-4 *1 (-569)) (-5 *2 (-114))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-569)) (-5 *2 (-114))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-419 (-558))) (-4 *1 (-567 *3)) (-4 *3 (-13 (-416) (-1232)))))
- ((*1 *1 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1232)))))
- ((*1 *1 *2 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1232)))))) 
-(((*1 *1 *2 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1232)))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1232)))))) 
+  (-12 (-5 *2 (-419 (-558))) (-4 *1 (-567 *3)) (-4 *3 (-13 (-416) (-1224)))))
+ ((*1 *1 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224)))))
+ ((*1 *1 *2 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224)))))) 
+(((*1 *1 *2 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224)))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-567 *2)) (-4 *2 (-13 (-416) (-1224)))))) 
 (((*1 *2 *1 *3)
-  (-12 (-4 *1 (-567 *3)) (-4 *3 (-13 (-416) (-1232))) (-5 *2 (-114))))) 
+  (-12 (-4 *1 (-567 *3)) (-4 *3 (-13 (-416) (-1224))) (-5 *2 (-114))))) 
 (((*1 *2 *3 *3) (-12 (-5 *3 (-558)) (-5 *2 (-114)) (-5 *1 (-566))))) 
 (((*1 *2 *2 *2) (-12 (-5 *2 (-558)) (-5 *1 (-566))))) 
 (((*1 *2 *2) (-12 (-5 *2 (-558)) (-5 *1 (-566))))) 
 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1272 *5))
-   (-4 *5 (-13 (-27) (-433 *4))) (-4 *4 (-13 (-569) (-1067 (-558))))
-   (-4 *7 (-1272 (-419 *6))) (-5 *1 (-565 *4 *5 *6 *7 *2))
+  (|partial| -12 (-5 *3 (-1 *6 *6)) (-4 *6 (-1264 *5))
+   (-4 *5 (-13 (-27) (-433 *4))) (-4 *4 (-13 (-569) (-1059 (-558))))
+   (-4 *7 (-1264 (-419 *6))) (-5 *1 (-565 *4 *5 *6 *7 *2))
    (-4 *2 (-355 *5 *6 *7))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1272 *6)) (-4 *6 (-13 (-27) (-433 *5)))
-   (-4 *5 (-13 (-569) (-1067 (-558)))) (-4 *8 (-1272 (-419 *7)))
+  (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1264 *6)) (-4 *6 (-13 (-27) (-433 *5)))
+   (-4 *5 (-13 (-569) (-1059 (-558)))) (-4 *8 (-1264 (-419 *7)))
    (-5 *2 (-595 *3)) (-5 *1 (-565 *5 *6 *7 *8 *3)) (-4 *3 (-355 *6 *7 *8))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1272 *6)) (-4 *6 (-13 (-27) (-433 *5)))
-   (-4 *5 (-13 (-569) (-1067 (-558)))) (-4 *8 (-1272 (-419 *7)))
+  (-12 (-5 *4 (-1 *7 *7)) (-4 *7 (-1264 *6)) (-4 *6 (-13 (-27) (-433 *5)))
+   (-4 *5 (-13 (-569) (-1059 (-558)))) (-4 *8 (-1264 (-419 *7)))
    (-5 *2 (-595 *3)) (-5 *1 (-565 *5 *6 *7 *8 *3)) (-4 *3 (-355 *6 *7 *8))))) 
 (((*1 *2 *3 *4 *4 *5)
-  (-12 (-5 *4 (-628 *3)) (-5 *5 (-1 (-1200 *3) (-1200 *3)))
+  (-12 (-5 *4 (-628 *3)) (-5 *5 (-1 (-1192 *3) (-1192 *3)))
    (-4 *3 (-13 (-27) (-433 *6))) (-4 *6 (-569)) (-5 *2 (-595 *3))
    (-5 *1 (-564 *6 *3))))) 
 (((*1 *2 *1 *1) (-12 (-4 *1 (-557)) (-5 *2 (-114))))) 
@@ -12448,156 +12360,156 @@
 (((*1 *1 *1 *1 *1) (-4 *1 (-557)))) 
 (((*1 *1 *1 *1) (-4 *1 (-557)))) 
 (((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *4 (-1 (-3 (-558) #1="failed") *5)) (-4 *5 (-1078))
-   (-5 *2 (-558)) (-5 *1 (-555 *5 *3)) (-4 *3 (-1272 *5))))
+  (|partial| -12 (-5 *4 (-1 (-3 (-558) #1="failed") *5)) (-4 *5 (-1070))
+   (-5 *2 (-558)) (-5 *1 (-555 *5 *3)) (-4 *3 (-1264 *5))))
  ((*1 *2 *3 *4 *2 *5)
-  (|partial| -12 (-5 *5 (-1 (-3 (-558) #1#) *4)) (-4 *4 (-1078)) (-5 *2 (-558))
-   (-5 *1 (-555 *4 *3)) (-4 *3 (-1272 *4))))
+  (|partial| -12 (-5 *5 (-1 (-3 (-558) #1#) *4)) (-4 *4 (-1070)) (-5 *2 (-558))
+   (-5 *1 (-555 *4 *3)) (-4 *3 (-1264 *4))))
  ((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *5 (-1 (-3 (-558) #1#) *4)) (-4 *4 (-1078)) (-5 *2 (-558))
-   (-5 *1 (-555 *4 *3)) (-4 *3 (-1272 *4))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-319)) (-5 *1 (-467 *3 *2)) (-4 *2 (-1272 *3))))
- ((*1 *2 *2 *3) (-12 (-4 *3 (-319)) (-5 *1 (-472 *3 *2)) (-4 *2 (-1272 *3))))
+  (|partial| -12 (-5 *5 (-1 (-3 (-558) #1#) *4)) (-4 *4 (-1070)) (-5 *2 (-558))
+   (-5 *1 (-555 *4 *3)) (-4 *3 (-1264 *4))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-319)) (-5 *1 (-467 *3 *2)) (-4 *2 (-1264 *3))))
+ ((*1 *2 *2 *3) (-12 (-4 *3 (-319)) (-5 *1 (-472 *3 *2)) (-4 *2 (-1264 *3))))
  ((*1 *2 *2 *3)
   (-12 (-4 *3 (-319)) (-14 *4 *3) (-14 *5 (-1 *3 *3 (-791)))
-   (-5 *1 (-551 *3 *2 *4 *5)) (-4 *2 (-1272 *3))))) 
+   (-5 *1 (-551 *3 *2 *4 *5)) (-4 *2 (-1264 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-1272 *4)) (-5 *1 (-551 *4 *2 *5 *6))
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-1264 *4)) (-5 *1 (-551 *4 *2 *5 *6))
    (-4 *4 (-319)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-791)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-1272 *4)) (-5 *1 (-551 *4 *2 *5 *6))
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-1264 *4)) (-5 *1 (-551 *4 *2 *5 *6))
    (-4 *4 (-319)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-791)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 *6)) (-5 *4 (-661 (-1206))) (-4 *6 (-376))
-   (-5 *2 (-661 (-305 (-973 *6)))) (-5 *1 (-550 *5 *6 *7)) (-4 *5 (-464))
-   (-4 *7 (-13 (-376) (-868)))))) 
+  (-12 (-5 *3 (-661 *6)) (-5 *4 (-661 (-1198))) (-4 *6 (-376))
+   (-5 *2 (-661 (-305 (-965 *6)))) (-5 *1 (-550 *5 *6 *7)) (-4 *5 (-464))
+   (-4 *7 (-13 (-376) (-860)))))) 
 (((*1 *2 *3 *3 *4 *5)
-  (-12 (-5 *3 (-661 (-973 *6))) (-5 *4 (-661 (-1206))) (-4 *6 (-464))
+  (-12 (-5 *3 (-661 (-965 *6))) (-5 *4 (-661 (-1198))) (-4 *6 (-464))
    (-5 *2 (-661 (-661 *7))) (-5 *1 (-550 *6 *7 *5)) (-4 *7 (-376))
-   (-4 *5 (-13 (-376) (-868)))))) 
+   (-4 *5 (-13 (-376) (-860)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1200 *5)) (-4 *5 (-464)) (-5 *2 (-661 *6))
-   (-5 *1 (-550 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-868)))))
+  (-12 (-5 *3 (-1192 *5)) (-4 *5 (-464)) (-5 *2 (-661 *6))
+   (-5 *1 (-550 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-860)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-973 *5)) (-4 *5 (-464)) (-5 *2 (-661 *6))
-   (-5 *1 (-550 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-868)))))) 
+  (-12 (-5 *3 (-965 *5)) (-4 *5 (-464)) (-5 *2 (-661 *6))
+   (-5 *1 (-550 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-860)))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-51)) (-5 *1 (-547))))
- ((*1 *2 *3) (-12 (-5 *3 (-547)) (-5 *1 (-548 *2)) (-4 *2 (-1246))))) 
+ ((*1 *2 *3) (-12 (-5 *3 (-547)) (-5 *1 (-548 *2)) (-4 *2 (-1238))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1206)) (-5 *2 (-547)) (-5 *1 (-548 *4)) (-4 *4 (-1246))))) 
+  (-12 (-5 *3 (-1198)) (-5 *2 (-547)) (-5 *1 (-548 *4)) (-4 *4 (-1238))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-419 (-558))) (-5 *1 (-108))))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-661 (-547))) (-5 *1 (-547))))) 
-(((*1 *1 *1 *2) (-12 (-5 *2 (-661 (-1206))) (-5 *1 (-547))))) 
+(((*1 *1 *1 *2) (-12 (-5 *2 (-661 (-1198))) (-5 *1 (-547))))) 
 (((*1 *1 *1) (-5 *1 (-547)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1188)) (-5 *1 (-547))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-547))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-661 (-547))) (-5 *2 (-1206)) (-5 *1 (-547))))) 
-(((*1 *2 *2 *3) (-12 (-5 *2 (-1206)) (-5 *3 (-661 (-547))) (-5 *1 (-547))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1180)) (-5 *1 (-547))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-547))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-661 (-547))) (-5 *2 (-1198)) (-5 *1 (-547))))) 
+(((*1 *2 *2 *3) (-12 (-5 *2 (-1198)) (-5 *3 (-661 (-547))) (-5 *1 (-547))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-709 *6)) (-5 *5 (-1 (-417 (-1200 *6)) (-1200 *6)))
+  (-12 (-5 *3 (-709 *6)) (-5 *5 (-1 (-417 (-1192 *6)) (-1192 *6)))
    (-4 *6 (-376))
    (-5 *2
     (-661
      (-2 (|:| |outval| *7) (|:| |outmult| (-558))
       (|:| |outvect| (-661 (-709 *7))))))
-   (-5 *1 (-544 *6 *7 *4)) (-4 *7 (-376)) (-4 *4 (-13 (-376) (-868)))))) 
+   (-5 *1 (-544 *6 *7 *4)) (-4 *7 (-376)) (-4 *4 (-13 (-376) (-860)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1200 *5)) (-4 *5 (-376)) (-5 *2 (-661 *6))
-   (-5 *1 (-544 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-868)))))) 
+  (-12 (-5 *3 (-1192 *5)) (-4 *5 (-376)) (-5 *2 (-661 *6))
+   (-5 *1 (-544 *5 *6 *4)) (-4 *6 (-376)) (-4 *4 (-13 (-376) (-860)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-709 *4)) (-4 *4 (-376)) (-5 *2 (-1200 *4))
-   (-5 *1 (-544 *4 *5 *6)) (-4 *5 (-376)) (-4 *6 (-13 (-376) (-868)))))) 
+  (-12 (-5 *3 (-709 *4)) (-4 *4 (-376)) (-5 *2 (-1192 *4))
+   (-5 *1 (-544 *4 *5 *6)) (-4 *5 (-376)) (-4 *6 (-13 (-376) (-860)))))) 
 (((*1 *2 *3)
   (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-542 *3)) (-4 *3 (-13 (-746) (-25)))))) 
 (((*1 *2)
   (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-542 *3)) (-4 *3 (-13 (-746) (-25)))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-541))))
+(((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-541))))
  ((*1 *1 *2) (-12 (-5 *2 (-402)) (-5 *1 (-541))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-541))))) 
-(((*1 *2 *1 *2) (-12 (-5 *2 (-1149)) (-5 *1 (-541))))) 
+(((*1 *2 *1 *2) (-12 (-5 *2 (-1141)) (-5 *1 (-541))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-946)) (-4 *4 (-381)) (-4 *4 (-376)) (-5 *2 (-1200 *1))
+  (-12 (-5 *3 (-938)) (-4 *4 (-381)) (-4 *4 (-376)) (-5 *2 (-1192 *1))
    (-4 *1 (-341 *4))))
- ((*1 *2 *1) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-1200 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-5 *2 (-1192 *3))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-383 *3 *2)) (-4 *3 (-175)) (-4 *3 (-376)) (-4 *2 (-1272 *3))))
+  (-12 (-4 *1 (-383 *3 *2)) (-4 *3 (-175)) (-4 *3 (-376)) (-4 *2 (-1264 *3))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1296 *4)) (-4 *4 (-363)) (-5 *2 (-1200 *4)) (-5 *1 (-540 *4))))) 
+  (-12 (-5 *3 (-1288 *4)) (-4 *4 (-363)) (-5 *2 (-1192 *4)) (-5 *1 (-540 *4))))) 
 (((*1 *1) (-12 (-4 *1 (-341 *2)) (-4 *2 (-381)) (-4 *2 (-376))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-946)) (-5 *2 (-1296 *4)) (-5 *1 (-540 *4)) (-4 *4 (-363))))) 
+  (-12 (-5 *3 (-938)) (-5 *2 (-1288 *4)) (-5 *1 (-540 *4)) (-4 *4 (-363))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-1296 *4)) (-4 *4 (-430 *3)) (-4 *3 (-319)) (-4 *3 (-569))
+  (-12 (-5 *2 (-1288 *4)) (-4 *4 (-430 *3)) (-4 *3 (-319)) (-4 *3 (-569))
    (-5 *1 (-43 *3 *4))))
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- ((*1 *2) (-12 (-4 *3 (-376)) (-5 *2 (-1296 *1)) (-4 *1 (-341 *3))))
+  (-12 (-5 *3 (-938)) (-4 *4 (-376)) (-5 *2 (-1288 *1)) (-4 *1 (-341 *4))))
+ ((*1 *2) (-12 (-4 *3 (-376)) (-5 *2 (-1288 *1)) (-4 *1 (-341 *3))))
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-  (-12 (-4 *3 (-175)) (-4 *4 (-1272 *3)) (-5 *2 (-1296 *1))
+  (-12 (-4 *3 (-175)) (-4 *4 (-1264 *3)) (-5 *2 (-1288 *1))
    (-4 *1 (-422 *3 *4))))
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-   (-5 *1 (-425 *3 *4 *5 *6)) (-4 *6 (-13 (-422 *4 *5) (-1067 *4)))))
+  (-12 (-4 *3 (-319)) (-4 *4 (-1012 *3)) (-4 *5 (-1264 *4)) (-5 *2 (-1288 *6))
+   (-5 *1 (-425 *3 *4 *5 *6)) (-4 *6 (-13 (-422 *4 *5) (-1059 *4)))))
  ((*1 *2 *1)
-  (-12 (-4 *3 (-319)) (-4 *4 (-1020 *3)) (-4 *5 (-1272 *4)) (-5 *2 (-1296 *6))
+  (-12 (-4 *3 (-319)) (-4 *4 (-1012 *3)) (-4 *5 (-1264 *4)) (-5 *2 (-1288 *6))
    (-5 *1 (-427 *3 *4 *5 *6 *7)) (-4 *6 (-422 *4 *5)) (-14 *7 *2)))
- ((*1 *2) (-12 (-4 *3 (-175)) (-5 *2 (-1296 *1)) (-4 *1 (-430 *3))))
+ ((*1 *2) (-12 (-4 *3 (-175)) (-5 *2 (-1288 *1)) (-4 *1 (-430 *3))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-946)) (-5 *2 (-1296 (-1296 *4))) (-5 *1 (-540 *4))
+  (-12 (-5 *3 (-938)) (-5 *2 (-1288 (-1288 *4))) (-5 *1 (-540 *4))
    (-4 *4 (-363))))) 
 (((*1 *2 *1)
   (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-4 *3 (-381)) (-5 *2 (-114))))
  ((*1 *2 *3)
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-(((*1 *2 *1) (-12 (-4 *1 (-381)) (-5 *2 (-946))))
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  ((*1 *2 *3)
-  (-12 (-5 *3 (-1296 *4)) (-4 *4 (-363)) (-5 *2 (-946)) (-5 *1 (-540 *4))))) 
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 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1296 *4)) (-5 *3 (-558)) (-4 *4 (-363)) (-5 *1 (-540 *4))))) 
+  (-12 (-5 *2 (-1288 *4)) (-5 *3 (-558)) (-4 *4 (-363)) (-5 *1 (-540 *4))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-1296 *4)) (-5 *3 (-1149)) (-4 *4 (-363)) (-5 *1 (-540 *4))))) 
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 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1296 *4)) (-5 *3 (-791)) (-4 *4 (-363)) (-5 *1 (-540 *4))))) 
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 (((*1 *2 *2 *3 *4)
-  (-12 (-5 *2 (-1296 *5)) (-5 *3 (-791)) (-5 *4 (-1149)) (-4 *5 (-363))
+  (-12 (-5 *2 (-1288 *5)) (-5 *3 (-791)) (-5 *4 (-1141)) (-4 *5 (-363))
    (-5 *1 (-540 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-791)) (-5 *2 (-1200 *4)) (-5 *1 (-540 *4)) (-4 *4 (-363))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-1296 *4)) (-4 *4 (-363)) (-5 *2 (-1200 *4)) (-5 *1 (-540 *4))))) 
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 (((*1 *2 *3 *4)
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+  (-12 (-5 *3 (-1288 (-661 (-2 (|:| -3822 *4) (|:| -2631 (-1141))))))
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 (((*1 *2 *1) (-12 (-4 *1 (-539)) (-5 *2 (-711 (-130)))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-539)) (-5 *2 (-711 (-562)))))) 
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 (((*1 *2 *1) (-12 (-4 *1 (-539)) (-5 *2 (-711 (-559)))))) 
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 (((*1 *2 *1) (-12 (-4 *1 (-539)) (-5 *2 (-711 (-560)))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-539)) (-5 *2 (-711 (-1253)))))) 
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 (((*1 *2 *1 *3) (-12 (-4 *1 (-539)) (-5 *3 (-131)) (-5 *2 (-791))))) 
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 (((*1 *2 *2)
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    (-5 *1 (-533 *3 *4 *5 *2)) (-4 *2 (-706 *3 *4 *5))))) 
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-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1246)) (-5 *1 (-339 *3))))
+(((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-529))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1156)) (-5 *1 (-529))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1238)) (-5 *1 (-339 *3))))
  ((*1 *1 *2)
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-(((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-339 *3)) (-4 *3 (-1246))))
+  (-12 (-5 *2 (-661 *3)) (-4 *3 (-1238)) (-5 *1 (-528 *3 *4)) (-14 *4 (-558))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-339 *3)) (-4 *3 (-1238))))
  ((*1 *2 *1)
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-(((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-339 *3)) (-4 *3 (-1246))))
+  (-12 (-5 *2 (-791)) (-5 *1 (-528 *3 *4)) (-4 *3 (-1238)) (-14 *4 (-558))))) 
+(((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-339 *3)) (-4 *3 (-1238))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-558)) (-5 *1 (-528 *3 *4)) (-4 *3 (-1246)) (-14 *4 *2)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-339 *3)) (-4 *3 (-1246))))
+  (-12 (-5 *2 (-558)) (-5 *1 (-528 *3 *4)) (-4 *3 (-1238)) (-14 *4 *2)))) 
+(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-339 *3)) (-4 *3 (-1238))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-114)) (-5 *1 (-528 *3 *4)) (-4 *3 (-1246)) (-14 *4 (-558))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-521 *3 *2)) (-4 *3 (-102)) (-4 *2 (-872))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-528 *3 *4)) (-4 *3 (-1238)) (-14 *4 (-558))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-521 *3 *2)) (-4 *3 (-102)) (-4 *2 (-864))))) 
 (((*1 *1) (-5 *1 (-518)))) 
 (((*1 *1 *1 *2 *2)
   (-12 (-5 *2 (-558)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 *2) (-14 *4 (-791))
@@ -12608,171 +12520,171 @@
  ((*1 *2 *2 *3)
   (-12
    (-5 *2
-    (-516 (-419 (-558)) (-246 *5 (-791)) (-886 *4) (-255 *4 (-419 (-558)))))
-   (-5 *3 (-661 (-886 *4))) (-14 *4 (-661 (-1206))) (-14 *5 (-791))
+    (-516 (-419 (-558)) (-246 *5 (-791)) (-878 *4) (-255 *4 (-419 (-558)))))
+   (-5 *3 (-661 (-878 *4))) (-14 *4 (-661 (-1198))) (-14 *5 (-791))
    (-5 *1 (-517 *4 *5))))) 
 (((*1 *2 *3)
-  (-12 (-14 *4 (-661 (-1206))) (-14 *5 (-791))
+  (-12 (-14 *4 (-661 (-1198))) (-14 *5 (-791))
    (-5 *2
     (-661
-     (-516 (-419 (-558)) (-246 *5 (-791)) (-886 *4) (-255 *4 (-419 (-558))))))
+     (-516 (-419 (-558)) (-246 *5 (-791)) (-878 *4) (-255 *4 (-419 (-558))))))
    (-5 *1 (-517 *4 *5))
    (-5 *3
-    (-516 (-419 (-558)) (-246 *5 (-791)) (-886 *4) (-255 *4 (-419 (-558)))))))) 
+    (-516 (-419 (-558)) (-246 *5 (-791)) (-878 *4) (-255 *4 (-419 (-558)))))))) 
 (((*1 *2 *2)
   (-12
    (-5 *2
-    (-516 (-419 (-558)) (-246 *4 (-791)) (-886 *3) (-255 *3 (-419 (-558)))))
-   (-14 *3 (-661 (-1206))) (-14 *4 (-791)) (-5 *1 (-517 *3 *4))))) 
+    (-516 (-419 (-558)) (-246 *4 (-791)) (-878 *3) (-255 *3 (-419 (-558)))))
+   (-14 *3 (-661 (-1198))) (-14 *4 (-791)) (-5 *1 (-517 *3 *4))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-516 (-419 (-558)) (-246 *5 (-791)) (-886 *4) (-255 *4 (-419 (-558)))))
-   (-14 *4 (-661 (-1206))) (-14 *5 (-791)) (-5 *2 (-114))
+    (-516 (-419 (-558)) (-246 *5 (-791)) (-878 *4) (-255 *4 (-419 (-558)))))
+   (-14 *4 (-661 (-1198))) (-14 *5 (-791)) (-5 *2 (-114))
    (-5 *1 (-517 *4 *5))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-516 (-419 (-558)) (-246 *5 (-791)) (-886 *4) (-255 *4 (-419 (-558)))))
-   (-14 *4 (-661 (-1206))) (-14 *5 (-791)) (-5 *2 (-114))
+    (-516 (-419 (-558)) (-246 *5 (-791)) (-878 *4) (-255 *4 (-419 (-558)))))
+   (-14 *4 (-661 (-1198))) (-14 *5 (-791)) (-5 *2 (-114))
    (-5 *1 (-517 *4 *5))))) 
 (((*1 *2 *3 *1)
-  (-12 (-4 *4 (-376)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-114))
-   (-5 *1 (-516 *4 *5 *6 *3)) (-4 *3 (-977 *4 *5 *6))))) 
+  (-12 (-4 *4 (-376)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-114))
+   (-5 *1 (-516 *4 *5 *6 *3)) (-4 *3 (-969 *4 *5 *6))))) 
 (((*1 *2 *3)
   (-12 (-5 *3 (-229)) (-5 *2 (-114)) (-5 *1 (-314 *4 *5)) (-14 *4 *3)
    (-14 *5 *3)))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1118 (-863 (-229)))) (-5 *3 (-229)) (-5 *2 (-114))
+  (-12 (-5 *4 (-1110 (-855 (-229)))) (-5 *3 (-229)) (-5 *2 (-114))
    (-5 *1 (-315))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *2 (-114))
-   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-977 *3 *4 *5))))) 
+  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *2 (-114))
+   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-969 *3 *4 *5))))) 
 (((*1 *2 *3 *1)
-  (-12 (-4 *4 (-376)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-114))
-   (-5 *1 (-516 *4 *5 *6 *3)) (-4 *3 (-977 *4 *5 *6))))) 
+  (-12 (-4 *4 (-376)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-114))
+   (-5 *1 (-516 *4 *5 *6 *3)) (-4 *3 (-969 *4 *5 *6))))) 
 (((*1 *2 *1)
-  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *2 (-114))
-   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-977 *3 *4 *5))))
+  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *2 (-114))
+   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-969 *3 *4 *5))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-661 *6)) (-4 *6 (-869)) (-4 *4 (-376)) (-4 *5 (-815))
-   (-5 *2 (-114)) (-5 *1 (-516 *4 *5 *6 *7)) (-4 *7 (-977 *4 *5 *6))))) 
+  (-12 (-5 *3 (-661 *6)) (-4 *6 (-861)) (-4 *4 (-376)) (-4 *5 (-815))
+   (-5 *2 (-114)) (-5 *1 (-516 *4 *5 *6 *7)) (-4 *7 (-969 *4 *5 *6))))) 
 (((*1 *1 *1 *2)
-  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-516 *3 *4 *5 *2))
-   (-4 *2 (-977 *3 *4 *5))))
+  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-516 *3 *4 *5 *2))
+   (-4 *2 (-969 *3 *4 *5))))
  ((*1 *1 *1 *1)
-  (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-869)) (-5 *1 (-516 *2 *3 *4 *5))
-   (-4 *5 (-977 *2 *3 *4))))) 
+  (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-861)) (-5 *1 (-516 *2 *3 *4 *5))
+   (-4 *5 (-969 *2 *3 *4))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-661 *6)) (-4 *6 (-869)) (-4 *4 (-376)) (-4 *5 (-815))
+  (-12 (-5 *3 (-661 *6)) (-4 *6 (-861)) (-4 *4 (-376)) (-4 *5 (-815))
    (-5 *2
     (-2 (|:| |mval| (-709 *4)) (|:| |invmval| (-709 *4))
      (|:| |genIdeal| (-516 *4 *5 *6 *7))))
-   (-5 *1 (-516 *4 *5 *6 *7)) (-4 *7 (-977 *4 *5 *6))))) 
+   (-5 *1 (-516 *4 *5 *6 *7)) (-4 *7 (-969 *4 *5 *6))))) 
 (((*1 *1 *2)
   (-12
    (-5 *2
     (-2 (|:| |mval| (-709 *3)) (|:| |invmval| (-709 *3))
      (|:| |genIdeal| (-516 *3 *4 *5 *6))))
-   (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-516 *3 *4 *5 *6))
-   (-4 *6 (-977 *3 *4 *5))))) 
+   (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-516 *3 *4 *5 *6))
+   (-4 *6 (-969 *3 *4 *5))))) 
 (((*1 *1 *1)
-  (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-869)) (-5 *1 (-516 *2 *3 *4 *5))
-   (-4 *5 (-977 *2 *3 *4))))) 
+  (-12 (-4 *2 (-376)) (-4 *3 (-815)) (-4 *4 (-861)) (-5 *1 (-516 *2 *3 *4 *5))
+   (-4 *5 (-969 *2 *3 *4))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-349 *3 *4 *5 *6)) (-4 *3 (-376)) (-4 *4 (-1272 *3))
-   (-4 *5 (-1272 (-419 *4))) (-4 *6 (-355 *3 *4 *5))
+  (-12 (-4 *1 (-349 *3 *4 *5 *6)) (-4 *3 (-376)) (-4 *4 (-1264 *3))
+   (-4 *5 (-1264 (-419 *4))) (-4 *6 (-355 *3 *4 *5))
    (-5 *2 (-425 *4 (-419 *4) *5 *6))))
  ((*1 *1 *2)
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-   (-4 *4 (-1020 *3)) (-4 *5 (-1272 *4)) (-4 *3 (-319))
+  (-12 (-5 *2 (-1288 *6)) (-4 *6 (-13 (-422 *4 *5) (-1059 *4)))
+   (-4 *4 (-1012 *3)) (-4 *5 (-1264 *4)) (-4 *3 (-319))
    (-5 *1 (-425 *3 *4 *5 *6))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-376)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-516 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-376)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-516 *3 *4 *5 *6))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-376)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-516 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-376)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-516 *3 *4 *5 *6))))) 
 (((*1 *2 *1)
-  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *2 (-114))
-   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-977 *3 *4 *5))))) 
+  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *2 (-114))
+   (-5 *1 (-516 *3 *4 *5 *6)) (-4 *6 (-969 *3 *4 *5))))) 
 (((*1 *1 *1 *2 *3)
-  (-12 (-5 *3 (-661 *6)) (-4 *6 (-869)) (-4 *4 (-376)) (-4 *5 (-815))
-   (-5 *1 (-516 *4 *5 *6 *2)) (-4 *2 (-977 *4 *5 *6))))
+  (-12 (-5 *3 (-661 *6)) (-4 *6 (-861)) (-4 *4 (-376)) (-4 *5 (-815))
+   (-5 *1 (-516 *4 *5 *6 *2)) (-4 *2 (-969 *4 *5 *6))))
  ((*1 *1 *1 *2)
-  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-516 *3 *4 *5 *2))
-   (-4 *2 (-977 *3 *4 *5))))) 
+  (-12 (-4 *3 (-376)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-516 *3 *4 *5 *2))
+   (-4 *2 (-969 *3 *4 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *6 (-631 (-1206)))
-   (-4 *4 (-376)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-5 *2 (-1195 (-661 (-973 *4)) (-661 (-305 (-973 *4)))))
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-969 *4 *5 *6)) (-4 *6 (-631 (-1198)))
+   (-4 *4 (-376)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-5 *2 (-1187 (-661 (-965 *4)) (-661 (-305 (-965 *4)))))
    (-5 *1 (-516 *4 *5 *6 *7))))) 
 (((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-946)) (-5 *2 (-1302)) (-5 *1 (-217 *4))
+  (-12 (-5 *3 (-938)) (-5 *2 (-1294)) (-5 *1 (-217 *4))
    (-4 *4
-    (-13 (-869)
-     (-10 -8 (-15 -4307 ((-1188) $ (-1206))) (-15 -4124 (*2 $))
-      (-15 -2183 (*2 $)))))))
+    (-13 (-861)
+     (-10 -8 (-15 -4230 ((-1180) $ (-1198))) (-15 -4047 (*2 $))
+      (-15 -2175 (*2 $)))))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-1302)) (-5 *1 (-217 *3))
+  (-12 (-5 *2 (-1294)) (-5 *1 (-217 *3))
    (-4 *3
-    (-13 (-869)
-     (-10 -8 (-15 -4307 ((-1188) $ (-1206))) (-15 -4124 (*2 $))
-      (-15 -2183 (*2 $)))))))
- ((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-514))))) 
+    (-13 (-861)
+     (-10 -8 (-15 -4230 ((-1180) $ (-1198))) (-15 -4047 (*2 $))
+      (-15 -2175 (*2 $)))))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-514))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1078)) (-4 *7 (-1078)) (-4 *6 (-1272 *5))
-   (-5 *2 (-1200 (-1200 *7))) (-5 *1 (-513 *5 *6 *4 *7)) (-4 *4 (-1272 *6))))) 
+  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1070)) (-4 *7 (-1070)) (-4 *6 (-1264 *5))
+   (-5 *2 (-1192 (-1192 *7))) (-5 *1 (-513 *5 *6 *4 *7)) (-4 *4 (-1264 *6))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8)) (-5 *4 (-709 (-1200 *8)))
-   (-4 *5 (-1078)) (-4 *8 (-1078)) (-4 *6 (-1272 *5)) (-5 *2 (-709 *6))
-   (-5 *1 (-513 *5 *6 *7 *8)) (-4 *7 (-1272 *6))))) 
+  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8)) (-5 *4 (-709 (-1192 *8)))
+   (-4 *5 (-1070)) (-4 *8 (-1070)) (-4 *6 (-1264 *5)) (-5 *2 (-709 *6))
+   (-5 *1 (-513 *5 *6 *7 *8)) (-4 *7 (-1264 *6))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *7)) (-5 *4 (-1200 *7))
-   (-4 *5 (-1078)) (-4 *7 (-1078)) (-4 *2 (-1272 *5))
-   (-5 *1 (-513 *5 *2 *6 *7)) (-4 *6 (-1272 *2))))) 
+  (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *7)) (-5 *4 (-1192 *7))
+   (-4 *5 (-1070)) (-4 *7 (-1070)) (-4 *2 (-1264 *5))
+   (-5 *1 (-513 *5 *2 *6 *7)) (-4 *6 (-1264 *2))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *5 *7)) (-5 *4 (-1200 *7)) (-4 *5 (-1078)) (-4 *7 (-1078))
-   (-4 *2 (-1272 *5)) (-5 *1 (-513 *5 *2 *6 *7)) (-4 *6 (-1272 *2))))
+  (-12 (-5 *3 (-1 *5 *7)) (-5 *4 (-1192 *7)) (-4 *5 (-1070)) (-4 *7 (-1070))
+   (-4 *2 (-1264 *5)) (-5 *1 (-513 *5 *2 *6 *7)) (-4 *6 (-1264 *2))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1078)) (-4 *7 (-1078)) (-4 *4 (-1272 *5))
-   (-5 *2 (-1200 *7)) (-5 *1 (-513 *5 *4 *6 *7)) (-4 *6 (-1272 *4))))) 
+  (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-1070)) (-4 *7 (-1070)) (-4 *4 (-1264 *5))
+   (-5 *2 (-1192 *7)) (-5 *1 (-513 *5 *4 *6 *7)) (-4 *6 (-1264 *4))))) 
 (((*1 *2 *2 *2)
   (-12
    (-5 *2
-    (-2 (|:| -2230 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
-   (-4 *3 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $))))) (-4 *4 (-1272 *3))
+    (-2 (|:| -2222 (-709 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-709 *3))))
+   (-4 *3 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $))))) (-4 *4 (-1264 *3))
    (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-709 *3)) (-4 *3 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $)))))
-   (-4 *4 (-1272 *3)) (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))) 
+  (-12 (-5 *2 (-709 *3)) (-4 *3 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $)))))
+   (-4 *4 (-1264 *3)) (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-709 *3)) (-4 *3 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $)))))
-   (-4 *4 (-1272 *3)) (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))
+  (-12 (-5 *2 (-709 *3)) (-4 *3 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $)))))
+   (-4 *4 (-1264 *3)) (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))
  ((*1 *2 *2 *2 *3)
-  (-12 (-5 *2 (-709 *3)) (-4 *3 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $)))))
-   (-4 *4 (-1272 *3)) (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))) 
+  (-12 (-5 *2 (-709 *3)) (-4 *3 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $)))))
+   (-4 *4 (-1264 *3)) (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))) 
 (((*1 *2 *2 *2)
-  (-12 (-5 *2 (-791)) (-4 *3 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $)))))
-   (-4 *4 (-1272 *3)) (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))) 
+  (-12 (-5 *2 (-791)) (-4 *3 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $)))))
+   (-4 *4 (-1264 *3)) (-5 *1 (-511 *3 *4 *5)) (-4 *5 (-422 *3 *4))))) 
 (((*1 *2 *3 *3 *2 *4)
   (-12 (-5 *3 (-709 *2)) (-5 *4 (-558))
-   (-4 *2 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $))))) (-4 *5 (-1272 *2))
+   (-4 *2 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $))))) (-4 *5 (-1264 *2))
    (-5 *1 (-511 *2 *5 *6)) (-4 *6 (-422 *2 *5))))) 
 (((*1 *2 *3 *2 *4)
   (-12 (-5 *3 (-709 *2)) (-5 *4 (-791))
-   (-4 *2 (-13 (-319) (-10 -8 (-15 -4478 ((-417 $) $))))) (-4 *5 (-1272 *2))
+   (-4 *2 (-13 (-319) (-10 -8 (-15 -4401 ((-417 $) $))))) (-4 *5 (-1264 *2))
    (-5 *1 (-511 *2 *5 *6)) (-4 *6 (-422 *2 *5))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-791)) (-4 *5 (-363)) (-4 *6 (-1272 *5))
+  (-12 (-5 *4 (-791)) (-4 *5 (-363)) (-4 *6 (-1264 *5))
    (-5 *2
     (-661
-     (-2 (|:| -2230 (-709 *6)) (|:| |basisDen| *6)
+     (-2 (|:| -2222 (-709 *6)) (|:| |basisDen| *6)
       (|:| |basisInv| (-709 *6)))))
    (-5 *1 (-510 *5 *6 *7))
    (-5 *3
-    (-2 (|:| -2230 (-709 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-709 *6))))
-   (-4 *7 (-1272 *6))))) 
+    (-2 (|:| -2222 (-709 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-709 *6))))
+   (-4 *7 (-1264 *6))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
@@ -12781,90 +12693,90 @@
       (|:| |xpnt| (-558)))))
    (-5 *1 (-417 *3)) (-4 *3 (-569))))
  ((*1 *2 *3 *4 *4 *4)
-  (-12 (-5 *4 (-791)) (-4 *3 (-363)) (-4 *5 (-1272 *3))
-   (-5 *2 (-661 (-1200 *3))) (-5 *1 (-510 *3 *5 *6)) (-4 *6 (-1272 *5))))) 
+  (-12 (-5 *4 (-791)) (-4 *3 (-363)) (-4 *5 (-1264 *3))
+   (-5 *2 (-661 (-1192 *3))) (-5 *1 (-510 *3 *5 *6)) (-4 *6 (-1264 *5))))) 
 (((*1 *2 *1 *1) (-12 (-5 *2 (-114)) (-5 *1 (-507))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-503))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-503))))) 
 (((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1246))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1238))
    (-4 *4 (-385 *3)) (-4 *5 (-385 *3))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4503)) (-4 *1 (-501 *3))
-   (-4 *3 (-1246))))) 
+  (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4426)) (-4 *1 (-501 *3))
+   (-4 *3 (-1238))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-114) *4)) (|has| *1 (-6 -4502)) (-4 *1 (-501 *4))
-   (-4 *4 (-1246)) (-5 *2 (-114))))) 
+  (-12 (-5 *3 (-1 (-114) *4)) (|has| *1 (-6 -4425)) (-4 *1 (-501 *4))
+   (-4 *4 (-1238)) (-5 *2 (-114))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-114) *4)) (|has| *1 (-6 -4502)) (-4 *1 (-501 *4))
-   (-4 *4 (-1246)) (-5 *2 (-114))))) 
+  (-12 (-5 *3 (-1 (-114) *4)) (|has| *1 (-6 -4425)) (-4 *1 (-501 *4))
+   (-4 *4 (-1238)) (-5 *2 (-114))))) 
 (((*1 *2 *3 *1)
-  (-12 (|has| *1 (-6 -4502)) (-4 *1 (-501 *3)) (-4 *3 (-1246)) (-4 *3 (-1130))
+  (-12 (|has| *1 (-6 -4425)) (-4 *1 (-501 *3)) (-4 *3 (-1238)) (-4 *3 (-1122))
    (-5 *2 (-791))))
  ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-114) *4)) (|has| *1 (-6 -4502)) (-4 *1 (-501 *4))
-   (-4 *4 (-1246)) (-5 *2 (-791))))) 
+  (-12 (-5 *3 (-1 (-114) *4)) (|has| *1 (-6 -4425)) (-4 *1 (-501 *4))
+   (-4 *4 (-1238)) (-5 *2 (-791))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-419 (-558))) (-5 *1 (-499))))) 
 (((*1 *2 *3)
   (-12 (-5 *3 (-661 (-558))) (-5 *2 (-558)) (-5 *1 (-498 *4))
-   (-4 *4 (-1272 *2))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1272 (-558))) (-5 *1 (-498 *3))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1272 (-558))) (-5 *1 (-498 *3))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-661 *2)) (-5 *1 (-498 *2)) (-4 *2 (-1272 (-558)))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-869)) (-5 *1 (-496 *3))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-661 (-898))) (-5 *1 (-495))))) 
+   (-4 *4 (-1264 *2))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1264 (-558))) (-5 *1 (-498 *3))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1264 (-558))) (-5 *1 (-498 *3))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-661 *2)) (-5 *1 (-498 *2)) (-4 *2 (-1264 (-558)))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-861)) (-5 *1 (-496 *3))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-661 (-890))) (-5 *1 (-495))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-661 (-518))) (-5 *1 (-49))))
- ((*1 *2 *1) (-12 (-5 *2 (-661 (-898))) (-5 *1 (-495))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-661 (-890))) (-5 *1 (-495))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-661 (-558))) (-5 *1 (-255 *3 *4)) (-14 *3 (-661 (-1206)))
-   (-4 *4 (-1078))))
+  (-12 (-5 *2 (-661 (-558))) (-5 *1 (-255 *3 *4)) (-14 *3 (-661 (-1198)))
+   (-4 *4 (-1070))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-661 (-558))) (-14 *3 (-661 (-1206))) (-5 *1 (-466 *3 *4 *5))
-   (-4 *4 (-1078)) (-4 *5 (-245 (-4464 *3) (-791)))))
+  (-12 (-5 *2 (-661 (-558))) (-14 *3 (-661 (-1198))) (-5 *1 (-466 *3 *4 *5))
+   (-4 *4 (-1070)) (-4 *5 (-245 (-4387 *3) (-791)))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-661 (-558))) (-5 *1 (-493 *3 *4)) (-14 *3 (-661 (-1206)))
-   (-4 *4 (-1078))))) 
+  (-12 (-5 *2 (-661 (-558))) (-5 *1 (-493 *3 *4)) (-14 *3 (-661 (-1198)))
+   (-4 *4 (-1070))))) 
 (((*1 *2 *3 *3 *3 *3) (-12 (-5 *3 (-558)) (-5 *2 (-114)) (-5 *1 (-492))))) 
 (((*1 *2 *2 *2) (-12 (-5 *2 (-558)) (-5 *1 (-492))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 (-886 *5))) (-14 *5 (-661 (-1206))) (-4 *6 (-464))
+  (-12 (-5 *4 (-661 (-878 *5))) (-14 *5 (-661 (-1198))) (-4 *6 (-464))
    (-5 *2 (-2 (|:| |dpolys| (-661 (-255 *5 *6))) (|:| |coords| (-661 (-558)))))
    (-5 *1 (-483 *5 *6 *7)) (-5 *3 (-661 (-255 *5 *6))) (-4 *7 (-464))))) 
 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-661 (-493 *4 *5))) (-5 *3 (-661 (-886 *4)))
-   (-14 *4 (-661 (-1206))) (-4 *5 (-464)) (-5 *1 (-483 *4 *5 *6))
+  (|partial| -12 (-5 *2 (-661 (-493 *4 *5))) (-5 *3 (-661 (-878 *4)))
+   (-14 *4 (-661 (-1198))) (-4 *5 (-464)) (-5 *1 (-483 *4 *5 *6))
    (-4 *6 (-464))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 (-886 *5))) (-14 *5 (-661 (-1206))) (-4 *6 (-464))
+  (-12 (-5 *4 (-661 (-878 *5))) (-14 *5 (-661 (-1198))) (-4 *6 (-464))
    (-5 *2 (-661 (-661 (-255 *5 *6)))) (-5 *1 (-483 *5 *6 *7))
    (-5 *3 (-661 (-255 *5 *6))) (-4 *7 (-464))))) 
 (((*1 *1) (-5 *1 (-480)))) 
 (((*1 *1 *2 *3 *3 *4 *5)
-  (-12 (-5 *2 (-661 (-661 (-970 (-229))))) (-5 *3 (-661 (-896)))
-   (-5 *4 (-661 (-946))) (-5 *5 (-661 (-270))) (-5 *1 (-480))))
+  (-12 (-5 *2 (-661 (-661 (-962 (-229))))) (-5 *3 (-661 (-888)))
+   (-5 *4 (-661 (-938))) (-5 *5 (-661 (-270))) (-5 *1 (-480))))
  ((*1 *1 *2 *3 *3 *4)
-  (-12 (-5 *2 (-661 (-661 (-970 (-229))))) (-5 *3 (-661 (-896)))
-   (-5 *4 (-661 (-946))) (-5 *1 (-480))))
- ((*1 *1 *2) (-12 (-5 *2 (-661 (-661 (-970 (-229))))) (-5 *1 (-480))))
+  (-12 (-5 *2 (-661 (-661 (-962 (-229))))) (-5 *3 (-661 (-888)))
+   (-5 *4 (-661 (-938))) (-5 *1 (-480))))
+ ((*1 *1 *2) (-12 (-5 *2 (-661 (-661 (-962 (-229))))) (-5 *1 (-480))))
  ((*1 *1 *1) (-5 *1 (-480)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-661 (-970 (-229))))) (-5 *1 (-480))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 (-1118 (-391)))) (-5 *1 (-270))))
+(((*1 *2 *1) (-12 (-5 *2 (-661 (-661 (-962 (-229))))) (-5 *1 (-480))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 (-1110 (-391)))) (-5 *1 (-270))))
  ((*1 *2 *3 *2)
-  (-12 (-5 *2 (-661 (-1118 (-391)))) (-5 *3 (-661 (-270))) (-5 *1 (-271))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-661 (-1118 (-391)))) (-5 *1 (-480))))
- ((*1 *2 *1) (-12 (-5 *2 (-661 (-1118 (-391)))) (-5 *1 (-480))))) 
+  (-12 (-5 *2 (-661 (-1110 (-391)))) (-5 *3 (-661 (-270))) (-5 *1 (-271))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-661 (-1110 (-391)))) (-5 *1 (-480))))
+ ((*1 *2 *1) (-12 (-5 *2 (-661 (-1110 (-391)))) (-5 *1 (-480))))) 
 (((*1 *2 *1 *3 *4 *4 *5)
-  (-12 (-5 *3 (-970 (-229))) (-5 *4 (-896)) (-5 *5 (-946)) (-5 *2 (-1302))
+  (-12 (-5 *3 (-962 (-229))) (-5 *4 (-888)) (-5 *5 (-938)) (-5 *2 (-1294))
    (-5 *1 (-480))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-970 (-229))) (-5 *2 (-1302)) (-5 *1 (-480))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-962 (-229))) (-5 *2 (-1294)) (-5 *1 (-480))))
  ((*1 *2 *1 *3 *4 *4 *5)
-  (-12 (-5 *3 (-661 (-970 (-229)))) (-5 *4 (-896)) (-5 *5 (-946))
-   (-5 *2 (-1302)) (-5 *1 (-480))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-970 (-229))) (-5 *2 (-1302)) (-5 *1 (-480))))) 
+  (-12 (-5 *3 (-661 (-962 (-229)))) (-5 *4 (-888)) (-5 *5 (-938))
+   (-5 *2 (-1294)) (-5 *1 (-480))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-962 (-229))) (-5 *2 (-1294)) (-5 *1 (-480))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-661 (-661 (-970 (-229))))) (-5 *3 (-661 (-896)))
+  (-12 (-5 *2 (-661 (-661 (-962 (-229))))) (-5 *3 (-661 (-888)))
    (-5 *1 (-480))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-661 (-970 (-229))))) (-5 *2 (-661 (-229)))
+  (-12 (-5 *3 (-661 (-661 (-962 (-229))))) (-5 *2 (-661 (-229)))
    (-5 *1 (-480))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-270))))
  ((*1 *2 *3 *2) (-12 (-5 *2 (-114)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))
@@ -12875,186 +12787,186 @@
 (((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-479))))
  ((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-479))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-946)) (-5 *2 (-1296 (-1296 (-558)))) (-5 *1 (-478))))) 
+  (-12 (-5 *3 (-938)) (-5 *2 (-1288 (-1288 (-558)))) (-5 *1 (-478))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1296 (-1296 (-558)))) (-5 *3 (-946)) (-5 *1 (-478))))) 
+  (-12 (-5 *2 (-1288 (-1288 (-558)))) (-5 *3 (-938)) (-5 *1 (-478))))) 
 (((*1 *2 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-869)) (-4 *5 (-815)) (-4 *6 (-569))
-   (-4 *7 (-977 *6 *5 *3)) (-5 *1 (-474 *5 *3 *6 *7 *2))
+  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-861)) (-4 *5 (-815)) (-4 *6 (-569))
+   (-4 *7 (-969 *6 *5 *3)) (-5 *1 (-474 *5 *3 *6 *7 *2))
    (-4 *2
-    (-13 (-1067 (-419 (-558))) (-376)
-     (-10 -8 (-15 -4453 ($ *7)) (-15 -3476 (*7 $)) (-15 -3475 (*7 $)))))))) 
+    (-13 (-1059 (-419 (-558))) (-376)
+     (-10 -8 (-15 -4376 ($ *7)) (-15 -3399 (*7 $)) (-15 -3398 (*7 $)))))))) 
 (((*1 *2 *1)
-  (-12 (-14 *3 (-661 (-1206))) (-4 *4 (-175))
+  (-12 (-14 *3 (-661 (-1198))) (-4 *4 (-175))
    (-14 *6
-    (-1 (-114) (-2 (|:| -2639 *5) (|:| -2640 *2))
-     (-2 (|:| -2639 *5) (|:| -2640 *2))))
-   (-4 *2 (-245 (-4464 *3) (-791))) (-5 *1 (-473 *3 *4 *5 *2 *6 *7))
-   (-4 *5 (-869)) (-4 *7 (-977 *4 *2 (-886 *3)))))) 
+    (-1 (-114) (-2 (|:| -2631 *5) (|:| -2632 *2))
+     (-2 (|:| -2631 *5) (|:| -2632 *2))))
+   (-4 *2 (-245 (-4387 *3) (-791))) (-5 *1 (-473 *3 *4 *5 *2 *6 *7))
+   (-4 *5 (-861)) (-4 *7 (-969 *4 *2 (-878 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-14 *3 (-661 (-1206))) (-4 *4 (-175)) (-4 *5 (-245 (-4464 *3) (-791)))
+  (-12 (-14 *3 (-661 (-1198))) (-4 *4 (-175)) (-4 *5 (-245 (-4387 *3) (-791)))
    (-14 *6
-    (-1 (-114) (-2 (|:| -2639 *2) (|:| -2640 *5))
-     (-2 (|:| -2639 *2) (|:| -2640 *5))))
-   (-4 *2 (-869)) (-5 *1 (-473 *3 *4 *2 *5 *6 *7))
-   (-4 *7 (-977 *4 *5 (-886 *3)))))) 
+    (-1 (-114) (-2 (|:| -2631 *2) (|:| -2632 *5))
+     (-2 (|:| -2631 *2) (|:| -2632 *5))))
+   (-4 *2 (-861)) (-5 *1 (-473 *3 *4 *2 *5 *6 *7))
+   (-4 *7 (-969 *4 *5 (-878 *3)))))) 
 (((*1 *1 *2 *3 *4)
-  (-12 (-14 *5 (-661 (-1206))) (-4 *2 (-175)) (-4 *4 (-245 (-4464 *5) (-791)))
+  (-12 (-14 *5 (-661 (-1198))) (-4 *2 (-175)) (-4 *4 (-245 (-4387 *5) (-791)))
    (-14 *6
-    (-1 (-114) (-2 (|:| -2639 *3) (|:| -2640 *4))
-     (-2 (|:| -2639 *3) (|:| -2640 *4))))
-   (-5 *1 (-473 *5 *2 *3 *4 *6 *7)) (-4 *3 (-869))
-   (-4 *7 (-977 *2 *4 (-886 *5)))))) 
+    (-1 (-114) (-2 (|:| -2631 *3) (|:| -2632 *4))
+     (-2 (|:| -2631 *3) (|:| -2632 *4))))
+   (-5 *1 (-473 *5 *2 *3 *4 *6 *7)) (-4 *3 (-861))
+   (-4 *7 (-969 *2 *4 (-878 *5)))))) 
 (((*1 *1 *2 *3 *1)
-  (-12 (-14 *4 (-661 (-1206))) (-4 *2 (-175)) (-4 *3 (-245 (-4464 *4) (-791)))
+  (-12 (-14 *4 (-661 (-1198))) (-4 *2 (-175)) (-4 *3 (-245 (-4387 *4) (-791)))
    (-14 *6
-    (-1 (-114) (-2 (|:| -2639 *5) (|:| -2640 *3))
-     (-2 (|:| -2639 *5) (|:| -2640 *3))))
-   (-5 *1 (-473 *4 *2 *5 *3 *6 *7)) (-4 *5 (-869))
-   (-4 *7 (-977 *2 *3 (-886 *4)))))) 
+    (-1 (-114) (-2 (|:| -2631 *5) (|:| -2632 *3))
+     (-2 (|:| -2631 *5) (|:| -2632 *3))))
+   (-5 *1 (-473 *4 *2 *5 *3 *6 *7)) (-4 *5 (-861))
+   (-4 *7 (-969 *2 *3 (-878 *4)))))) 
 (((*1 *2 *3 *2 *4 *5)
-  (-12 (-5 *2 (-661 *3)) (-5 *5 (-946)) (-4 *3 (-1272 *4)) (-4 *4 (-319))
+  (-12 (-5 *2 (-661 *3)) (-5 *5 (-938)) (-4 *3 (-1264 *4)) (-4 *4 (-319))
    (-5 *1 (-472 *4 *3))))) 
 (((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *6 (-946)) (-4 *5 (-319)) (-4 *3 (-1272 *5))
+  (-12 (-5 *6 (-938)) (-4 *5 (-319)) (-4 *3 (-1264 *5))
    (-5 *2 (-2 (|:| |plist| (-661 *3)) (|:| |modulo| *5))) (-5 *1 (-472 *5 *3))
    (-5 *4 (-661 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 *5)) (-4 *5 (-1272 *3)) (-4 *3 (-319)) (-5 *2 (-114))
+  (-12 (-5 *4 (-661 *5)) (-4 *5 (-1264 *3)) (-4 *3 (-319)) (-5 *2 (-114))
    (-5 *1 (-467 *3 *5))))) 
 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *5 (-1296 (-661 *3))) (-4 *4 (-319)) (-5 *2 (-661 *3))
-   (-5 *1 (-467 *4 *3)) (-4 *3 (-1272 *4))))) 
+  (|partial| -12 (-5 *5 (-1288 (-661 *3))) (-4 *4 (-319)) (-5 *2 (-661 *3))
+   (-5 *1 (-467 *4 *3)) (-4 *3 (-1264 *4))))) 
 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *3 (-791)) (-4 *4 (-319)) (-4 *6 (-1272 *4))
-   (-5 *2 (-1296 (-661 *6))) (-5 *1 (-467 *4 *6)) (-5 *5 (-661 *6))))) 
+  (|partial| -12 (-5 *3 (-791)) (-4 *4 (-319)) (-4 *6 (-1264 *4))
+   (-5 *2 (-1288 (-661 *6))) (-5 *1 (-467 *4 *6)) (-5 *5 (-661 *6))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1272 *5)) (-4 *5 (-319)) (-5 *2 (-791))
+  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1264 *5)) (-4 *5 (-319)) (-5 *2 (-791))
    (-5 *1 (-467 *5 *3))))) 
 (((*1 *2)
   (|partial| -12 (-4 *3 (-569)) (-4 *3 (-175))
-   (-5 *2 (-2 (|:| |particular| *1) (|:| -2230 (-661 *1)))) (-4 *1 (-380 *3))))
+   (-5 *2 (-2 (|:| |particular| *1) (|:| -2222 (-661 *1)))) (-4 *1 (-380 *3))))
  ((*1 *2)
   (|partial| -12
    (-5 *2
     (-2 (|:| |particular| (-465 *3 *4 *5 *6))
-     (|:| -2230 (-661 (-465 *3 *4 *5 *6)))))
-   (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-175)) (-14 *4 (-946))
-   (-14 *5 (-661 (-1206))) (-14 *6 (-1296 (-709 *3)))))) 
+     (|:| -2222 (-661 (-465 *3 *4 *5 *6)))))
+   (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-175)) (-14 *4 (-938))
+   (-14 *5 (-661 (-1198))) (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2)
   (|partial| -12 (-4 *3 (-569)) (-4 *3 (-175))
-   (-5 *2 (-2 (|:| |particular| *1) (|:| -2230 (-661 *1)))) (-4 *1 (-380 *3))))
+   (-5 *2 (-2 (|:| |particular| *1) (|:| -2222 (-661 *1)))) (-4 *1 (-380 *3))))
  ((*1 *2)
   (|partial| -12
    (-5 *2
     (-2 (|:| |particular| (-465 *3 *4 *5 *6))
-     (|:| -2230 (-661 (-465 *3 *4 *5 *6)))))
-   (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-175)) (-14 *4 (-946))
-   (-14 *5 (-661 (-1206))) (-14 *6 (-1296 (-709 *3)))))) 
+     (|:| -2222 (-661 (-465 *3 *4 *5 *6)))))
+   (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-175)) (-14 *4 (-938))
+   (-14 *5 (-661 (-1198))) (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1296 (-1206))) (-5 *3 (-1296 (-465 *4 *5 *6 *7)))
-   (-5 *1 (-465 *4 *5 *6 *7)) (-4 *4 (-175)) (-14 *5 (-946))
-   (-14 *6 (-661 (-1206))) (-14 *7 (-1296 (-709 *4)))))
+  (-12 (-5 *2 (-1288 (-1198))) (-5 *3 (-1288 (-465 *4 *5 *6 *7)))
+   (-5 *1 (-465 *4 *5 *6 *7)) (-4 *4 (-175)) (-14 *5 (-938))
+   (-14 *6 (-661 (-1198))) (-14 *7 (-1288 (-709 *4)))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1206)) (-5 *3 (-1296 (-465 *4 *5 *6 *7)))
-   (-5 *1 (-465 *4 *5 *6 *7)) (-4 *4 (-175)) (-14 *5 (-946)) (-14 *6 (-661 *2))
-   (-14 *7 (-1296 (-709 *4)))))
+  (-12 (-5 *2 (-1198)) (-5 *3 (-1288 (-465 *4 *5 *6 *7)))
+   (-5 *1 (-465 *4 *5 *6 *7)) (-4 *4 (-175)) (-14 *5 (-938)) (-14 *6 (-661 *2))
+   (-14 *7 (-1288 (-709 *4)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-465 *3 *4 *5 *6))) (-5 *1 (-465 *3 *4 *5 *6))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))
+  (-12 (-5 *2 (-1288 (-465 *3 *4 *5 *6))) (-5 *1 (-465 *3 *4 *5 *6))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 (-1206))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-175))
-   (-14 *4 (-946)) (-14 *5 (-661 (-1206))) (-14 *6 (-1296 (-709 *3)))))
+  (-12 (-5 *2 (-1288 (-1198))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-175))
+   (-14 *4 (-938)) (-14 *5 (-661 (-1198))) (-14 *6 (-1288 (-709 *3)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1206)) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-175))
-   (-14 *4 (-946)) (-14 *5 (-661 *2)) (-14 *6 (-1296 (-709 *3)))))
+  (-12 (-5 *2 (-1198)) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-175))
+   (-14 *4 (-938)) (-14 *5 (-661 *2)) (-14 *6 (-1288 (-709 *3)))))
  ((*1 *1)
-  (-12 (-5 *1 (-465 *2 *3 *4 *5)) (-4 *2 (-175)) (-14 *3 (-946))
-   (-14 *4 (-661 (-1206))) (-14 *5 (-1296 (-709 *2)))))) 
+  (-12 (-5 *1 (-465 *2 *3 *4 *5)) (-4 *2 (-175)) (-14 *3 (-938))
+   (-14 *4 (-661 (-1198))) (-14 *5 (-1288 (-709 *2)))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-175)) (-5 *2 (-1200 (-973 *4))) (-5 *1 (-429 *3 *4))
+  (-12 (-4 *4 (-175)) (-5 *2 (-1192 (-965 *4))) (-5 *1 (-429 *3 *4))
    (-4 *3 (-430 *4))))
  ((*1 *2)
   (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-4 *3 (-376))
-   (-5 *2 (-1200 (-973 *3)))))
+   (-5 *2 (-1192 (-965 *3)))))
  ((*1 *2)
-  (-12 (-5 *2 (-1200 (-419 (-973 *3)))) (-5 *1 (-465 *3 *4 *5 *6))
-   (-4 *3 (-569)) (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-1192 (-419 (-965 *3)))) (-5 *1 (-465 *3 *4 *5 *6))
+   (-4 *3 (-569)) (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-1200 (-419 (-973 *3)))) (-5 *1 (-465 *3 *4 *5 *6))
-   (-4 *3 (-569)) (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-1192 (-419 (-965 *3)))) (-5 *1 (-465 *3 *4 *5 *6))
+   (-4 *3 (-569)) (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-419 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-419 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-419 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-419 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-175)) (-5 *2 (-1200 (-973 *4))) (-5 *1 (-429 *3 *4))
+  (-12 (-4 *4 (-175)) (-5 *2 (-1192 (-965 *4))) (-5 *1 (-429 *3 *4))
    (-4 *3 (-430 *4))))
  ((*1 *2)
   (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-4 *3 (-376))
-   (-5 *2 (-1200 (-973 *3)))))
+   (-5 *2 (-1192 (-965 *3)))))
  ((*1 *2)
-  (-12 (-5 *2 (-1200 (-419 (-973 *3)))) (-5 *1 (-465 *3 *4 *5 *6))
-   (-4 *3 (-569)) (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-1192 (-419 (-965 *3)))) (-5 *1 (-465 *3 *4 *5 *6))
+   (-4 *3 (-569)) (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-1200 (-419 (-973 *3)))) (-5 *1 (-465 *3 *4 *5 *6))
-   (-4 *3 (-569)) (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-1192 (-419 (-965 *3)))) (-5 *1 (-465 *3 *4 *5 *6))
+   (-4 *3 (-569)) (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-419 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-419 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-419 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-419 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-419 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-419 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-419 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-419 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-419 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-419 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-419 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))) 
+  (-12 (-5 *2 (-419 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1296 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175))
-   (-5 *2 (-661 (-973 *4)))))
+  (-12 (-5 *3 (-1288 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175))
+   (-5 *2 (-661 (-965 *4)))))
  ((*1 *2)
-  (-12 (-4 *4 (-175)) (-5 *2 (-661 (-973 *4))) (-5 *1 (-429 *3 *4))
+  (-12 (-4 *4 (-175)) (-5 *2 (-661 (-965 *4))) (-5 *1 (-429 *3 *4))
    (-4 *3 (-430 *4))))
- ((*1 *2) (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-5 *2 (-661 (-973 *3)))))
+ ((*1 *2) (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-5 *2 (-661 (-965 *3)))))
  ((*1 *2)
-  (-12 (-5 *2 (-661 (-973 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
-   (-4 *3 (-175)) (-14 *4 (-946)) (-14 *5 (-661 (-1206)))
-   (-14 *6 (-1296 (-709 *3)))))
+  (-12 (-5 *2 (-661 (-965 *3))) (-5 *1 (-465 *3 *4 *5 *6)) (-4 *3 (-569))
+   (-4 *3 (-175)) (-14 *4 (-938)) (-14 *5 (-661 (-1198)))
+   (-14 *6 (-1288 (-709 *3)))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1296 (-465 *4 *5 *6 *7))) (-5 *2 (-661 (-973 *4)))
-   (-5 *1 (-465 *4 *5 *6 *7)) (-4 *4 (-569)) (-4 *4 (-175)) (-14 *5 (-946))
-   (-14 *6 (-661 (-1206))) (-14 *7 (-1296 (-709 *4)))))) 
+  (-12 (-5 *3 (-1288 (-465 *4 *5 *6 *7))) (-5 *2 (-661 (-965 *4)))
+   (-5 *1 (-465 *4 *5 *6 *7)) (-4 *4 (-569)) (-4 *4 (-175)) (-14 *5 (-938))
+   (-14 *6 (-661 (-1198))) (-14 *7 (-1288 (-709 *4)))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-661 *1)) (-4 *1 (-464))))
  ((*1 *1 *1 *1) (-4 *1 (-464)))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-791))
-   (-5 *1 (-462 *4 *5 *6 *3)) (-4 *3 (-977 *4 *5 *6))))) 
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-791))
+   (-5 *1 (-462 *4 *5 *6 *3)) (-4 *3 (-969 *4 *5 *6))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-2 (|:| |totdeg| (-791)) (|:| -2222 *4))) (-5 *5 (-791))
-   (-4 *4 (-977 *6 *7 *8)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-869))
+  (-12 (-5 *3 (-2 (|:| |totdeg| (-791)) (|:| -2214 *4))) (-5 *5 (-791))
+   (-4 *4 (-969 *6 *7 *8)) (-4 *6 (-464)) (-4 *7 (-815)) (-4 *8 (-861))
    (-5 *2
     (-2 (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) (|:| |polj| *4)))
    (-5 *1 (-462 *6 *7 *8 *4))))) 
@@ -13063,62 +12975,62 @@
    (-5 *3
     (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-791)) (|:| |poli| *7)
      (|:| |polj| *7)))
-   (-4 *5 (-815)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-464)) (-4 *6 (-869))
+   (-4 *5 (-815)) (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-464)) (-4 *6 (-861))
    (-5 *2 (-114)) (-5 *1 (-462 *4 *5 *6 *7))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-558)) (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869))
-   (-5 *2 (-1302)) (-5 *1 (-462 *4 *5 *6 *7)) (-4 *7 (-977 *4 *5 *6))))) 
+  (-12 (-5 *3 (-558)) (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861))
+   (-5 *2 (-1294)) (-5 *1 (-462 *4 *5 *6 *7)) (-4 *7 (-969 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *2 (-1302)) (-5 *1 (-462 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-661 *7)) (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *2 (-1294)) (-5 *1 (-462 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *4 *2 *2 *2 *2)
   (-12 (-5 *2 (-558))
    (-5 *3
     (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-791)) (|:| |poli| *4)
      (|:| |polj| *4)))
-   (-4 *6 (-815)) (-4 *4 (-977 *5 *6 *7)) (-4 *5 (-464)) (-4 *7 (-869))
+   (-4 *6 (-815)) (-4 *4 (-969 *5 *6 *7)) (-4 *5 (-464)) (-4 *7 (-861))
    (-5 *1 (-462 *5 *6 *7 *4))))) 
 (((*1 *2 *3 *4 *4 *2 *2 *2)
   (-12 (-5 *2 (-558))
    (-5 *3
     (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-791)) (|:| |poli| *4)
      (|:| |polj| *4)))
-   (-4 *6 (-815)) (-4 *4 (-977 *5 *6 *7)) (-4 *5 (-464)) (-4 *7 (-869))
+   (-4 *6 (-815)) (-4 *4 (-969 *5 *6 *7)) (-4 *5 (-464)) (-4 *7 (-861))
    (-5 *1 (-462 *5 *6 *7 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-1302))
-   (-5 *1 (-462 *4 *5 *6 *3)) (-4 *3 (-977 *4 *5 *6))))) 
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-1294))
+   (-5 *1 (-462 *4 *5 *6 *3)) (-4 *3 (-969 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-869)) (-5 *2 (-558))
-   (-5 *1 (-462 *4 *5 *6 *3)) (-4 *3 (-977 *4 *5 *6))))) 
+  (-12 (-4 *4 (-464)) (-4 *5 (-815)) (-4 *6 (-861)) (-5 *2 (-558))
+   (-5 *1 (-462 *4 *5 *6 *3)) (-4 *3 (-969 *4 *5 *6))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-464)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-462 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-464)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-462 *3 *4 *5 *6))))) 
 (((*1 *2 *2 *2)
   (-12
    (-5 *2
     (-661
      (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-791)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *4 (-815)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-464)) (-4 *5 (-869))
+   (-4 *4 (-815)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-464)) (-4 *5 (-861))
    (-5 *1 (-462 *3 *4 *5 *6))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
     (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-791)) (|:| |poli| *2)
      (|:| |polj| *2)))
-   (-4 *5 (-815)) (-4 *2 (-977 *4 *5 *6)) (-5 *1 (-462 *4 *5 *6 *2))
-   (-4 *4 (-464)) (-4 *6 (-869))))) 
+   (-4 *5 (-815)) (-4 *2 (-969 *4 *5 *6)) (-5 *1 (-462 *4 *5 *6 *2))
+   (-4 *4 (-464)) (-4 *6 (-861))))) 
 (((*1 *2 *3 *4 *2)
-  (-12 (-5 *2 (-661 (-2 (|:| |totdeg| (-791)) (|:| -2222 *3)))) (-5 *4 (-791))
-   (-4 *3 (-977 *5 *6 *7)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-869))
+  (-12 (-5 *2 (-661 (-2 (|:| |totdeg| (-791)) (|:| -2214 *3)))) (-5 *4 (-791))
+   (-4 *3 (-969 *5 *6 *7)) (-4 *5 (-464)) (-4 *6 (-815)) (-4 *7 (-861))
    (-5 *1 (-462 *5 *6 *7 *3))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-869)) (-5 *1 (-462 *3 *4 *5 *2))
-   (-4 *2 (-977 *3 *4 *5))))) 
+  (-12 (-4 *3 (-464)) (-4 *4 (-815)) (-4 *5 (-861)) (-5 *1 (-462 *3 *4 *5 *2))
+   (-4 *2 (-969 *3 *4 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 *3)) (-4 *3 (-977 *5 *6 *7)) (-4 *5 (-464)) (-4 *6 (-815))
-   (-4 *7 (-869)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
+  (-12 (-5 *4 (-661 *3)) (-4 *3 (-969 *5 *6 *7)) (-4 *5 (-464)) (-4 *6 (-815))
+   (-4 *7 (-861)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
    (-5 *1 (-462 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *2)
   (-12
@@ -13126,7 +13038,7 @@
     (-661
      (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-791)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *3 (-815)) (-4 *6 (-977 *4 *3 *5)) (-4 *4 (-464)) (-4 *5 (-869))
+   (-4 *3 (-815)) (-4 *6 (-969 *4 *3 *5)) (-4 *4 (-464)) (-4 *5 (-861))
    (-5 *1 (-462 *4 *3 *5 *6))))) 
 (((*1 *2 *2)
   (-12
@@ -13134,7 +13046,7 @@
     (-661
      (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-791)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *4 (-815)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-464)) (-4 *5 (-869))
+   (-4 *4 (-815)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-464)) (-4 *5 (-861))
    (-5 *1 (-462 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *2)
   (-12
@@ -13142,158 +13054,158 @@
     (-661
      (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-791)) (|:| |poli| *3)
       (|:| |polj| *3))))
-   (-4 *5 (-815)) (-4 *3 (-977 *4 *5 *6)) (-4 *4 (-464)) (-4 *6 (-869))
+   (-4 *5 (-815)) (-4 *3 (-969 *4 *5 *6)) (-4 *4 (-464)) (-4 *6 (-861))
    (-5 *1 (-462 *4 *5 *6 *3))))) 
 (((*1 *2 *3 *3 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *3 (-815)) (-4 *5 (-869)) (-5 *2 (-114))
-   (-5 *1 (-462 *4 *3 *5 *6)) (-4 *6 (-977 *4 *3 *5))))) 
+  (-12 (-4 *4 (-464)) (-4 *3 (-815)) (-4 *5 (-861)) (-5 *2 (-114))
+   (-5 *1 (-462 *4 *3 *5 *6)) (-4 *6 (-969 *4 *3 *5))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-464)) (-4 *3 (-815)) (-4 *5 (-869)) (-5 *2 (-114))
-   (-5 *1 (-462 *4 *3 *5 *6)) (-4 *6 (-977 *4 *3 *5))))) 
+  (-12 (-4 *4 (-464)) (-4 *3 (-815)) (-4 *5 (-861)) (-5 *2 (-114))
+   (-5 *1 (-462 *4 *3 *5 *6)) (-4 *6 (-969 *4 *3 *5))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
     (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-791)) (|:| |poli| *7)
      (|:| |polj| *7)))
-   (-4 *5 (-815)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-464)) (-4 *6 (-869))
+   (-4 *5 (-815)) (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-464)) (-4 *6 (-861))
    (-5 *2 (-114)) (-5 *1 (-462 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-661 *7)) (-5 *3 (-558)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-464))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *1 (-462 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-661 *7)) (-5 *3 (-558)) (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-464))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *1 (-462 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-977 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *1 (-462 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-969 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *1 (-462 *4 *5 *6 *2))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-977 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *1 (-462 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-969 *4 *5 *6)) (-4 *4 (-464)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *1 (-462 *4 *5 *6 *2))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-661 (-661 *7))) (-5 *1 (-461 *4 *5 *6 *7))
+  (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-969 *4 *5 *6)) (-5 *2 (-661 (-661 *7))) (-5 *1 (-461 *4 *5 *6 *7))
    (-5 *3 (-661 *7))))
  ((*1 *2 *3 *3 *4)
-  (-12 (-5 *4 (-114)) (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) (-4 *7 (-869))
-   (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-661 (-661 *8))) (-5 *1 (-461 *5 *6 *7 *8))
+  (-12 (-5 *4 (-114)) (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) (-4 *7 (-861))
+   (-4 *8 (-969 *5 *6 *7)) (-5 *2 (-661 (-661 *8))) (-5 *1 (-461 *5 *6 *7 *8))
    (-5 *3 (-661 *8))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-661 (-661 *7))) (-5 *1 (-461 *4 *5 *6 *7))
+  (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-969 *4 *5 *6)) (-5 *2 (-661 (-661 *7))) (-5 *1 (-461 *4 *5 *6 *7))
    (-5 *3 (-661 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-114)) (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) (-4 *7 (-869))
-   (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-661 (-661 *8))) (-5 *1 (-461 *5 *6 *7 *8))
+  (-12 (-5 *4 (-114)) (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) (-4 *7 (-861))
+   (-4 *8 (-969 *5 *6 *7)) (-5 *2 (-661 (-661 *8))) (-5 *1 (-461 *5 *6 *7 *8))
    (-5 *3 (-661 *8))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-815)) (-4 *6 (-869))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-661 (-661 *7))) (-5 *1 (-461 *4 *5 *6 *7))
+  (-12 (-4 *4 (-13 (-319) (-149))) (-4 *5 (-815)) (-4 *6 (-861))
+   (-4 *7 (-969 *4 *5 *6)) (-5 *2 (-661 (-661 *7))) (-5 *1 (-461 *4 *5 *6 *7))
    (-5 *3 (-661 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-114)) (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) (-4 *7 (-869))
-   (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-661 (-661 *8))) (-5 *1 (-461 *5 *6 *7 *8))
+  (-12 (-5 *4 (-114)) (-4 *5 (-13 (-319) (-149))) (-4 *6 (-815)) (-4 *7 (-861))
+   (-4 *8 (-969 *5 *6 *7)) (-5 *2 (-661 (-661 *8))) (-5 *1 (-461 *5 *6 *7 *8))
    (-5 *3 (-661 *8))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-661 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-319)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-5 *1 (-460 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-661 *6)) (-4 *6 (-969 *3 *4 *5)) (-4 *3 (-319)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-5 *1 (-460 *3 *4 *5 *6))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-661 *7)) (-5 *3 (-1188)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-319))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *1 (-460 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-661 *7)) (-5 *3 (-1180)) (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-319))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *1 (-460 *4 *5 *6 *7))))
  ((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-661 *7)) (-5 *3 (-1188)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-319))
-   (-4 *5 (-815)) (-4 *6 (-869)) (-5 *1 (-460 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-661 *7)) (-5 *3 (-1180)) (-4 *7 (-969 *4 *5 *6)) (-4 *4 (-319))
+   (-4 *5 (-815)) (-4 *6 (-861)) (-5 *1 (-460 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-661 *2)) (-4 *2 (-977 *4 *5 *6)) (-4 *4 (-319)) (-4 *5 (-815))
-   (-4 *6 (-869)) (-5 *1 (-460 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-661 *2)) (-4 *2 (-969 *4 *5 *6)) (-4 *4 (-319)) (-4 *5 (-815))
+   (-4 *6 (-861)) (-5 *1 (-460 *4 *5 *6 *2))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-661 (-558))) (-5 *1 (-458)) (-5 *3 (-558))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1078))))
+  (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1070))))
  ((*1 *2)
-  (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1078))))) 
+  (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1070))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-558)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1078))))) 
+  (-12 (-5 *2 (-558)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1070))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-558)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1078))))) 
-(((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-457 *3)) (-4 *3 (-1078))))) 
-(((*1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-1078))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-1078))))
- ((*1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-1078))))) 
+  (-12 (-5 *2 (-558)) (-5 *1 (-457 *3)) (-4 *3 (-416)) (-4 *3 (-1070))))) 
+(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-457 *3)) (-4 *3 (-1070))))) 
+(((*1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-1070))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-1070))))
+ ((*1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-457 *3)) (-4 *3 (-1070))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-791)) (-5 *4 (-558)) (-5 *1 (-457 *2)) (-4 *2 (-1078))))) 
+  (-12 (-5 *3 (-791)) (-5 *4 (-558)) (-5 *1 (-457 *2)) (-4 *2 (-1070))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-946)) (-5 *4 (-417 *6)) (-4 *6 (-1272 *5)) (-4 *5 (-1078))
+  (-12 (-5 *3 (-938)) (-5 *4 (-417 *6)) (-4 *6 (-1264 *5)) (-4 *5 (-1070))
    (-5 *2 (-661 *6)) (-5 *1 (-456 *5 *6))))) 
 (((*1 *2 *3 *2)
-  (|partial| -12 (-5 *3 (-946)) (-5 *1 (-454 *2)) (-4 *2 (-1272 (-558)))))
+  (|partial| -12 (-5 *3 (-938)) (-5 *1 (-454 *2)) (-4 *2 (-1264 (-558)))))
  ((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-946)) (-5 *4 (-791)) (-5 *1 (-454 *2))
-   (-4 *2 (-1272 (-558)))))
+  (|partial| -12 (-5 *3 (-938)) (-5 *4 (-791)) (-5 *1 (-454 *2))
+   (-4 *2 (-1264 (-558)))))
  ((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-946)) (-5 *4 (-661 (-791))) (-5 *1 (-454 *2))
-   (-4 *2 (-1272 (-558)))))
+  (|partial| -12 (-5 *3 (-938)) (-5 *4 (-661 (-791))) (-5 *1 (-454 *2))
+   (-4 *2 (-1264 (-558)))))
  ((*1 *2 *3 *2 *4 *5)
-  (|partial| -12 (-5 *3 (-946)) (-5 *4 (-661 (-791))) (-5 *5 (-791))
-   (-5 *1 (-454 *2)) (-4 *2 (-1272 (-558)))))
+  (|partial| -12 (-5 *3 (-938)) (-5 *4 (-661 (-791))) (-5 *5 (-791))
+   (-5 *1 (-454 *2)) (-4 *2 (-1264 (-558)))))
  ((*1 *2 *3 *2 *4 *5 *6)
-  (|partial| -12 (-5 *3 (-946)) (-5 *4 (-661 (-791))) (-5 *5 (-791))
-   (-5 *6 (-114)) (-5 *1 (-454 *2)) (-4 *2 (-1272 (-558)))))
+  (|partial| -12 (-5 *3 (-938)) (-5 *4 (-661 (-791))) (-5 *5 (-791))
+   (-5 *6 (-114)) (-5 *1 (-454 *2)) (-4 *2 (-1264 (-558)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-946)) (-5 *4 (-417 *2)) (-4 *2 (-1272 *5)) (-5 *1 (-456 *5 *2))
-   (-4 *5 (-1078))))) 
+  (-12 (-5 *3 (-938)) (-5 *4 (-417 *2)) (-4 *2 (-1264 *5)) (-5 *1 (-456 *5 *2))
+   (-4 *5 (-1070))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-2 (|:| -4239 *4) (|:| -4455 (-558)))))
-   (-4 *4 (-1272 (-558))) (-5 *2 (-756 (-791))) (-5 *1 (-454 *4))))
+  (-12 (-5 *3 (-661 (-2 (|:| -4162 *4) (|:| -4378 (-558)))))
+   (-4 *4 (-1264 (-558))) (-5 *2 (-756 (-791))) (-5 *1 (-454 *4))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-417 *5)) (-4 *5 (-1272 *4)) (-4 *4 (-1078))
+  (-12 (-5 *3 (-417 *5)) (-4 *5 (-1264 *4)) (-4 *4 (-1070))
    (-5 *2 (-756 (-791))) (-5 *1 (-456 *4 *5))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-1078)) (-5 *1 (-456 *3 *2)) (-4 *2 (-1272 *3))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-1078)) (-5 *1 (-456 *3 *2)) (-4 *2 (-1272 *3))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-1070)) (-5 *1 (-456 *3 *2)) (-4 *2 (-1264 *3))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-1070)) (-5 *1 (-456 *3 *2)) (-4 *2 (-1264 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-1078)) (-4 *2 (-13 (-416) (-1067 *4) (-376) (-1232) (-296)))
-   (-5 *1 (-455 *4 *3 *2)) (-4 *3 (-1272 *4))))) 
+  (-12 (-4 *4 (-1070)) (-4 *2 (-13 (-416) (-1059 *4) (-376) (-1224) (-296)))
+   (-5 *1 (-455 *4 *3 *2)) (-4 *3 (-1264 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-1078)) (-4 *2 (-13 (-416) (-1067 *4) (-376) (-1232) (-296)))
-   (-5 *1 (-455 *4 *3 *2)) (-4 *3 (-1272 *4))))) 
+  (-12 (-4 *4 (-1070)) (-4 *2 (-13 (-416) (-1059 *4) (-376) (-1224) (-296)))
+   (-5 *1 (-455 *4 *3 *2)) (-4 *3 (-1264 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-791)) (-4 *5 (-1078)) (-5 *2 (-558)) (-5 *1 (-455 *5 *3 *6))
-   (-4 *3 (-1272 *5)) (-4 *6 (-13 (-416) (-1067 *5) (-376) (-1232) (-296)))))
+  (-12 (-5 *4 (-791)) (-4 *5 (-1070)) (-5 *2 (-558)) (-5 *1 (-455 *5 *3 *6))
+   (-4 *3 (-1264 *5)) (-4 *6 (-13 (-416) (-1059 *5) (-376) (-1224) (-296)))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-1078)) (-5 *2 (-558)) (-5 *1 (-455 *4 *3 *5))
-   (-4 *3 (-1272 *4)) (-4 *5 (-13 (-416) (-1067 *4) (-376) (-1232) (-296)))))) 
+  (-12 (-4 *4 (-1070)) (-5 *2 (-558)) (-5 *1 (-455 *4 *3 *5))
+   (-4 *3 (-1264 *4)) (-4 *5 (-13 (-416) (-1059 *4) (-376) (-1224) (-296)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-1078)) (-5 *2 (-558)) (-5 *1 (-455 *4 *3 *5))
-   (-4 *3 (-1272 *4)) (-4 *5 (-13 (-416) (-1067 *4) (-376) (-1232) (-296)))))) 
+  (-12 (-4 *4 (-1070)) (-5 *2 (-558)) (-5 *1 (-455 *4 *3 *5))
+   (-4 *3 (-1264 *4)) (-4 *5 (-13 (-416) (-1059 *4) (-376) (-1224) (-296)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-1078)) (-4 *2 (-13 (-416) (-1067 *4) (-376) (-1232) (-296)))
-   (-5 *1 (-455 *4 *3 *2)) (-4 *3 (-1272 *4))))
+  (-12 (-4 *4 (-1070)) (-4 *2 (-13 (-416) (-1059 *4) (-376) (-1224) (-296)))
+   (-5 *1 (-455 *4 *3 *2)) (-4 *3 (-1264 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-946)) (-4 *5 (-1078))
-   (-4 *2 (-13 (-416) (-1067 *5) (-376) (-1232) (-296)))
-   (-5 *1 (-455 *5 *3 *2)) (-4 *3 (-1272 *5))))) 
+  (-12 (-5 *4 (-938)) (-4 *5 (-1070))
+   (-4 *2 (-13 (-416) (-1059 *5) (-376) (-1224) (-296)))
+   (-5 *1 (-455 *5 *3 *2)) (-4 *3 (-1264 *5))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-1078)) (-5 *2 (-558)) (-5 *1 (-455 *4 *3 *5))
-   (-4 *3 (-1272 *4)) (-4 *5 (-13 (-416) (-1067 *4) (-376) (-1232) (-296)))))) 
+  (-12 (-4 *4 (-1070)) (-5 *2 (-558)) (-5 *1 (-455 *4 *3 *5))
+   (-4 *3 (-1264 *4)) (-4 *5 (-13 (-416) (-1059 *4) (-376) (-1224) (-296)))))) 
 (((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *4 (-114)) (-5 *5 (-1126 (-791))) (-5 *6 (-791))
+  (-12 (-5 *4 (-114)) (-5 *5 (-1118 (-791))) (-5 *6 (-791))
    (-5 *2
     (-2 (|:| |contp| (-558))
-     (|:| -1995 (-661 (-2 (|:| |irr| *3) (|:| -2634 (-558)))))))
-   (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *2 (-2 (|:| -3054 (-558)) (|:| -1995 (-661 *3)))) (-5 *1 (-454 *3))
-   (-4 *3 (-1272 (-558)))))) 
+     (|:| -1987 (-661 (-2 (|:| |irr| *3) (|:| -2626 (-558)))))))
+   (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2 *3)
+  (-12 (-5 *2 (-2 (|:| -2977 (-558)) (|:| -1987 (-661 *3)))) (-5 *1 (-454 *3))
+   (-4 *3 (-1264 (-558)))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-417 *3)) (-4 *3 (-569))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-2 (|:| -4239 *4) (|:| -4455 (-558)))))
-   (-4 *4 (-1272 (-558))) (-5 *2 (-791)) (-5 *1 (-454 *4))))) 
-(((*1 *2) (-12 (-5 *2 (-946)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))
- ((*1 *2 *2) (-12 (-5 *2 (-946)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2) (-12 (-5 *2 (-946)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))
- ((*1 *2 *2) (-12 (-5 *2 (-946)) (-5 *1 (-454 *3)) (-4 *3 (-1272 (-558)))))) 
+  (-12 (-5 *3 (-661 (-2 (|:| -4162 *4) (|:| -4378 (-558)))))
+   (-4 *4 (-1264 (-558))) (-5 *2 (-791)) (-5 *1 (-454 *4))))) 
+(((*1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))
+ ((*1 *2 *2) (-12 (-5 *2 (-938)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))
+ ((*1 *2 *2) (-12 (-5 *2 (-938)) (-5 *1 (-454 *3)) (-4 *3 (-1264 (-558)))))) 
 (((*1 *1 *2 *3)
   (-12
    (-5 *3
@@ -13305,15 +13217,15 @@
   (-12
    (-5 *3
     (-2 (|:| |contp| (-558))
-     (|:| -1995 (-661 (-2 (|:| |irr| *4) (|:| -2634 (-558)))))))
-   (-4 *4 (-1272 (-558))) (-5 *2 (-417 *4)) (-5 *1 (-454 *4))))) 
+     (|:| -1987 (-661 (-2 (|:| |irr| *4) (|:| -2626 (-558)))))))
+   (-4 *4 (-1264 (-558))) (-5 *2 (-417 *4)) (-5 *1 (-454 *4))))) 
 (((*1 *2 *2) (-12 (-5 *2 (-402)) (-5 *1 (-449))))
  ((*1 *2 *2 *2) (-12 (-5 *2 (-402)) (-5 *1 (-449))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-449))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-449))))) 
-(((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-449))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-449))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-449))))) 
+(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-449))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-3 (|:| |fst| (-446)) (|:| -4417 "void"))) (-5 *1 (-448))))) 
+  (-12 (-5 *2 (-3 (|:| |fst| (-446)) (|:| -4340 "void"))) (-5 *1 (-448))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-448))))) 
 (((*1 *1) (-5 *1 (-448)))) 
 (((*1 *1) (-5 *1 (-448)))) 
@@ -13323,185 +13235,185 @@
 (((*1 *1) (-5 *1 (-448)))) 
 (((*1 *1) (-5 *1 (-448)))) 
 (((*1 *2 *3)
-  (|partial| -12 (-4 *5 (-1067 (-48))) (-4 *4 (-13 (-569) (-1067 (-558))))
-   (-4 *5 (-433 *4)) (-5 *2 (-417 (-1200 (-48)))) (-5 *1 (-447 *4 *5 *3))
-   (-4 *3 (-1272 *5))))) 
+  (|partial| -12 (-4 *5 (-1059 (-48))) (-4 *4 (-13 (-569) (-1059 (-558))))
+   (-4 *5 (-433 *4)) (-5 *2 (-417 (-1192 (-48)))) (-5 *1 (-447 *4 *5 *3))
+   (-4 *3 (-1264 *5))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-569) (-1067 (-558)))) (-4 *5 (-433 *4))
+  (-12 (-4 *4 (-13 (-569) (-1059 (-558)))) (-4 *5 (-433 *4))
    (-5 *2
-    (-3 (|:| |overq| (-1200 (-419 (-558)))) (|:| |overan| (-1200 (-48)))
-     (|:| -3115 (-114))))
-   (-5 *1 (-447 *4 *5 *3)) (-4 *3 (-1272 *5))))) 
+    (-3 (|:| |overq| (-1192 (-419 (-558)))) (|:| |overan| (-1192 (-48)))
+     (|:| -3038 (-114))))
+   (-5 *1 (-447 *4 *5 *3)) (-4 *3 (-1264 *5))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-4 *4 (-13 (-569) (-1067 (-558)))) (-4 *5 (-433 *4))
-   (-5 *2 (-417 (-1200 (-419 (-558))))) (-5 *1 (-447 *4 *5 *3))
-   (-4 *3 (-1272 *5))))) 
+  (|partial| -12 (-4 *4 (-13 (-569) (-1059 (-558)))) (-4 *5 (-433 *4))
+   (-5 *2 (-417 (-1192 (-419 (-558))))) (-5 *1 (-447 *4 *5 *3))
+   (-4 *3 (-1264 *5))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-569) (-1067 (-558)))) (-4 *5 (-433 *4)) (-5 *2 (-417 *3))
-   (-5 *1 (-447 *4 *5 *3)) (-4 *3 (-1272 *5))))) 
+  (-12 (-4 *4 (-13 (-569) (-1059 (-558)))) (-4 *5 (-433 *4)) (-5 *2 (-417 *3))
+   (-5 *1 (-447 *4 *5 *3)) (-4 *3 (-1264 *5))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-446))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-446))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-446))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-446))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-446))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-13 (-569) (-1067 (-558)))) (-5 *2 (-1302)) (-5 *1 (-445 *3 *4))
+  (-12 (-4 *3 (-13 (-569) (-1059 (-558)))) (-5 *2 (-1294)) (-5 *1 (-445 *3 *4))
    (-4 *4 (-433 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-569) (-1067 (-558)))) (-5 *2 (-419 (-558)))
+  (-12 (-4 *4 (-13 (-569) (-1059 (-558)))) (-5 *2 (-419 (-558)))
    (-5 *1 (-445 *4 *3)) (-4 *3 (-433 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-628 *3)) (-4 *3 (-433 *5)) (-4 *5 (-13 (-569) (-1067 (-558))))
-   (-5 *2 (-1200 (-419 (-558)))) (-5 *1 (-445 *5 *3))))) 
+  (-12 (-5 *4 (-628 *3)) (-4 *3 (-433 *5)) (-4 *5 (-13 (-569) (-1059 (-558))))
+   (-5 *2 (-1192 (-419 (-558)))) (-5 *1 (-445 *5 *3))))) 
 (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-443 *3 *2)) (-4 *2 (-433 *3))))) 
 (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-443 *3 *2)) (-4 *2 (-433 *3))))) 
 (((*1 *1 *2 *3)
   (-12 (-5 *1 (-441 *3 *2)) (-4 *3 (-13 (-175) (-38 (-419 (-558)))))
-   (-4 *2 (-13 (-869) (-21)))))) 
+   (-4 *2 (-13 (-861) (-21)))))) 
 (((*1 *1 *2 *3)
   (-12 (-5 *1 (-441 *3 *2)) (-4 *3 (-13 (-175) (-38 (-419 (-558)))))
-   (-4 *2 (-13 (-869) (-21)))))) 
+   (-4 *2 (-13 (-861) (-21)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1206)) (-4 *5 (-13 (-319) (-149) (-1067 (-558)) (-658 (-558))))
-   (-5 *2 (-595 *3)) (-5 *1 (-440 *5 *3)) (-4 *3 (-13 (-1232) (-29 *5)))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-438 *3)) (-4 *3 (-1130)) (-5 *2 (-791))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-438 *2)) (-4 *2 (-1130)) (-4 *2 (-381))))) 
-(((*1 *1) (-12 (-4 *1 (-438 *2)) (-4 *2 (-381)) (-4 *2 (-1130))))) 
+  (-12 (-5 *4 (-1198)) (-4 *5 (-13 (-319) (-149) (-1059 (-558)) (-658 (-558))))
+   (-5 *2 (-595 *3)) (-5 *1 (-440 *5 *3)) (-4 *3 (-13 (-1224) (-29 *5)))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-438 *3)) (-4 *3 (-1122)) (-5 *2 (-791))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-438 *2)) (-4 *2 (-1122)) (-4 *2 (-381))))) 
+(((*1 *1) (-12 (-4 *1 (-438 *2)) (-4 *2 (-381)) (-4 *2 (-1122))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-464) (-1067 (-558)) (-658 (-558))))
-   (-5 *1 (-435 *3 *2 *4 *5)) (-4 *2 (-13 (-27) (-1232) (-433 *3)))
-   (-14 *4 (-1206)) (-14 *5 *2)))
+  (-12 (-4 *3 (-13 (-464) (-1059 (-558)) (-658 (-558))))
+   (-5 *1 (-435 *3 *2 *4 *5)) (-4 *2 (-13 (-27) (-1224) (-433 *3)))
+   (-14 *4 (-1198)) (-14 *5 *2)))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-464) (-1067 (-558)) (-658 (-558))))
-   (-4 *2 (-13 (-27) (-1232) (-433 *3) (-10 -8 (-15 -4453 ($ *4)))))
-   (-4 *4 (-868))
+  (-12 (-4 *3 (-13 (-464) (-1059 (-558)) (-658 (-558))))
+   (-4 *2 (-13 (-27) (-1224) (-433 *3) (-10 -8 (-15 -4376 ($ *4)))))
+   (-4 *4 (-860))
    (-4 *5
-    (-13 (-1275 *2 *4) (-376) (-1232)
-     (-10 -8 (-15 -4265 ($ $)) (-15 -4319 ($ $)))))
-   (-5 *1 (-436 *3 *2 *4 *5 *6 *7)) (-4 *6 (-1012 *5)) (-14 *7 (-1206))))) 
+    (-13 (-1267 *2 *4) (-376) (-1224)
+     (-10 -8 (-15 -4188 ($ $)) (-15 -4242 ($ $)))))
+   (-5 *1 (-436 *3 *2 *4 *5 *6 *7)) (-4 *6 (-1004 *5)) (-14 *7 (-1198))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *4 (-114)) (-4 *6 (-13 (-464) (-1067 (-558)) (-658 (-558))))
-   (-4 *3 (-13 (-27) (-1232) (-433 *6) (-10 -8 (-15 -4453 ($ *7)))))
-   (-4 *7 (-868))
+  (-12 (-5 *4 (-114)) (-4 *6 (-13 (-464) (-1059 (-558)) (-658 (-558))))
+   (-4 *3 (-13 (-27) (-1224) (-433 *6) (-10 -8 (-15 -4376 ($ *7)))))
+   (-4 *7 (-860))
    (-4 *8
-    (-13 (-1275 *3 *7) (-376) (-1232)
-     (-10 -8 (-15 -4265 ($ $)) (-15 -4319 ($ $)))))
+    (-13 (-1267 *3 *7) (-376) (-1224)
+     (-10 -8 (-15 -4188 ($ $)) (-15 -4242 ($ $)))))
    (-5 *2
     (-3 (|:| |%series| *8)
-     (|:| |%problem| (-2 (|:| |func| (-1188)) (|:| |prob| (-1188))))))
-   (-5 *1 (-436 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1188)) (-4 *9 (-1012 *8))
-   (-14 *10 (-1206))))) 
+     (|:| |%problem| (-2 (|:| |func| (-1180)) (|:| |prob| (-1180))))))
+   (-5 *1 (-436 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1180)) (-4 *9 (-1004 *8))
+   (-14 *10 (-1198))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *4 (-114)) (-4 *6 (-13 (-464) (-1067 (-558)) (-658 (-558))))
-   (-4 *3 (-13 (-27) (-1232) (-433 *6) (-10 -8 (-15 -4453 ($ *7)))))
-   (-4 *7 (-868))
+  (-12 (-5 *4 (-114)) (-4 *6 (-13 (-464) (-1059 (-558)) (-658 (-558))))
+   (-4 *3 (-13 (-27) (-1224) (-433 *6) (-10 -8 (-15 -4376 ($ *7)))))
+   (-4 *7 (-860))
    (-4 *8
-    (-13 (-1275 *3 *7) (-376) (-1232)
-     (-10 -8 (-15 -4265 ($ $)) (-15 -4319 ($ $)))))
+    (-13 (-1267 *3 *7) (-376) (-1224)
+     (-10 -8 (-15 -4188 ($ $)) (-15 -4242 ($ $)))))
    (-5 *2
     (-3 (|:| |%series| *8)
-     (|:| |%problem| (-2 (|:| |func| (-1188)) (|:| |prob| (-1188))))))
-   (-5 *1 (-436 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1188)) (-4 *9 (-1012 *8))
-   (-14 *10 (-1206))))) 
+     (|:| |%problem| (-2 (|:| |func| (-1180)) (|:| |prob| (-1180))))))
+   (-5 *1 (-436 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1180)) (-4 *9 (-1004 *8))
+   (-14 *10 (-1198))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-114)) (-4 *5 (-13 (-464) (-1067 (-558)) (-658 (-558))))
+  (-12 (-5 *4 (-114)) (-4 *5 (-13 (-464) (-1059 (-558)) (-658 (-558))))
    (-5 *2
     (-3 (|:| |%expansion| (-325 *5 *3 *6 *7))
-     (|:| |%problem| (-2 (|:| |func| (-1188)) (|:| |prob| (-1188))))))
-   (-5 *1 (-435 *5 *3 *6 *7)) (-4 *3 (-13 (-27) (-1232) (-433 *5)))
-   (-14 *6 (-1206)) (-14 *7 *3)))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-338 *3 *4)) (-4 *3 (-1078)) (-4 *4 (-814)) (-5 *2 (-114))))
- ((*1 *2 *1) (-12 (-4 *1 (-433 *3)) (-4 *3 (-1130)) (-5 *2 (-114))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-338 *2 *3)) (-4 *3 (-814)) (-4 *2 (-1078))))
- ((*1 *2 *1) (-12 (-4 *1 (-433 *2)) (-4 *2 (-1130))))) 
+     (|:| |%problem| (-2 (|:| |func| (-1180)) (|:| |prob| (-1180))))))
+   (-5 *1 (-435 *5 *3 *6 *7)) (-4 *3 (-13 (-27) (-1224) (-433 *5)))
+   (-14 *6 (-1198)) (-14 *7 *3)))) 
+(((*1 *2 *1)
+  (-12 (-4 *1 (-338 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-814)) (-5 *2 (-114))))
+ ((*1 *2 *1) (-12 (-4 *1 (-433 *3)) (-4 *3 (-1122)) (-5 *2 (-114))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-338 *2 *3)) (-4 *3 (-814)) (-4 *2 (-1070))))
+ ((*1 *2 *1) (-12 (-4 *1 (-433 *2)) (-4 *2 (-1122))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1206)) (-5 *3 (-661 *1)) (-4 *1 (-433 *4)) (-4 *4 (-1130))))
+  (-12 (-5 *2 (-1198)) (-5 *3 (-661 *1)) (-4 *1 (-433 *4)) (-4 *4 (-1122))))
  ((*1 *1 *2 *1 *1 *1 *1)
-  (-12 (-5 *2 (-1206)) (-4 *1 (-433 *3)) (-4 *3 (-1130))))
- ((*1 *1 *2 *1 *1 *1) (-12 (-5 *2 (-1206)) (-4 *1 (-433 *3)) (-4 *3 (-1130))))
- ((*1 *1 *2 *1 *1) (-12 (-5 *2 (-1206)) (-4 *1 (-433 *3)) (-4 *3 (-1130))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1206)) (-4 *1 (-433 *3)) (-4 *3 (-1130))))) 
+  (-12 (-5 *2 (-1198)) (-4 *1 (-433 *3)) (-4 *3 (-1122))))
+ ((*1 *1 *2 *1 *1 *1) (-12 (-5 *2 (-1198)) (-4 *1 (-433 *3)) (-4 *3 (-1122))))
+ ((*1 *1 *2 *1 *1) (-12 (-5 *2 (-1198)) (-4 *1 (-433 *3)) (-4 *3 (-1122))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1198)) (-4 *1 (-433 *3)) (-4 *3 (-1122))))) 
 (((*1 *2 *1)
-  (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1130))
-   (-5 *2 (-2 (|:| -4461 (-558)) (|:| |var| (-628 *1)))) (-4 *1 (-433 *3))))) 
+  (|partial| -12 (-4 *3 (-25)) (-4 *3 (-1122))
+   (-5 *2 (-2 (|:| -4384 (-558)) (|:| |var| (-628 *1)))) (-4 *1 (-433 *3))))) 
 (((*1 *2 *2 *2) (-12 (-5 *2 (-417 *3)) (-4 *3 (-569)) (-5 *1 (-431 *3))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1296 *3)) (-4 *3 (-376)) (-4 *1 (-341 *3))))
+(((*1 *1 *2) (-12 (-5 *2 (-1288 *3)) (-4 *3 (-376)) (-4 *1 (-341 *3))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1296 *3)) (-4 *3 (-1272 *4)) (-4 *4 (-1251))
-   (-4 *1 (-355 *4 *3 *5)) (-4 *5 (-1272 (-419 *3)))))
+  (-12 (-5 *2 (-1288 *3)) (-4 *3 (-1264 *4)) (-4 *4 (-1243))
+   (-4 *1 (-355 *4 *3 *5)) (-4 *5 (-1264 (-419 *3)))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1296 *4)) (-5 *3 (-1296 *1)) (-4 *4 (-175)) (-4 *1 (-380 *4))))
+  (-12 (-5 *2 (-1288 *4)) (-5 *3 (-1288 *1)) (-4 *4 (-175)) (-4 *1 (-380 *4))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1296 *4)) (-5 *3 (-1296 *1)) (-4 *4 (-175))
-   (-4 *1 (-383 *4 *5)) (-4 *5 (-1272 *4))))
+  (-12 (-5 *2 (-1288 *4)) (-5 *3 (-1288 *1)) (-4 *4 (-175))
+   (-4 *1 (-383 *4 *5)) (-4 *5 (-1264 *4))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 *3)) (-4 *3 (-175)) (-4 *1 (-422 *3 *4))
-   (-4 *4 (-1272 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1296 *3)) (-4 *3 (-175)) (-4 *1 (-430 *3))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1296 *1)) (-4 *1 (-380 *2)) (-4 *2 (-175))))
+  (-12 (-5 *2 (-1288 *3)) (-4 *3 (-175)) (-4 *1 (-422 *3 *4))
+   (-4 *4 (-1264 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1288 *3)) (-4 *3 (-175)) (-4 *1 (-430 *3))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1288 *1)) (-4 *1 (-380 *2)) (-4 *2 (-175))))
  ((*1 *2) (-12 (-4 *2 (-175)) (-5 *1 (-429 *3 *2)) (-4 *3 (-430 *2))))
  ((*1 *2) (-12 (-4 *1 (-430 *2)) (-4 *2 (-175))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1296 *1)) (-4 *1 (-380 *2)) (-4 *2 (-175))))
+(((*1 *2 *3) (-12 (-5 *3 (-1288 *1)) (-4 *1 (-380 *2)) (-4 *2 (-175))))
  ((*1 *2) (-12 (-4 *2 (-175)) (-5 *1 (-429 *3 *2)) (-4 *3 (-430 *2))))
  ((*1 *2) (-12 (-4 *1 (-430 *2)) (-4 *2 (-175))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1296 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) (-5 *2 (-709 *4))))
+  (-12 (-5 *3 (-1288 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) (-5 *2 (-709 *4))))
  ((*1 *2)
   (-12 (-4 *4 (-175)) (-5 *2 (-709 *4)) (-5 *1 (-429 *3 *4))
    (-4 *3 (-430 *4))))
  ((*1 *2) (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-5 *2 (-709 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1296 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) (-5 *2 (-709 *4))))
+  (-12 (-5 *3 (-1288 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) (-5 *2 (-709 *4))))
  ((*1 *2)
   (-12 (-4 *4 (-175)) (-5 *2 (-709 *4)) (-5 *1 (-429 *3 *4))
    (-4 *3 (-430 *4))))
  ((*1 *2) (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-5 *2 (-709 *3))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1296 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) (-5 *2 (-709 *4))))
+  (-12 (-5 *3 (-1288 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) (-5 *2 (-709 *4))))
  ((*1 *2 *1) (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-5 *2 (-709 *3))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1296 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) (-5 *2 (-709 *4))))
+  (-12 (-5 *3 (-1288 *1)) (-4 *1 (-380 *4)) (-4 *4 (-175)) (-5 *2 (-709 *4))))
  ((*1 *2 *1) (-12 (-4 *1 (-430 *3)) (-4 *3 (-175)) (-5 *2 (-709 *3))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-425 *3 *4 *5 *6)) (-4 *6 (-1067 *4)) (-4 *3 (-319))
-   (-4 *4 (-1020 *3)) (-4 *5 (-1272 *4)) (-4 *6 (-422 *4 *5))
-   (-14 *7 (-1296 *6)) (-5 *1 (-427 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-425 *3 *4 *5 *6)) (-4 *6 (-1059 *4)) (-4 *3 (-319))
+   (-4 *4 (-1012 *3)) (-4 *5 (-1264 *4)) (-4 *6 (-422 *4 *5))
+   (-14 *7 (-1288 *6)) (-5 *1 (-427 *3 *4 *5 *6 *7))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1296 *6)) (-4 *6 (-422 *4 *5)) (-4 *4 (-1020 *3))
-   (-4 *5 (-1272 *4)) (-4 *3 (-319)) (-5 *1 (-427 *3 *4 *5 *6 *7))
+  (-12 (-5 *2 (-1288 *6)) (-4 *6 (-422 *4 *5)) (-4 *4 (-1012 *3))
+   (-4 *5 (-1264 *4)) (-4 *3 (-319)) (-5 *1 (-427 *3 *4 *5 *6 *7))
    (-14 *7 *2)))) 
 (((*1 *1 *1)
-  (-12 (-4 *2 (-319)) (-4 *3 (-1020 *2)) (-4 *4 (-1272 *3))
-   (-5 *1 (-425 *2 *3 *4 *5)) (-4 *5 (-13 (-422 *3 *4) (-1067 *3)))))) 
+  (-12 (-4 *2 (-319)) (-4 *3 (-1012 *2)) (-4 *4 (-1264 *3))
+   (-5 *1 (-425 *2 *3 *4 *5)) (-4 *5 (-13 (-422 *3 *4) (-1059 *3)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-791)) (-5 *4 (-1296 *2)) (-4 *5 (-319)) (-4 *6 (-1020 *5))
-   (-4 *2 (-13 (-422 *6 *7) (-1067 *6))) (-5 *1 (-425 *5 *6 *7 *2))
-   (-4 *7 (-1272 *6))))) 
+  (-12 (-5 *3 (-791)) (-5 *4 (-1288 *2)) (-4 *5 (-319)) (-4 *6 (-1012 *5))
+   (-4 *2 (-13 (-422 *6 *7) (-1059 *6))) (-5 *1 (-425 *5 *6 *7 *2))
+   (-4 *7 (-1264 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1296 *1)) (-4 *1 (-383 *4 *5)) (-4 *4 (-175))
-   (-4 *5 (-1272 *4)) (-5 *2 (-709 *4))))
+  (-12 (-5 *3 (-1288 *1)) (-4 *1 (-383 *4 *5)) (-4 *4 (-175))
+   (-4 *5 (-1264 *4)) (-5 *2 (-709 *4))))
  ((*1 *2)
-  (-12 (-4 *4 (-175)) (-4 *5 (-1272 *4)) (-5 *2 (-709 *4))
+  (-12 (-4 *4 (-175)) (-4 *5 (-1264 *4)) (-5 *2 (-709 *4))
    (-5 *1 (-421 *3 *4 *5)) (-4 *3 (-422 *4 *5))))
  ((*1 *2)
-  (-12 (-4 *1 (-422 *3 *4)) (-4 *3 (-175)) (-4 *4 (-1272 *3))
+  (-12 (-4 *1 (-422 *3 *4)) (-4 *3 (-175)) (-4 *4 (-1264 *3))
    (-5 *2 (-709 *3))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1296 *1)) (-4 *1 (-383 *4 *5)) (-4 *4 (-175))
-   (-4 *5 (-1272 *4)) (-5 *2 (-709 *4))))
+  (-12 (-5 *3 (-1288 *1)) (-4 *1 (-383 *4 *5)) (-4 *4 (-175))
+   (-4 *5 (-1264 *4)) (-5 *2 (-709 *4))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-422 *3 *4)) (-4 *3 (-175)) (-4 *4 (-1272 *3))
+  (-12 (-4 *1 (-422 *3 *4)) (-4 *3 (-175)) (-4 *4 (-1264 *3))
    (-5 *2 (-709 *3))))) 
 (((*1 *1 *2 *3) (-12 (-5 *3 (-558)) (-5 *1 (-417 *2)) (-4 *2 (-569))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-661 (-2 (|:| |gen| *3) (|:| -4450 (-558))))) (-5 *1 (-374 *3))
-   (-4 *3 (-1130))))
+  (-12 (-5 *2 (-661 (-2 (|:| |gen| *3) (|:| -4373 (-558))))) (-5 *1 (-374 *3))
+   (-4 *3 (-1122))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-399 *3)) (-4 *3 (-1130))
-   (-5 *2 (-661 (-2 (|:| |gen| *3) (|:| -4450 (-791)))))))
+  (-12 (-4 *1 (-399 *3)) (-4 *3 (-1122))
+   (-5 *2 (-661 (-2 (|:| |gen| *3) (|:| -4373 (-791)))))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-661 (-2 (|:| -4239 *3) (|:| -2640 (-558))))) (-5 *1 (-417 *3))
+  (-12 (-5 *2 (-661 (-2 (|:| -4162 *3) (|:| -2632 (-558))))) (-5 *1 (-417 *3))
    (-4 *3 (-569))))) 
 (((*1 *1 *2 *3) (-12 (-5 *3 (-558)) (-5 *1 (-417 *2)) (-4 *2 (-569))))) 
 (((*1 *2 *1 *2) (-12 (-5 *2 (-558)) (-5 *1 (-417 *3)) (-4 *3 (-569))))) 
@@ -13518,92 +13430,92 @@
  ((*1 *2 *1) (-12 (-5 *1 (-417 *2)) (-4 *2 (-569))))) 
 (((*1 *1 *1) (-12 (-5 *1 (-417 *2)) (-4 *2 (-569))))) 
 (((*1 *1 *2 *3) (-12 (-5 *2 (-791)) (-5 *3 (-114)) (-5 *1 (-110))))
- ((*1 *2 *2) (-12 (-5 *2 (-946)) (|has| *1 (-6 -4493)) (-4 *1 (-416))))
- ((*1 *2) (-12 (-4 *1 (-416)) (-5 *2 (-946))))) 
+ ((*1 *2 *2) (-12 (-5 *2 (-938)) (|has| *1 (-6 -4416)) (-4 *1 (-416))))
+ ((*1 *2) (-12 (-4 *1 (-416)) (-5 *2 (-938))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-558)) (|has| *1 (-6 -4493)) (-4 *1 (-416)) (-5 *2 (-946))))) 
+  (-12 (-5 *3 (-558)) (|has| *1 (-6 -4416)) (-4 *1 (-416)) (-5 *2 (-938))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-558)) (|has| *1 (-6 -4493)) (-4 *1 (-416)) (-5 *2 (-946))))) 
+  (-12 (-5 *3 (-558)) (|has| *1 (-6 -4416)) (-4 *1 (-416)) (-5 *2 (-938))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-363)) (-5 *2 (-791))))
  ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-414)) (-5 *2 (-791))))) 
 (((*1 *1 *1 *2) (-12 (-4 *1 (-414)) (-5 *2 (-791))))
  ((*1 *1 *1) (-4 *1 (-414)))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-419 *4)) (-4 *4 (-1272 *3)) (-4 *3 (-13 (-376) (-149)))
+  (-12 (-5 *2 (-419 *4)) (-4 *4 (-1264 *3)) (-4 *3 (-13 (-376) (-149)))
    (-5 *1 (-411 *3 *4))))) 
 (((*1 *2 *1)
-  (-12 (-4 *2 (-1272 *3)) (-5 *1 (-411 *3 *2)) (-4 *3 (-13 (-376) (-149)))))) 
+  (-12 (-4 *2 (-1264 *3)) (-5 *1 (-411 *3 *2)) (-4 *3 (-13 (-376) (-149)))))) 
 (((*1 *2 *1)
   (-12 (-4 *3 (-13 (-376) (-149)))
-   (-5 *2 (-661 (-2 (|:| -2640 (-791)) (|:| -4280 *4) (|:| |num| *4))))
-   (-5 *1 (-411 *3 *4)) (-4 *4 (-1272 *3))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-661 (-1188))) (-5 *1 (-407))))) 
+   (-5 *2 (-661 (-2 (|:| -2632 (-791)) (|:| -4203 *4) (|:| |num| *4))))
+   (-5 *1 (-411 *3 *4)) (-4 *4 (-1264 *3))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-661 (-1180))) (-5 *1 (-407))))) 
 (((*1 *2 *3 *4 *5 *6)
   (-12 (-5 *5 (-661 (-661 (-3 (|:| |array| *6) (|:| |scalar| *3)))))
-   (-5 *4 (-661 (-3 (|:| |array| (-661 *3)) (|:| |scalar| (-1206)))))
-   (-5 *6 (-661 (-1206))) (-5 *3 (-1206)) (-5 *2 (-1132)) (-5 *1 (-407))))
+   (-5 *4 (-661 (-3 (|:| |array| (-661 *3)) (|:| |scalar| (-1198)))))
+   (-5 *6 (-661 (-1198))) (-5 *3 (-1198)) (-5 *2 (-1124)) (-5 *1 (-407))))
  ((*1 *2 *3 *4 *5 *6 *3)
   (-12 (-5 *5 (-661 (-661 (-3 (|:| |array| *6) (|:| |scalar| *3)))))
-   (-5 *4 (-661 (-3 (|:| |array| (-661 *3)) (|:| |scalar| (-1206)))))
-   (-5 *6 (-661 (-1206))) (-5 *3 (-1206)) (-5 *2 (-1132)) (-5 *1 (-407))))
+   (-5 *4 (-661 (-3 (|:| |array| (-661 *3)) (|:| |scalar| (-1198)))))
+   (-5 *6 (-661 (-1198))) (-5 *3 (-1198)) (-5 *2 (-1124)) (-5 *1 (-407))))
  ((*1 *2 *3 *4 *5 *4)
-  (-12 (-5 *4 (-661 (-1206))) (-5 *5 (-1209)) (-5 *3 (-1206)) (-5 *2 (-1132))
+  (-12 (-5 *4 (-661 (-1198))) (-5 *5 (-1201)) (-5 *3 (-1198)) (-5 *2 (-1124))
    (-5 *1 (-407))))) 
-(((*1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-405))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-402)) (-5 *2 (-1302)) (-5 *1 (-405))))
- ((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-405))))) 
-(((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-405))))) 
-(((*1 *2) (-12 (-5 *2 (-1177 (-1188))) (-5 *1 (-405))))) 
-(((*1 *2) (-12 (-5 *2 (-1177 (-1188))) (-5 *1 (-405))))) 
-(((*1 *2 *1)
-  (-12 (-5 *2 (-885)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 (-791)) (-14 *4 (-791))
+(((*1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-405))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-402)) (-5 *2 (-1294)) (-5 *1 (-405))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-405))))) 
+(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-405))))) 
+(((*1 *2) (-12 (-5 *2 (-1169 (-1180))) (-5 *1 (-405))))) 
+(((*1 *2) (-12 (-5 *2 (-1169 (-1180))) (-5 *1 (-405))))) 
+(((*1 *2 *1)
+  (-12 (-5 *2 (-877)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 (-791)) (-14 *4 (-791))
    (-4 *5 (-175))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-885)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 (-791)) (-14 *4 (-791))
+  (-12 (-5 *2 (-877)) (-5 *1 (-404 *3 *4 *5)) (-14 *3 (-791)) (-14 *4 (-791))
    (-4 *5 (-175))))) 
-(((*1 *1 *2 *2 *2) (-12 (-5 *2 (-1188)) (-4 *1 (-403))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-1188))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-1188))))) 
+(((*1 *1 *2 *2 *2) (-12 (-5 *2 (-1180)) (-4 *1 (-403))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-1180))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-1180))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-114))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-114))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-403)) (-5 *2 (-114))))) 
-(((*1 *1 *1 *1) (-12 (-4 *1 (-399 *2)) (-4 *2 (-1130))))) 
-(((*1 *1 *1 *1) (-12 (-4 *1 (-399 *2)) (-4 *2 (-1130))))) 
+(((*1 *1 *1 *1) (-12 (-4 *1 (-399 *2)) (-4 *2 (-1122))))) 
+(((*1 *1 *1 *1) (-12 (-4 *1 (-399 *2)) (-4 *2 (-1122))))) 
 (((*1 *2 *1 *1)
-  (-12 (-4 *3 (-1130)) (-5 *2 (-2 (|:| |lm| *1) (|:| |mm| *1) (|:| |rm| *1)))
+  (-12 (-4 *3 (-1122)) (-5 *2 (-2 (|:| |lm| *1) (|:| |mm| *1) (|:| |rm| *1)))
    (-4 *1 (-399 *3))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-397 *3 *4)) (-4 *3 (-1078)) (-4 *4 (-1130))
+  (-12 (-4 *1 (-397 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-1122))
    (-5 *2 (-2 (|:| |k| *4) (|:| |c| *3)))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-661 (-419 (-973 (-558))))) (-5 *4 (-661 (-1206)))
-   (-5 *2 (-661 (-661 *5))) (-5 *1 (-393 *5)) (-4 *5 (-13 (-868) (-376)))))
+  (-12 (-5 *3 (-661 (-419 (-965 (-558))))) (-5 *4 (-661 (-1198)))
+   (-5 *2 (-661 (-661 *5))) (-5 *1 (-393 *5)) (-4 *5 (-13 (-860) (-376)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-973 (-558)))) (-5 *2 (-661 *4)) (-5 *1 (-393 *4))
-   (-4 *4 (-13 (-868) (-376)))))) 
+  (-12 (-5 *3 (-419 (-965 (-558)))) (-5 *2 (-661 *4)) (-5 *1 (-393 *4))
+   (-4 *4 (-13 (-860) (-376)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-973 (-171 (-558))))) (-5 *2 (-661 (-171 *4)))
-   (-5 *1 (-392 *4)) (-4 *4 (-13 (-376) (-868)))))
+  (-12 (-5 *3 (-419 (-965 (-171 (-558))))) (-5 *2 (-661 (-171 *4)))
+   (-5 *1 (-392 *4)) (-4 *4 (-13 (-376) (-860)))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-661 (-419 (-973 (-171 (-558)))))) (-5 *4 (-661 (-1206)))
+  (-12 (-5 *3 (-661 (-419 (-965 (-171 (-558)))))) (-5 *4 (-661 (-1198)))
    (-5 *2 (-661 (-661 (-171 *5)))) (-5 *1 (-392 *5))
-   (-4 *5 (-13 (-376) (-868)))))) 
+   (-4 *5 (-13 (-376) (-860)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-419 (-973 (-171 (-558))))))
-   (-5 *2 (-661 (-661 (-305 (-973 (-171 *4)))))) (-5 *1 (-392 *4))
-   (-4 *4 (-13 (-376) (-868)))))
+  (-12 (-5 *3 (-661 (-419 (-965 (-171 (-558))))))
+   (-5 *2 (-661 (-661 (-305 (-965 (-171 *4)))))) (-5 *1 (-392 *4))
+   (-4 *4 (-13 (-376) (-860)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-305 (-419 (-973 (-171 (-558)))))))
-   (-5 *2 (-661 (-661 (-305 (-973 (-171 *4)))))) (-5 *1 (-392 *4))
-   (-4 *4 (-13 (-376) (-868)))))
+  (-12 (-5 *3 (-661 (-305 (-419 (-965 (-171 (-558)))))))
+   (-5 *2 (-661 (-661 (-305 (-965 (-171 *4)))))) (-5 *1 (-392 *4))
+   (-4 *4 (-13 (-376) (-860)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-419 (-973 (-171 (-558)))))
-   (-5 *2 (-661 (-305 (-973 (-171 *4))))) (-5 *1 (-392 *4))
-   (-4 *4 (-13 (-376) (-868)))))
+  (-12 (-5 *3 (-419 (-965 (-171 (-558)))))
+   (-5 *2 (-661 (-305 (-965 (-171 *4))))) (-5 *1 (-392 *4))
+   (-4 *4 (-13 (-376) (-860)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-305 (-419 (-973 (-171 (-558))))))
-   (-5 *2 (-661 (-305 (-973 (-171 *4))))) (-5 *1 (-392 *4))
-   (-4 *4 (-13 (-376) (-868)))))) 
+  (-12 (-5 *3 (-305 (-419 (-965 (-171 (-558))))))
+   (-5 *2 (-661 (-305 (-965 (-171 *4))))) (-5 *1 (-392 *4))
+   (-4 *4 (-13 (-376) (-860)))))) 
 (((*1 *2 *1 *1) (-12 (-5 *2 (-558)) (-5 *1 (-391))))) 
 (((*1 *2 *1 *3 *3) (-12 (-5 *3 (-791)) (-5 *2 (-419 (-558))) (-5 *1 (-229))))
  ((*1 *2 *1 *3) (-12 (-5 *3 (-791)) (-5 *2 (-419 (-558))) (-5 *1 (-229))))
@@ -13613,47 +13525,47 @@
  ((*1 *1) (-5 *1 (-391)))) 
 (((*1 *1 *1) (-5 *1 (-229)))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-661 (-1206))) (-14 *3 (-661 (-1206)))
+  (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-661 (-1198))) (-14 *3 (-661 (-1198)))
    (-4 *4 (-401))))
  ((*1 *1 *1) (-5 *1 (-391))) ((*1 *1) (-5 *1 (-391)))) 
 (((*1 *1) (-5 *1 (-229))) ((*1 *1) (-5 *1 (-391)))) 
-(((*1 *2 *3) (-12 (-5 *3 (-791)) (-5 *2 (-1302)) (-5 *1 (-391))))
- ((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-391))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-791)) (-5 *2 (-1302)) (-5 *1 (-391))))
- ((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-391))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-791)) (-5 *2 (-1302)) (-5 *1 (-391))))
- ((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-391))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-791)) (-5 *2 (-1302)) (-5 *1 (-391))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-791)) (-5 *2 (-1294)) (-5 *1 (-391))))
+ ((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-391))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-791)) (-5 *2 (-1294)) (-5 *1 (-391))))
+ ((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-391))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-791)) (-5 *2 (-1294)) (-5 *1 (-391))))
+ ((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-391))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-791)) (-5 *2 (-1294)) (-5 *1 (-391))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1246)) (-5 *1 (-388 *4 *2))
-   (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4503))))))) 
+  (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1238)) (-5 *1 (-388 *4 *2))
+   (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4426))))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1246)) (-5 *1 (-388 *4 *2))
-   (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4503))))))) 
+  (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1238)) (-5 *1 (-388 *4 *2))
+   (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4426))))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1246)) (-5 *1 (-388 *4 *2))
-   (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4503))))))) 
+  (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *4 (-1238)) (-5 *1 (-388 *4 *2))
+   (-4 *2 (-13 (-385 *4) (-10 -7 (-6 -4426))))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-692 *3)) (-4 *3 (-869)) (-4 *1 (-387 *3 *4)) (-4 *4 (-175))))) 
+  (-12 (-5 *2 (-692 *3)) (-4 *3 (-861)) (-4 *1 (-387 *3 *4)) (-4 *4 (-175))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-385 *3)) (-4 *3 (-1246)) (-4 *3 (-869)) (-5 *2 (-114))))
+  (-12 (-4 *1 (-385 *3)) (-4 *3 (-1238)) (-4 *3 (-861)) (-5 *2 (-114))))
  ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *1 (-385 *4)) (-4 *4 (-1246))
+  (-12 (-5 *3 (-1 (-114) *4 *4)) (-4 *1 (-385 *4)) (-4 *4 (-1238))
    (-5 *2 (-114))))) 
 (((*1 *1 *1 *1 *2)
-  (-12 (-5 *2 (-558)) (|has| *1 (-6 -4503)) (-4 *1 (-385 *3)) (-4 *3 (-1246))))) 
+  (-12 (-5 *2 (-558)) (|has| *1 (-6 -4426)) (-4 *1 (-385 *3)) (-4 *3 (-1238))))) 
 (((*1 *1 *1)
-  (-12 (|has| *1 (-6 -4503)) (-4 *1 (-385 *2)) (-4 *2 (-1246)) (-4 *2 (-869))))
+  (-12 (|has| *1 (-6 -4426)) (-4 *1 (-385 *2)) (-4 *2 (-1238)) (-4 *2 (-861))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 (-114) *3 *3)) (|has| *1 (-6 -4503)) (-4 *1 (-385 *3))
-   (-4 *3 (-1246))))) 
-(((*1 *2) (-12 (-4 *3 (-175)) (-5 *2 (-1296 *1)) (-4 *1 (-380 *3))))) 
+  (-12 (-5 *2 (-1 (-114) *3 *3)) (|has| *1 (-6 -4426)) (-4 *1 (-385 *3))
+   (-4 *3 (-1238))))) 
+(((*1 *2) (-12 (-4 *3 (-175)) (-5 *2 (-1288 *1)) (-4 *1 (-380 *3))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-380 *2)) (-4 *2 (-175))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-380 *2)) (-4 *2 (-175))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-380 *2)) (-4 *2 (-175))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-380 *2)) (-4 *2 (-175))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-1200 *3))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-1200 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-1192 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-1192 *3))))) 
 (((*1 *2)
   (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) (-4 *3 (-380 *4))))
  ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) 
@@ -13698,313 +13610,313 @@
   (-12 (-4 *4 (-175)) (-5 *2 (-114)) (-5 *1 (-379 *3 *4)) (-4 *3 (-380 *4))))
  ((*1 *2) (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-5 *2 (-114))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-175)) (-5 *2 (-661 (-1296 *4))) (-5 *1 (-379 *3 *4))
+  (-12 (-4 *4 (-175)) (-5 *2 (-661 (-1288 *4))) (-5 *1 (-379 *3 *4))
    (-4 *3 (-380 *4))))
  ((*1 *2)
   (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-4 *3 (-569))
-   (-5 *2 (-661 (-1296 *3)))))) 
+   (-5 *2 (-661 (-1288 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-4 *3 (-569)) (-5 *2 (-1200 *3))))) 
+  (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-4 *3 (-569)) (-5 *2 (-1192 *3))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-4 *3 (-569)) (-5 *2 (-1200 *3))))) 
+  (-12 (-4 *1 (-380 *3)) (-4 *3 (-175)) (-4 *3 (-569)) (-5 *2 (-1192 *3))))) 
 (((*1 *1) (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-569)) (-4 *2 (-175))))) 
 (((*1 *1) (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-569)) (-4 *2 (-175))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *3 (-1188)) (-4 *1 (-378 *2 *4)) (-4 *2 (-1130)) (-4 *4 (-1130))))
- ((*1 *1 *2) (-12 (-4 *1 (-378 *2 *3)) (-4 *2 (-1130)) (-4 *3 (-1130))))) 
+  (-12 (-5 *3 (-1180)) (-4 *1 (-378 *2 *4)) (-4 *2 (-1122)) (-4 *4 (-1122))))
+ ((*1 *1 *2) (-12 (-4 *1 (-378 *2 *3)) (-4 *2 (-1122)) (-4 *3 (-1122))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1188)) (-4 *1 (-378 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+  (-12 (-5 *2 (-1180)) (-4 *1 (-378 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122))))) 
 (((*1 *1 *1) (-4 *1 (-176)))
- ((*1 *1 *1) (-12 (-4 *1 (-378 *2 *3)) (-4 *2 (-1130)) (-4 *3 (-1130))))) 
+ ((*1 *1 *1) (-12 (-4 *1 (-378 *2 *3)) (-4 *2 (-1122)) (-4 *3 (-1122))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-378 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-1130)) (-5 *2 (-1188))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-378 *3 *2)) (-4 *3 (-1130)) (-4 *2 (-1130))))) 
-(((*1 *2 *1 *2) (-12 (-4 *1 (-378 *3 *2)) (-4 *3 (-1130)) (-4 *2 (-1130))))) 
+  (-12 (-4 *1 (-378 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-1122)) (-5 *2 (-1180))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-378 *3 *2)) (-4 *3 (-1122)) (-4 *2 (-1122))))) 
+(((*1 *2 *1 *2) (-12 (-4 *1 (-378 *3 *2)) (-4 *3 (-1122)) (-4 *2 (-1122))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1200 *4)) (-4 *4 (-363))
+  (-12 (-5 *3 (-1192 *4)) (-4 *4 (-363))
    (-4 *2
     (-13 (-414)
-     (-10 -7 (-15 -4453 (*2 *4)) (-15 -2228 ((-946) *2))
-      (-15 -2230 ((-1296 *2) (-946))) (-15 -4435 (*2 *2)))))
+     (-10 -7 (-15 -4376 (*2 *4)) (-15 -2220 ((-938) *2))
+      (-15 -2222 ((-1288 *2) (-938))) (-15 -4358 (*2 *2)))))
    (-5 *1 (-370 *2 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-363)) (-5 *2 (-985 (-1200 *4))) (-5 *1 (-369 *4))
-   (-5 *3 (-1200 *4))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1200 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
+  (-12 (-4 *4 (-363)) (-5 *2 (-977 (-1192 *4))) (-5 *1 (-369 *4))
+   (-5 *3 (-1192 *4))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1192 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1200 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
+  (|partial| -12 (-5 *2 (-1192 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1200 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
+  (|partial| -12 (-5 *2 (-1192 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1200 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
+  (|partial| -12 (-5 *2 (-1192 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1200 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
+  (|partial| -12 (-5 *2 (-1192 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1200 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
+  (|partial| -12 (-5 *2 (-1192 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-946)) (-5 *2 (-1200 *4)) (-5 *1 (-369 *4)) (-4 *4 (-363))))) 
+  (-12 (-5 *3 (-938)) (-5 *2 (-1192 *4)) (-5 *1 (-369 *4)) (-4 *4 (-363))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-946)) (-5 *2 (-1200 *4)) (-5 *1 (-369 *4)) (-4 *4 (-363))))) 
+  (-12 (-5 *3 (-938)) (-5 *2 (-1192 *4)) (-5 *1 (-369 *4)) (-4 *4 (-363))))) 
 (((*1 *2 *3)
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-   (-4 *7 (-1272 (-419 *6))) (-5 *2 (-661 (-973 *5)))
+  (-12 (-5 *3 (-1198)) (-4 *5 (-1243)) (-4 *6 (-1264 *5))
+   (-4 *7 (-1264 (-419 *6))) (-5 *2 (-661 (-965 *5)))
    (-5 *1 (-354 *4 *5 *6 *7)) (-4 *4 (-355 *5 *6 *7))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1206)) (-4 *1 (-355 *4 *5 *6)) (-4 *4 (-1251))
-   (-4 *5 (-1272 *4)) (-4 *6 (-1272 (-419 *5))) (-4 *4 (-376))
-   (-5 *2 (-661 (-973 *4)))))) 
+  (-12 (-5 *3 (-1198)) (-4 *1 (-355 *4 *5 *6)) (-4 *4 (-1243))
+   (-4 *5 (-1264 *4)) (-4 *6 (-1264 (-419 *5))) (-4 *4 (-376))
+   (-5 *2 (-661 (-965 *4)))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-1251)) (-4 *5 (-1272 *4)) (-4 *6 (-1272 (-419 *5)))
+  (-12 (-4 *4 (-1243)) (-4 *5 (-1264 *4)) (-4 *6 (-1264 (-419 *5)))
    (-5 *2 (-661 (-661 *4))) (-5 *1 (-354 *3 *4 *5 *6))
    (-4 *3 (-355 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1251)) (-4 *4 (-1272 *3))
-   (-4 *5 (-1272 (-419 *4))) (-4 *3 (-381)) (-5 *2 (-661 (-661 *3)))))) 
+  (-12 (-4 *1 (-355 *3 *4 *5)) (-4 *3 (-1243)) (-4 *4 (-1264 *3))
+   (-4 *5 (-1264 (-419 *4))) (-4 *3 (-381)) (-5 *2 (-661 (-661 *3)))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-114)) (-5 *1 (-352 *3 *4 *5)) (-14 *3 (-661 (-1206)))
-   (-14 *4 (-661 (-1206))) (-4 *5 (-401))))
+  (-12 (-5 *2 (-114)) (-5 *1 (-352 *3 *4 *5)) (-14 *3 (-661 (-1198)))
+   (-14 *4 (-661 (-1198))) (-4 *5 (-401))))
  ((*1 *2)
-  (-12 (-5 *2 (-114)) (-5 *1 (-352 *3 *4 *5)) (-14 *3 (-661 (-1206)))
-   (-14 *4 (-661 (-1206))) (-4 *5 (-401))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-352 *3 *4 *5)) (-14 *3 (-661 (-1198)))
+   (-14 *4 (-661 (-1198))) (-4 *5 (-401))))) 
 (((*1 *1 *2 *3 *3 *3 *4)
-  (-12 (-4 *4 (-376)) (-4 *3 (-1272 *4)) (-4 *5 (-1272 (-419 *3)))
+  (-12 (-4 *4 (-376)) (-4 *3 (-1264 *4)) (-4 *5 (-1264 (-419 *3)))
    (-4 *1 (-349 *4 *3 *5 *2)) (-4 *2 (-355 *4 *3 *5))))
  ((*1 *1 *2 *2 *3)
-  (-12 (-5 *3 (-558)) (-4 *2 (-376)) (-4 *4 (-1272 *2))
-   (-4 *5 (-1272 (-419 *4))) (-4 *1 (-349 *2 *4 *5 *6))
+  (-12 (-5 *3 (-558)) (-4 *2 (-376)) (-4 *4 (-1264 *2))
+   (-4 *5 (-1264 (-419 *4))) (-4 *1 (-349 *2 *4 *5 *6))
    (-4 *6 (-355 *2 *4 *5))))
  ((*1 *1 *2 *2)
-  (-12 (-4 *2 (-376)) (-4 *3 (-1272 *2)) (-4 *4 (-1272 (-419 *3)))
+  (-12 (-4 *2 (-376)) (-4 *3 (-1264 *2)) (-4 *4 (-1264 (-419 *3)))
    (-4 *1 (-349 *2 *3 *4 *5)) (-4 *5 (-355 *2 *3 *4))))
  ((*1 *1 *2)
-  (-12 (-4 *3 (-376)) (-4 *4 (-1272 *3)) (-4 *5 (-1272 (-419 *4)))
+  (-12 (-4 *3 (-376)) (-4 *4 (-1264 *3)) (-4 *5 (-1264 (-419 *4)))
    (-4 *1 (-349 *3 *4 *5 *2)) (-4 *2 (-355 *3 *4 *5))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-425 *4 (-419 *4) *5 *6)) (-4 *4 (-1272 *3))
-   (-4 *5 (-1272 (-419 *4))) (-4 *6 (-355 *3 *4 *5)) (-4 *3 (-376))
+  (-12 (-5 *2 (-425 *4 (-419 *4) *5 *6)) (-4 *4 (-1264 *3))
+   (-4 *5 (-1264 (-419 *4))) (-4 *6 (-355 *3 *4 *5)) (-4 *3 (-376))
    (-4 *1 (-349 *3 *4 *5 *6))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-349 *3 *4 *5 *6)) (-4 *3 (-376)) (-4 *4 (-1272 *3))
-   (-4 *5 (-1272 (-419 *4))) (-4 *6 (-355 *3 *4 *5)) (-5 *2 (-114))))) 
+  (-12 (-4 *1 (-349 *3 *4 *5 *6)) (-4 *3 (-376)) (-4 *4 (-1264 *3))
+   (-4 *5 (-1264 (-419 *4))) (-4 *6 (-355 *3 *4 *5)) (-5 *2 (-114))))) 
 (((*1 *2 *1)
-  (-12 (-4 *3 (-376)) (-4 *4 (-1272 *3)) (-4 *5 (-1272 (-419 *4)))
-   (-5 *2 (-1296 *6)) (-5 *1 (-346 *3 *4 *5 *6)) (-4 *6 (-355 *3 *4 *5))))) 
+  (-12 (-4 *3 (-376)) (-4 *4 (-1264 *3)) (-4 *5 (-1264 (-419 *4)))
+   (-5 *2 (-1288 *6)) (-5 *1 (-346 *3 *4 *5 *6)) (-4 *6 (-355 *3 *4 *5))))) 
 (((*1 *2 *1)
-  (-12 (-4 *3 (-376)) (-4 *4 (-1272 *3)) (-4 *5 (-1272 (-419 *4)))
-   (-5 *2 (-1296 *6)) (-5 *1 (-346 *3 *4 *5 *6)) (-4 *6 (-355 *3 *4 *5))))) 
+  (-12 (-4 *3 (-376)) (-4 *4 (-1264 *3)) (-4 *5 (-1264 (-419 *4)))
+   (-5 *2 (-1288 *6)) (-5 *1 (-346 *3 *4 *5 *6)) (-4 *6 (-355 *3 *4 *5))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-258)) (-5 *1 (-345))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-895 (-1211) (-791)))) (-5 *1 (-345))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-985 (-791))) (-5 *1 (-345))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-661 (-887 (-1203) (-791)))) (-5 *1 (-345))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-977 (-791))) (-5 *1 (-345))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-518)) (-5 *1 (-345))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1206)) (-5 *4 (-973 (-558))) (-5 *2 (-342)) (-5 *1 (-344))))) 
+  (-12 (-5 *3 (-1198)) (-5 *4 (-965 (-558))) (-5 *2 (-342)) (-5 *1 (-344))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1206)) (-5 *4 (-973 (-558))) (-5 *2 (-342)) (-5 *1 (-344))))) 
+  (-12 (-5 *3 (-1198)) (-5 *4 (-965 (-558))) (-5 *2 (-342)) (-5 *1 (-344))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1206)) (-5 *4 (-973 (-558))) (-5 *2 (-342)) (-5 *1 (-344))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-343 *3)) (-4 *3 (-869))))) 
+  (-12 (-5 *3 (-1198)) (-5 *4 (-965 (-558))) (-5 *2 (-342)) (-5 *1 (-344))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-343 *3)) (-4 *3 (-861))))) 
 (((*1 *1 *2 *3 *1)
-  (-12 (-5 *2 (-1121 (-973 (-558)))) (-5 *3 (-973 (-558))) (-5 *1 (-342))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1121 (-973 (-558)))) (-5 *1 (-342))))) 
-(((*1 *1 *2 *1) (-12 (-5 *2 (-1205)) (-5 *1 (-342))))) 
-(((*1 *1 *2 *1) (-12 (-5 *2 (-1205)) (-5 *1 (-342))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1149)) (-5 *1 (-342))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1149)) (-5 *1 (-342))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 (-1188))) (-5 *1 (-342))))
- ((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-342))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-342))))) 
+  (-12 (-5 *2 (-1113 (-965 (-558)))) (-5 *3 (-965 (-558))) (-5 *1 (-342))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1113 (-965 (-558)))) (-5 *1 (-342))))) 
+(((*1 *1 *2 *1) (-12 (-5 *2 (-1197)) (-5 *1 (-342))))) 
+(((*1 *1 *2 *1) (-12 (-5 *2 (-1197)) (-5 *1 (-342))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1141)) (-5 *1 (-342))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1141)) (-5 *1 (-342))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 (-1180))) (-5 *1 (-342))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-342))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-342))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-326 (-171 (-391)))) (-5 *1 (-342))))
  ((*1 *1 *2) (-12 (-5 *2 (-326 (-558))) (-5 *1 (-342))))
  ((*1 *1 *2) (-12 (-5 *2 (-326 (-391))) (-5 *1 (-342))))
@@ -14012,13 +13924,13 @@
  ((*1 *1 *2) (-12 (-5 *2 (-326 (-721))) (-5 *1 (-342))))
  ((*1 *1 *2) (-12 (-5 *2 (-326 (-719))) (-5 *1 (-342))))
  ((*1 *1) (-5 *1 (-342)))) 
-(((*1 *1 *2 *1 *1) (-12 (-5 *2 (-1205)) (-5 *1 (-342))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1205)) (-5 *1 (-342))))) 
+(((*1 *1 *2 *1 *1) (-12 (-5 *2 (-1197)) (-5 *1 (-342))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1197)) (-5 *1 (-342))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-661 (-342))) (-5 *1 (-342))))) 
 (((*1 *1) (-5 *1 (-342)))) 
 (((*1 *1) (-5 *1 (-342)))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 (-885))) (-5 *1 (-342))))) 
-(((*1 *1 *2 *3) (-12 (-5 *3 (-661 (-1206))) (-5 *2 (-1206)) (-5 *1 (-342))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 (-877))) (-5 *1 (-342))))) 
+(((*1 *1 *2 *3) (-12 (-5 *3 (-661 (-1198))) (-5 *2 (-1198)) (-5 *1 (-342))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
@@ -14035,85 +13947,85 @@
    (-5 *2
     (-3 (|:| |nullBranch| "null")
      (|:| |assignmentBranch|
-          (-2 (|:| |var| (-1206)) (|:| |arrayIndex| (-661 (-973 (-558))))
-           (|:| |rand| (-2 (|:| |ints2Floats?| (-114)) (|:| -3748 (-885))))))
+          (-2 (|:| |var| (-1198)) (|:| |arrayIndex| (-661 (-965 (-558))))
+           (|:| |rand| (-2 (|:| |ints2Floats?| (-114)) (|:| -3671 (-877))))))
      (|:| |arrayAssignmentBranch|
-          (-2 (|:| |var| (-1206)) (|:| |rand| (-885))
+          (-2 (|:| |var| (-1198)) (|:| |rand| (-877))
            (|:| |ints2Floats?| (-114))))
      (|:| |conditionalBranch|
-          (-2 (|:| |switch| (-1205)) (|:| |thenClause| (-342))
+          (-2 (|:| |switch| (-1197)) (|:| |thenClause| (-342))
            (|:| |elseClause| (-342))))
      (|:| |returnBranch|
-          (-2 (|:| -3900 (-114))
-           (|:| -3899 (-2 (|:| |ints2Floats?| (-114)) (|:| -3748 (-885))))))
-     (|:| |blockBranch| (-661 (-342))) (|:| |commentBranch| (-661 (-1188)))
-     (|:| |callBranch| (-1188))
+          (-2 (|:| -3823 (-114))
+           (|:| -3822 (-2 (|:| |ints2Floats?| (-114)) (|:| -3671 (-877))))))
+     (|:| |blockBranch| (-661 (-342))) (|:| |commentBranch| (-661 (-1180)))
+     (|:| |callBranch| (-1180))
      (|:| |forBranch|
-          (-2 (|:| -1646 (-1121 (-973 (-558)))) (|:| |span| (-973 (-558)))
-           (|:| -3728 (-342))))
-     (|:| |labelBranch| (-1149))
-     (|:| |loopBranch| (-2 (|:| |switch| (-1205)) (|:| -3728 (-342))))
+          (-2 (|:| -1638 (-1113 (-965 (-558)))) (|:| |span| (-965 (-558)))
+           (|:| -3651 (-342))))
+     (|:| |labelBranch| (-1141))
+     (|:| |loopBranch| (-2 (|:| |switch| (-1197)) (|:| -3651 (-342))))
      (|:| |commonBranch|
-          (-2 (|:| -4047 (-1206)) (|:| |contents| (-661 (-1206)))))
-     (|:| |printBranch| (-661 (-885)))))
+          (-2 (|:| -3970 (-1198)) (|:| |contents| (-661 (-1198)))))
+     (|:| |printBranch| (-661 (-877)))))
    (-5 *1 (-342))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-342))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1132)) (-5 *1 (-342))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1149)) (-5 *1 (-342))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-342))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1124)) (-5 *1 (-342))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1141)) (-5 *1 (-342))))) 
 (((*1 *1) (-12 (-4 *1 (-341 *2)) (-4 *2 (-381)) (-4 *2 (-376))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1200 *3)) (-4 *3 (-381)) (-4 *1 (-341 *3)) (-4 *3 (-376))))) 
+  (-12 (-5 *2 (-1192 *3)) (-4 *3 (-381)) (-4 *1 (-341 *3)) (-4 *3 (-376))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-4 *3 (-381)) (-5 *2 (-1200 *3))))) 
+  (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-4 *3 (-381)) (-5 *2 (-1192 *3))))) 
 (((*1 *2 *1 *1)
   (|partial| -12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-4 *3 (-381))
-   (-5 *2 (-1200 *3))))
+   (-5 *2 (-1192 *3))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-4 *3 (-381)) (-5 *2 (-1200 *3))))) 
+  (-12 (-4 *1 (-341 *3)) (-4 *3 (-376)) (-4 *3 (-381)) (-5 *2 (-1192 *3))))) 
 (((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-338 *3 *4)) (-4 *3 (-1078)) (-4 *4 (-814))))) 
+  (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-338 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-814))))) 
 (((*1 *1 *1 *2 *3 *1)
-  (-12 (-4 *1 (-338 *2 *3)) (-4 *2 (-1078)) (-4 *3 (-814))))) 
+  (-12 (-4 *1 (-338 *2 *3)) (-4 *2 (-1070)) (-4 *3 (-814))))) 
 (((*1 *1 *1 *1 *2)
-  (-12 (-5 *2 (-791)) (-4 *1 (-338 *3 *4)) (-4 *3 (-1078)) (-4 *4 (-814))
+  (-12 (-5 *2 (-791)) (-4 *1 (-338 *3 *4)) (-4 *3 (-1070)) (-4 *4 (-814))
    (-4 *3 (-175))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-558)) (-4 *1 (-335 *4 *2)) (-4 *4 (-1130)) (-4 *2 (-133))))) 
+  (-12 (-5 *3 (-558)) (-4 *1 (-335 *4 *2)) (-4 *4 (-1122)) (-4 *2 (-133))))) 
 (((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-335 *3 *4)) (-4 *3 (-1130)) (-4 *4 (-133))))) 
+  (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-335 *3 *4)) (-4 *3 (-1122)) (-4 *4 (-133))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-335 *2 *3)) (-4 *2 (-1130)) (-4 *3 (-133)) (-4 *3 (-814))))) 
+  (-12 (-4 *1 (-335 *2 *3)) (-4 *2 (-1122)) (-4 *3 (-133)) (-4 *3 (-814))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-558)) (-4 *4 (-815)) (-4 *5 (-869)) (-4 *2 (-1078))
-   (-5 *1 (-333 *4 *5 *2 *6)) (-4 *6 (-977 *2 *4 *5))))) 
+  (-12 (-5 *3 (-558)) (-4 *4 (-815)) (-4 *5 (-861)) (-4 *2 (-1070))
+   (-5 *1 (-333 *4 *5 *2 *6)) (-4 *6 (-969 *2 *4 *5))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1200 *7)) (-5 *3 (-558)) (-4 *7 (-977 *6 *4 *5)) (-4 *4 (-815))
-   (-4 *5 (-869)) (-4 *6 (-1078)) (-5 *1 (-333 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-1192 *7)) (-5 *3 (-558)) (-4 *7 (-969 *6 *4 *5)) (-4 *4 (-815))
+   (-4 *5 (-861)) (-4 *6 (-1070)) (-5 *1 (-333 *4 *5 *6 *7))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1200 *6)) (-4 *6 (-1078)) (-4 *4 (-815)) (-4 *5 (-869))
-   (-5 *2 (-1200 *7)) (-5 *1 (-333 *4 *5 *6 *7)) (-4 *7 (-977 *6 *4 *5))))) 
+  (-12 (-5 *3 (-1192 *6)) (-4 *6 (-1070)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-5 *2 (-1192 *7)) (-5 *1 (-333 *4 *5 *6 *7)) (-4 *7 (-969 *6 *4 *5))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1200 *7)) (-4 *7 (-977 *6 *4 *5)) (-4 *4 (-815)) (-4 *5 (-869))
-   (-4 *6 (-1078)) (-5 *2 (-1200 *6)) (-5 *1 (-333 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1192 *7)) (-4 *7 (-969 *6 *4 *5)) (-4 *4 (-815)) (-4 *5 (-861))
+   (-4 *6 (-1070)) (-5 *2 (-1192 *6)) (-5 *1 (-333 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1200 *9)) (-5 *4 (-661 *7)) (-5 *5 (-661 *8)) (-4 *7 (-869))
-   (-4 *8 (-1078)) (-4 *9 (-977 *8 *6 *7)) (-4 *6 (-815)) (-5 *2 (-1200 *8))
+  (-12 (-5 *3 (-1192 *9)) (-5 *4 (-661 *7)) (-5 *5 (-661 *8)) (-4 *7 (-861))
+   (-4 *8 (-1070)) (-4 *9 (-969 *8 *6 *7)) (-4 *6 (-815)) (-5 *2 (-1192 *8))
    (-5 *1 (-333 *6 *7 *8 *9))))) 
 (((*1 *2 *1)
   (-12 (-5 *2 (-419 (-558))) (-5 *1 (-331 *3 *4 *5)) (-4 *3 (-376))
-   (-14 *4 (-1206)) (-14 *5 *3)))) 
+   (-14 *4 (-1198)) (-14 *5 *3)))) 
 (((*1 *2 *3 *3 *3 *4 *5 *4 *6)
-  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1118 (-229)))
-   (-5 *6 (-558)) (-5 *2 (-1242 (-954))) (-5 *1 (-330))))
+  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1110 (-229)))
+   (-5 *6 (-558)) (-5 *2 (-1234 (-946))) (-5 *1 (-330))))
  ((*1 *2 *3 *3 *3 *4 *5 *4 *6 *7)
-  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1118 (-229)))
-   (-5 *6 (-558)) (-5 *7 (-1188)) (-5 *2 (-1242 (-954))) (-5 *1 (-330))))
+  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1110 (-229)))
+   (-5 *6 (-558)) (-5 *7 (-1180)) (-5 *2 (-1234 (-946))) (-5 *1 (-330))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7)
-  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1118 (-229)))
-   (-5 *6 (-229)) (-5 *7 (-558)) (-5 *2 (-1242 (-954))) (-5 *1 (-330))))
+  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1110 (-229)))
+   (-5 *6 (-229)) (-5 *7 (-558)) (-5 *2 (-1234 (-946))) (-5 *1 (-330))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
-  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1118 (-229)))
-   (-5 *6 (-229)) (-5 *7 (-558)) (-5 *8 (-1188)) (-5 *2 (-1242 (-954)))
+  (-12 (-5 *3 (-326 (-558))) (-5 *4 (-1 (-229) (-229))) (-5 *5 (-1110 (-229)))
+   (-5 *6 (-229)) (-5 *7 (-558)) (-5 *8 (-1180)) (-5 *2 (-1234 (-946)))
    (-5 *1 (-330))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-1 (-229) (-229))) (-5 *1 (-330)) (-5 *3 (-229))))) 
 (((*1 *2 *3 *4 *3 *3)
@@ -14151,33 +14063,33 @@
   (-12 (-5 *4 (-115)) (-5 *5 (-305 *3)) (-5 *6 (-661 *3)) (-4 *3 (-433 *7))
    (-4 *7 (-13 (-569) (-631 (-547)))) (-5 *2 (-51)) (-5 *1 (-329 *7 *3))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-114)) (-5 *1 (-326 *3)) (-4 *3 (-569)) (-4 *3 (-1130))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-326 *3)) (-4 *3 (-569)) (-4 *3 (-1122))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-558)) (-5 *1 (-326 *3)) (-4 *3 (-569)) (-4 *3 (-1130))))) 
+  (-12 (-5 *2 (-558)) (-5 *1 (-326 *3)) (-4 *3 (-569)) (-4 *3 (-1122))))) 
 (((*1 *2 *1 *1) (-12 (-4 *1 (-319)) (-5 *2 (-114))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-319)) (-5 *2 (-791))))) 
 (((*1 *2 *1 *1 *1)
   (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1)))
    (-4 *1 (-319))))
  ((*1 *2 *1 *1)
-  (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2648 *1)))
+  (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2640 *1)))
    (-4 *1 (-319))))) 
 (((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-661 *1)) (-4 *1 (-319))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-868)) (-5 *1 (-316 *3))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-860)) (-5 *1 (-316 *3))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *3 (-661 (-229))) (-5 *4 (-791)) (-5 *2 (-709 (-229)))
    (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-419 (-558))) (-5 *2 (-229)) (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-326 (-391))) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-973 (-229))) (-5 *2 (-229)) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-973 (-229))) (-5 *2 (-326 (-391))) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-965 (-229))) (-5 *2 (-229)) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-965 (-229))) (-5 *2 (-326 (-391))) (-5 *1 (-315))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
     (-2 (|:| |stiffness| (-391)) (|:| |stability| (-391))
      (|:| |expense| (-391)) (|:| |accuracy| (-391))
      (|:| |intermediateResults| (-391))))
-   (-5 *2 (-1064)) (-5 *1 (-315))))) 
+   (-5 *2 (-1056)) (-5 *1 (-315))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
@@ -14191,118 +14103,118 @@
            (|:| |bothSingular| "There are singularities at both end points")
            (|:| |notEvaluated| "End point continuity not yet evaluated")))
      (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1184 (-229)))
+          (-3 (|:| |str| (-1176 (-229)))
            (|:| |notEvaluated| "Internal singularities not yet evaluated")))
-     (|:| -1646
+     (|:| -1638
           (-3 (|:| |finite| "The range is finite")
            (|:| |lowerInfinite| "The bottom of range is infinite")
            (|:| |upperInfinite| "The top of range is infinite")
            (|:| |bothInfinite| "Both top and bottom points are infinite")
            (|:| |notEvaluated| "Range not yet evaluated")))))
-   (-5 *2 (-1064)) (-5 *1 (-315))))) 
+   (-5 *2 (-1056)) (-5 *1 (-315))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| -3146 (-391)) (|:| -4047 (-1188))
-     (|:| |explanations| (-661 (-1188)))))
-   (-5 *2 (-1064)) (-5 *1 (-315))))
+    (-2 (|:| -3069 (-391)) (|:| -3970 (-1180))
+     (|:| |explanations| (-661 (-1180)))))
+   (-5 *2 (-1056)) (-5 *1 (-315))))
  ((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| -3146 (-391)) (|:| -4047 (-1188))
-     (|:| |explanations| (-661 (-1188))) (|:| |extra| (-1064))))
-   (-5 *2 (-1064)) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-391)) (-5 *2 (-1188)) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1118 (-863 (-229)))) (-5 *2 (-229)) (-5 *1 (-195))))
- ((*1 *2 *3) (-12 (-5 *3 (-1118 (-863 (-229)))) (-5 *2 (-229)) (-5 *1 (-313))))
- ((*1 *2 *3) (-12 (-5 *3 (-1118 (-863 (-229)))) (-5 *2 (-229)) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1118 (-863 (-229)))) (-5 *2 (-229)) (-5 *1 (-195))))
- ((*1 *2 *3) (-12 (-5 *3 (-1118 (-863 (-229)))) (-5 *2 (-229)) (-5 *1 (-313))))
- ((*1 *2 *3) (-12 (-5 *3 (-1118 (-863 (-229)))) (-5 *2 (-229)) (-5 *1 (-315))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-1184 (-229))) (-5 *2 (-661 (-1188))) (-5 *1 (-195))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1184 (-229))) (-5 *2 (-661 (-1188))) (-5 *1 (-313))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1184 (-229))) (-5 *2 (-661 (-1188))) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-661 (-1188))) (-5 *1 (-195))))
- ((*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-661 (-1188))) (-5 *1 (-313))))
- ((*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-661 (-1188))) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-391)) (-5 *2 (-1188)) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1188)) (-5 *1 (-195))))
- ((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1188)) (-5 *1 (-313))))
- ((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1188)) (-5 *1 (-315))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-1296 (-326 (-229)))) (-5 *2 (-1296 (-326 (-391))))
+    (-2 (|:| -3069 (-391)) (|:| -3970 (-1180))
+     (|:| |explanations| (-661 (-1180))) (|:| |extra| (-1056))))
+   (-5 *2 (-1056)) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-391)) (-5 *2 (-1180)) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1110 (-855 (-229)))) (-5 *2 (-229)) (-5 *1 (-195))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1110 (-855 (-229)))) (-5 *2 (-229)) (-5 *1 (-313))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1110 (-855 (-229)))) (-5 *2 (-229)) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1110 (-855 (-229)))) (-5 *2 (-229)) (-5 *1 (-195))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1110 (-855 (-229)))) (-5 *2 (-229)) (-5 *1 (-313))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1110 (-855 (-229)))) (-5 *2 (-229)) (-5 *1 (-315))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-1176 (-229))) (-5 *2 (-661 (-1180))) (-5 *1 (-195))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1176 (-229))) (-5 *2 (-661 (-1180))) (-5 *1 (-313))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1176 (-229))) (-5 *2 (-661 (-1180))) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-661 (-1180))) (-5 *1 (-195))))
+ ((*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-661 (-1180))) (-5 *1 (-313))))
+ ((*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-661 (-1180))) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-391)) (-5 *2 (-1180)) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1180)) (-5 *1 (-195))))
+ ((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1180)) (-5 *1 (-313))))
+ ((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-1180)) (-5 *1 (-315))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-1288 (-326 (-229)))) (-5 *2 (-1288 (-326 (-391))))
    (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-326 (-229))) (-5 *2 (-326 (-391))) (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-1296 (-719))) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-661 (-229))) (-5 *2 (-1288 (-719))) (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-719)) (-5 *1 (-315))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-2 (|:| -3617 (-419 (-558))) (|:| -3616 (-419 (-558))))))
+  (-12 (-5 *3 (-661 (-2 (|:| -3540 (-419 (-558))) (|:| -3539 (-419 (-558))))))
    (-5 *2 (-661 (-229))) (-5 *1 (-315))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1118 (-863 (-229)))) (-5 *1 (-315))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1110 (-855 (-229)))) (-5 *1 (-315))))) 
 (((*1 *2 *3)
   (-12 (-5 *3 (-326 (-229))) (-5 *2 (-326 (-419 (-558)))) (-5 *1 (-315))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1296 (-326 (-229))))
+  (-12 (-5 *3 (-1288 (-326 (-229))))
    (-5 *2
     (-2 (|:| |additions| (-558)) (|:| |multiplications| (-558))
      (|:| |exponentiations| (-558)) (|:| |functionCalls| (-558))))
    (-5 *1 (-315))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3943 (-661 (-229)))))
+  (-12 (-5 *3 (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3866 (-661 (-229)))))
    (-5 *2 (-391)) (-5 *1 (-278))))
- ((*1 *2 *3) (-12 (-5 *3 (-1296 (-326 (-229)))) (-5 *2 (-391)) (-5 *1 (-315))))) 
+ ((*1 *2 *3) (-12 (-5 *3 (-1288 (-326 (-229)))) (-5 *2 (-391)) (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-326 (-229))) (-5 *2 (-229)) (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-326 (-229))) (-5 *2 (-419 (-558))) (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-229)) (-5 *2 (-419 (-558))) (-5 *1 (-315))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1118 (-863 (-391)))) (-5 *2 (-1118 (-863 (-229))))
+  (-12 (-5 *3 (-1110 (-855 (-391)))) (-5 *2 (-1110 (-855 (-229))))
    (-5 *1 (-315))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-863 (-391))) (-5 *2 (-863 (-229))) (-5 *1 (-315))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-855 (-391))) (-5 *2 (-855 (-229))) (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-326 (-391))) (-5 *2 (-326 (-229))) (-5 *1 (-315))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-391)) (-5 *2 (-229)) (-5 *1 (-315))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-973 (-419 (-558)))) (-5 *4 (-1206))
-   (-5 *5 (-1118 (-863 (-229)))) (-5 *2 (-661 (-229))) (-5 *1 (-313))))) 
+  (-12 (-5 *3 (-965 (-419 (-558)))) (-5 *4 (-1198))
+   (-5 *5 (-1110 (-855 (-229)))) (-5 *2 (-661 (-229))) (-5 *1 (-313))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
-   (-5 *2 (-1184 (-229))) (-5 *1 (-195))))
+   (-5 *2 (-1176 (-229))) (-5 *1 (-195))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-326 (-229))) (-5 *4 (-661 (-1206)))
-   (-5 *5 (-1118 (-863 (-229)))) (-5 *2 (-1184 (-229))) (-5 *1 (-313))))
+  (-12 (-5 *3 (-326 (-229))) (-5 *4 (-661 (-1198)))
+   (-5 *5 (-1110 (-855 (-229)))) (-5 *2 (-1176 (-229))) (-5 *1 (-313))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-1296 (-326 (-229)))) (-5 *4 (-661 (-1206)))
-   (-5 *5 (-1118 (-863 (-229)))) (-5 *2 (-1184 (-229))) (-5 *1 (-313))))) 
+  (-12 (-5 *3 (-1288 (-326 (-229)))) (-5 *4 (-661 (-1198)))
+   (-5 *5 (-1110 (-855 (-229)))) (-5 *2 (-1176 (-229))) (-5 *1 (-313))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1200 *1)) (-5 *4 (-1206)) (-4 *1 (-27)) (-5 *2 (-661 *1))))
- ((*1 *2 *3) (-12 (-5 *3 (-1200 *1)) (-4 *1 (-27)) (-5 *2 (-661 *1))))
- ((*1 *2 *3) (-12 (-5 *3 (-973 *1)) (-4 *1 (-27)) (-5 *2 (-661 *1))))
+  (-12 (-5 *3 (-1192 *1)) (-5 *4 (-1198)) (-4 *1 (-27)) (-5 *2 (-661 *1))))
+ ((*1 *2 *3) (-12 (-5 *3 (-1192 *1)) (-4 *1 (-27)) (-5 *2 (-661 *1))))
+ ((*1 *2 *3) (-12 (-5 *3 (-965 *1)) (-4 *1 (-27)) (-5 *2 (-661 *1))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-569)) (-5 *2 (-661 *1)) (-4 *1 (-29 *4))))
+  (-12 (-5 *3 (-1198)) (-4 *4 (-569)) (-5 *2 (-661 *1)) (-4 *1 (-29 *4))))
  ((*1 *2 *1) (-12 (-4 *3 (-569)) (-5 *2 (-661 *1)) (-4 *1 (-29 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-326 (-229))) (-5 *4 (-661 (-1206)))
-   (-5 *5 (-1118 (-863 (-229)))) (-5 *2 (-1184 (-229))) (-5 *1 (-313))))) 
+  (-12 (-5 *3 (-326 (-229))) (-5 *4 (-661 (-1198)))
+   (-5 *5 (-1110 (-855 (-229)))) (-5 *2 (-1176 (-229))) (-5 *1 (-313))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1206)) (-5 *5 (-1118 (-863 (-229))))
+  (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1198)) (-5 *5 (-1110 (-855 (-229))))
    (-5 *2 (-661 (-229))) (-5 *1 (-195))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1206)) (-5 *5 (-1118 (-863 (-229))))
+  (-12 (-5 *3 (-326 (-229))) (-5 *4 (-1198)) (-5 *5 (-1110 (-855 (-229))))
    (-5 *2 (-661 (-229))) (-5 *1 (-313))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *2 (-114)) (-5 *1 (-313))))) 
-(((*1 *1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-310)) (-4 *2 (-1246))))
+(((*1 *1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-310)) (-4 *2 (-1238))))
  ((*1 *1 *1 *2 *3)
   (-12 (-5 *2 (-661 (-628 *1))) (-5 *3 (-661 *1)) (-4 *1 (-310))))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-661 (-305 *1))) (-4 *1 (-310))))
@@ -14312,181 +14224,181 @@
 (((*1 *2 *1) (-12 (-5 *2 (-661 (-628 *1))) (-4 *1 (-310))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-661 (-628 *1))) (-4 *1 (-310))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-310)) (-5 *2 (-661 (-115)))))) 
-(((*1 *2 *1 *3) (-12 (-4 *1 (-310)) (-5 *3 (-1206)) (-5 *2 (-114))))
+(((*1 *2 *1 *3) (-12 (-4 *1 (-310)) (-5 *3 (-1198)) (-5 *2 (-114))))
  ((*1 *2 *1 *1) (-12 (-4 *1 (-310)) (-5 *2 (-114))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-628 *5)) (-4 *5 (-433 *4)) (-4 *4 (-1067 (-558)))
-   (-4 *4 (-569)) (-5 *2 (-1200 *5)) (-5 *1 (-32 *4 *5))))
+  (-12 (-5 *3 (-628 *5)) (-4 *5 (-433 *4)) (-4 *4 (-1059 (-558)))
+   (-4 *4 (-569)) (-5 *2 (-1192 *5)) (-5 *1 (-32 *4 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-628 *1)) (-4 *1 (-1078)) (-4 *1 (-310)) (-5 *2 (-1200 *1))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-323)) (-5 *1 (-308))))
- ((*1 *2 *3) (-12 (-5 *3 (-661 (-1188))) (-5 *2 (-323)) (-5 *1 (-308))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-323)) (-5 *1 (-308))))
+  (-12 (-5 *3 (-628 *1)) (-4 *1 (-1070)) (-4 *1 (-310)) (-5 *2 (-1192 *1))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-323)) (-5 *1 (-308))))
+ ((*1 *2 *3) (-12 (-5 *3 (-661 (-1180))) (-5 *2 (-323)) (-5 *1 (-308))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-323)) (-5 *1 (-308))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 (-1188))) (-5 *3 (-1188)) (-5 *2 (-323)) (-5 *1 (-308))))) 
+  (-12 (-5 *4 (-661 (-1180))) (-5 *3 (-1180)) (-5 *2 (-323)) (-5 *1 (-308))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-1078)) (-4 *4 (-1272 *3)) (-5 *1 (-166 *3 *4 *2))
-   (-4 *2 (-1272 *4))))
- ((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-1246))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1246))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1246))))) 
-(((*1 *1 *1) (|partial| -12 (-5 *1 (-305 *2)) (-4 *2 (-746)) (-4 *2 (-1246))))) 
-(((*1 *1 *1) (|partial| -12 (-5 *1 (-305 *2)) (-4 *2 (-746)) (-4 *2 (-1246))))) 
+  (-12 (-4 *3 (-1070)) (-4 *4 (-1264 *3)) (-5 *1 (-166 *3 *4 *2))
+   (-4 *2 (-1264 *4))))
+ ((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-1238))))) 
+(((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1238))))) 
+(((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1238))))) 
+(((*1 *1 *1) (|partial| -12 (-5 *1 (-305 *2)) (-4 *2 (-746)) (-4 *2 (-1238))))) 
+(((*1 *1 *1) (|partial| -12 (-5 *1 (-305 *2)) (-4 *2 (-746)) (-4 *2 (-1238))))) 
 (((*1 *2 *1)
   (-12 (-5 *2 (-661 (-305 *3))) (-5 *1 (-305 *3)) (-4 *3 (-569))
-   (-4 *3 (-1246))))) 
+   (-4 *3 (-1238))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-464))
    (-5 *2
     (-661
-     (-2 (|:| |eigval| (-3 (-419 (-973 *4)) (-1195 (-1206) (-973 *4))))
-      (|:| |eigmult| (-791)) (|:| |eigvec| (-661 (-709 (-419 (-973 *4))))))))
-   (-5 *1 (-304 *4)) (-5 *3 (-709 (-419 (-973 *4))))))) 
+     (-2 (|:| |eigval| (-3 (-419 (-965 *4)) (-1187 (-1198) (-965 *4))))
+      (|:| |eigmult| (-791)) (|:| |eigvec| (-661 (-709 (-419 (-965 *4))))))))
+   (-5 *1 (-304 *4)) (-5 *3 (-709 (-419 (-965 *4))))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-464))
    (-5 *2
     (-661
-     (-2 (|:| |eigval| (-3 (-419 (-973 *4)) (-1195 (-1206) (-973 *4))))
-      (|:| |geneigvec| (-661 (-709 (-419 (-973 *4))))))))
-   (-5 *1 (-304 *4)) (-5 *3 (-709 (-419 (-973 *4))))))) 
+     (-2 (|:| |eigval| (-3 (-419 (-965 *4)) (-1187 (-1198) (-965 *4))))
+      (|:| |geneigvec| (-661 (-709 (-419 (-965 *4))))))))
+   (-5 *1 (-304 *4)) (-5 *3 (-709 (-419 (-965 *4))))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *3 (-3 (-419 (-973 *6)) (-1195 (-1206) (-973 *6)))) (-5 *5 (-791))
-   (-4 *6 (-464)) (-5 *2 (-661 (-709 (-419 (-973 *6))))) (-5 *1 (-304 *6))
-   (-5 *4 (-709 (-419 (-973 *6))))))
+  (-12 (-5 *3 (-3 (-419 (-965 *6)) (-1187 (-1198) (-965 *6)))) (-5 *5 (-791))
+   (-4 *6 (-464)) (-5 *2 (-661 (-709 (-419 (-965 *6))))) (-5 *1 (-304 *6))
+   (-5 *4 (-709 (-419 (-965 *6))))))
  ((*1 *2 *3 *4)
   (-12
    (-5 *3
-    (-2 (|:| |eigval| (-3 (-419 (-973 *5)) (-1195 (-1206) (-973 *5))))
+    (-2 (|:| |eigval| (-3 (-419 (-965 *5)) (-1187 (-1198) (-965 *5))))
      (|:| |eigmult| (-791)) (|:| |eigvec| (-661 *4))))
-   (-4 *5 (-464)) (-5 *2 (-661 (-709 (-419 (-973 *5))))) (-5 *1 (-304 *5))
-   (-5 *4 (-709 (-419 (-973 *5))))))) 
+   (-4 *5 (-464)) (-5 *2 (-661 (-709 (-419 (-965 *5))))) (-5 *1 (-304 *5))
+   (-5 *4 (-709 (-419 (-965 *5))))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-3 (-419 (-973 *5)) (-1195 (-1206) (-973 *5)))) (-4 *5 (-464))
-   (-5 *2 (-661 (-709 (-419 (-973 *5))))) (-5 *1 (-304 *5))
-   (-5 *4 (-709 (-419 (-973 *5))))))) 
+  (-12 (-5 *3 (-3 (-419 (-965 *5)) (-1187 (-1198) (-965 *5)))) (-4 *5 (-464))
+   (-5 *2 (-661 (-709 (-419 (-965 *5))))) (-5 *1 (-304 *5))
+   (-5 *4 (-709 (-419 (-965 *5))))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-709 (-419 (-973 *4)))) (-4 *4 (-464))
-   (-5 *2 (-661 (-3 (-419 (-973 *4)) (-1195 (-1206) (-973 *4)))))
+  (-12 (-5 *3 (-709 (-419 (-965 *4)))) (-4 *4 (-464))
+   (-5 *2 (-661 (-3 (-419 (-965 *4)) (-1187 (-1198) (-965 *4)))))
    (-5 *1 (-304 *4))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-1114))) (-5 *1 (-303))))) 
-(((*1 *2 *3 *3 *1) (-12 (-5 *3 (-518)) (-5 *2 (-711 (-1132))) (-5 *1 (-303))))) 
-(((*1 *1 *2 *2 *3 *1) (-12 (-5 *2 (-518)) (-5 *3 (-1132)) (-5 *1 (-303))))) 
-(((*1 *2 *3 *1) (-12 (-5 *3 (-518)) (-5 *2 (-661 (-992))) (-5 *1 (-303))))) 
-(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-518)) (-5 *3 (-661 (-992))) (-5 *1 (-303))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-661 (-1106))) (-5 *1 (-303))))) 
+(((*1 *2 *3 *3 *1) (-12 (-5 *3 (-518)) (-5 *2 (-711 (-1124))) (-5 *1 (-303))))) 
+(((*1 *1 *2 *2 *3 *1) (-12 (-5 *2 (-518)) (-5 *3 (-1124)) (-5 *1 (-303))))) 
+(((*1 *2 *3 *1) (-12 (-5 *3 (-518)) (-5 *2 (-661 (-984))) (-5 *1 (-303))))) 
+(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-518)) (-5 *3 (-661 (-984))) (-5 *1 (-303))))) 
 (((*1 *1) (-5 *1 (-303)))) 
 (((*1 *1) (-5 *1 (-303)))) 
 (((*1 *1) (-5 *1 (-303)))) 
 (((*1 *2 *1 *3 *3 *2)
-  (-12 (-5 *3 (-558)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1246)) (-4 *4 (-385 *2))
+  (-12 (-5 *3 (-558)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1238)) (-4 *4 (-385 *2))
    (-4 *5 (-385 *2))))
  ((*1 *2 *1 *3 *2)
-  (-12 (|has| *1 (-6 -4503)) (-4 *1 (-300 *3 *2)) (-4 *3 (-1130))
-   (-4 *2 (-1246))))) 
-(((*1 *2 *3 *4)
-  (-12 (-4 *4 (-376)) (-5 *2 (-661 (-1184 *4))) (-5 *1 (-297 *4 *5))
-   (-5 *3 (-1184 *4)) (-4 *5 (-1289 *4))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1289 *3))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1289 *3))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1289 *3))))) 
-(((*1 *1 *1 *2) (-12 (-5 *2 (-1263 (-558))) (-4 *1 (-294 *3)) (-4 *3 (-1246))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-294 *3)) (-4 *3 (-1246))))) 
+  (-12 (|has| *1 (-6 -4426)) (-4 *1 (-300 *3 *2)) (-4 *3 (-1122))
+   (-4 *2 (-1238))))) 
+(((*1 *2 *3 *4)
+  (-12 (-4 *4 (-376)) (-5 *2 (-661 (-1176 *4))) (-5 *1 (-297 *4 *5))
+   (-5 *3 (-1176 *4)) (-4 *5 (-1281 *4))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1281 *3))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1281 *3))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-376)) (-5 *1 (-297 *3 *2)) (-4 *2 (-1281 *3))))) 
+(((*1 *1 *1 *2) (-12 (-5 *2 (-1255 (-558))) (-4 *1 (-294 *3)) (-4 *3 (-1238))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-558)) (-4 *1 (-294 *3)) (-4 *3 (-1238))))) 
 (((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 (-114) *3)) (|has| *1 (-6 -4502)) (-4 *1 (-242 *3))
-   (-4 *3 (-1130))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *1 (-294 *3)) (-4 *3 (-1246))))) 
+  (-12 (-5 *2 (-1 (-114) *3)) (|has| *1 (-6 -4425)) (-4 *1 (-242 *3))
+   (-4 *3 (-1122))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-114) *3)) (-4 *1 (-294 *3)) (-4 *3 (-1238))))) 
 (((*1 *1 *2 *3 *4)
   (-12 (-5 *2 (-598)) (-5 *3 (-609)) (-5 *4 (-303)) (-5 *1 (-292))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-598)) (-5 *1 (-292))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-609)) (-5 *1 (-292))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-303)) (-5 *1 (-292))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1211)) (-5 *1 (-291))))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-1132)) (-5 *1 (-291))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1203)) (-5 *1 (-291))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-1124)) (-5 *1 (-291))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-291))))) 
 (((*1 *2 *1) (|partial| -12 (-5 *2 (-518)) (-5 *1 (-291))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-291))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-419 (-558))) (-4 *4 (-13 (-569) (-1067 (-558)) (-658 (-558))))
-   (-5 *1 (-288 *4 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *4)))))) 
+  (-12 (-5 *3 (-419 (-558))) (-4 *4 (-13 (-569) (-1059 (-558)) (-658 (-558))))
+   (-5 *1 (-288 *4 *2)) (-4 *2 (-13 (-27) (-1224) (-433 *4)))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-628 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *4)))
-   (-4 *4 (-13 (-569) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-288 *4 *2))))) 
+  (-12 (-5 *3 (-628 *2)) (-4 *2 (-13 (-27) (-1224) (-433 *4)))
+   (-4 *4 (-13 (-569) (-1059 (-558)) (-658 (-558)))) (-5 *1 (-288 *4 *2))))) 
 (((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-661 (-628 *2))) (-5 *4 (-1206))
-   (-4 *2 (-13 (-27) (-1232) (-433 *5)))
-   (-4 *5 (-13 (-569) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-288 *5 *2))))) 
+  (|partial| -12 (-5 *3 (-661 (-628 *2))) (-5 *4 (-1198))
+   (-4 *2 (-13 (-27) (-1224) (-433 *5)))
+   (-4 *5 (-13 (-569) (-1059 (-558)) (-658 (-558)))) (-5 *1 (-288 *5 *2))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-569) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-288 *3 *2))
-   (-4 *2 (-13 (-27) (-1232) (-433 *3)))))
+  (-12 (-4 *3 (-13 (-569) (-1059 (-558)) (-658 (-558)))) (-5 *1 (-288 *3 *2))
+   (-4 *2 (-13 (-27) (-1224) (-433 *3)))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *3 (-1206)) (-4 *4 (-13 (-569) (-1067 (-558)) (-658 (-558))))
-   (-5 *1 (-288 *4 *2)) (-4 *2 (-13 (-27) (-1232) (-433 *4)))))) 
+  (-12 (-5 *3 (-1198)) (-4 *4 (-13 (-569) (-1059 (-558)) (-658 (-558))))
+   (-5 *1 (-288 *4 *2)) (-4 *2 (-13 (-27) (-1224) (-433 *4)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1206)) (-4 *5 (-13 (-569) (-1067 (-558)) (-658 (-558))))
+  (-12 (-5 *4 (-1198)) (-4 *5 (-13 (-569) (-1059 (-558)) (-658 (-558))))
    (-5 *2
     (-2 (|:| |func| *3) (|:| |kers| (-661 (-628 *3))) (|:| |vals| (-661 *3))))
-   (-5 *1 (-288 *5 *3)) (-4 *3 (-13 (-27) (-1232) (-433 *5)))))) 
+   (-5 *1 (-288 *5 *3)) (-4 *3 (-13 (-27) (-1224) (-433 *5)))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-569)) (-5 *2 (-114)) (-5 *1 (-287 *4 *3))
-   (-4 *3 (-13 (-433 *4) (-1031)))))) 
+   (-4 *3 (-13 (-433 *4) (-1023)))))) 
 (((*1 *2 *2 *3)
   (|partial| -12 (-5 *3 (-661 (-2 (|:| |func| *2) (|:| |pole| (-114)))))
-   (-4 *2 (-13 (-433 *4) (-1031))) (-4 *4 (-569)) (-5 *1 (-287 *4 *2))))) 
+   (-4 *2 (-13 (-433 *4) (-1023))) (-4 *4 (-569)) (-5 *1 (-287 *4 *2))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1031)))))) 
+  (-12 (-4 *3 (-569)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-433 *3) (-1023)))))) 
 (((*1 *2)
-  (-12 (-4 *2 (-13 (-433 *3) (-1031))) (-5 *1 (-287 *3 *2)) (-4 *3 (-569))))) 
+  (-12 (-4 *2 (-13 (-433 *3) (-1023))) (-5 *1 (-287 *3 *2)) (-4 *3 (-569))))) 
 (((*1 *2)
-  (-12 (-4 *2 (-13 (-433 *3) (-1031))) (-5 *1 (-287 *3 *2)) (-4 *3 (-569))))) 
+  (-12 (-4 *2 (-13 (-433 *3) (-1023))) (-5 *1 (-287 *3 *2)) (-4 *3 (-569))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-661 (-558))) (-5 *1 (-286))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-286))))) 
 (((*1 *2 *3)
@@ -14494,13 +14406,13 @@
    (-5 *3
     (-3
      (|:| |noa|
-          (-2 (|:| |fn| (-326 (-229))) (|:| -3943 (-661 (-229)))
-           (|:| |lb| (-661 (-863 (-229)))) (|:| |cf| (-661 (-326 (-229))))
-           (|:| |ub| (-661 (-863 (-229))))))
+          (-2 (|:| |fn| (-326 (-229))) (|:| -3866 (-661 (-229)))
+           (|:| |lb| (-661 (-855 (-229)))) (|:| |cf| (-661 (-326 (-229))))
+           (|:| |ub| (-661 (-855 (-229))))))
      (|:| |lsa|
-          (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3943 (-661 (-229)))))))
-   (-5 *2 (-661 (-1188))) (-5 *1 (-278))))) 
-(((*1 *2 *3 *2) (-12 (-5 *2 (-1064)) (-5 *3 (-1206)) (-5 *1 (-278))))) 
+          (-2 (|:| |lfn| (-661 (-326 (-229)))) (|:| -3866 (-661 (-229)))))))
+   (-5 *2 (-661 (-1180))) (-5 *1 (-278))))) 
+(((*1 *2 *3 *2) (-12 (-5 *2 (-1056)) (-5 *3 (-1198)) (-5 *1 (-278))))) 
 (((*1 *2 *3) (-12 (-5 *3 (-326 (-229))) (-5 *2 (-114)) (-5 *1 (-278))))) 
 (((*1 *2 *2) (-12 (-5 *2 (-661 (-326 (-229)))) (-5 *1 (-278))))) 
 (((*1 *2 *2) (-12 (-5 *2 (-661 (-326 (-229)))) (-5 *1 (-278))))) 
@@ -14513,271 +14425,271 @@
 (((*1 *2 *2)
   (-12
    (-5 *2
-    (-2 (|:| |fn| (-326 (-229))) (|:| -3943 (-661 (-229)))
-     (|:| |lb| (-661 (-863 (-229)))) (|:| |cf| (-661 (-326 (-229))))
-     (|:| |ub| (-661 (-863 (-229))))))
+    (-2 (|:| |fn| (-326 (-229))) (|:| -3866 (-661 (-229)))
+     (|:| |lb| (-661 (-855 (-229)))) (|:| |cf| (-661 (-326 (-229))))
+     (|:| |ub| (-661 (-855 (-229))))))
    (-5 *1 (-278))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-661 (-863 (-229)))) (-5 *4 (-229)) (-5 *2 (-661 *4))
+  (-12 (-5 *3 (-661 (-855 (-229)))) (-5 *4 (-229)) (-5 *2 (-661 *4))
    (-5 *1 (-278))))) 
 (((*1 *2 *1)
-  (-12 (-4 *3 (-240)) (-4 *3 (-1078)) (-4 *4 (-869)) (-4 *5 (-277 *4))
+  (-12 (-4 *3 (-240)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-277 *4))
    (-4 *6 (-815)) (-5 *2 (-1 *1 (-791))) (-4 *1 (-262 *3 *4 *5 *6))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-1078)) (-4 *3 (-869)) (-4 *5 (-277 *3)) (-4 *6 (-815))
+  (-12 (-4 *4 (-1070)) (-4 *3 (-861)) (-4 *5 (-277 *3)) (-4 *6 (-815))
    (-5 *2 (-1 *1 (-791))) (-4 *1 (-262 *4 *3 *5 *6))))
- ((*1 *1 *2 *3) (-12 (-5 *3 (-791)) (-4 *1 (-277 *2)) (-4 *2 (-869))))) 
+ ((*1 *1 *2 *3) (-12 (-5 *3 (-791)) (-4 *1 (-277 *2)) (-4 *2 (-861))))) 
 (((*1 *1 *1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-115))))
  ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-115))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1078)) (-4 *3 (-869))
+  (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1070)) (-4 *3 (-861))
    (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-791))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1078)) (-4 *4 (-869))
+  (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-861))
    (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-791))))
- ((*1 *2 *1) (-12 (-4 *1 (-277 *3)) (-4 *3 (-869)) (-5 *2 (-791))))) 
+ ((*1 *2 *1) (-12 (-4 *1 (-277 *3)) (-4 *3 (-861)) (-5 *2 (-791))))) 
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-661 (-270))) (-5 *4 (-1206)) (-5 *2 (-51))
+  (|partial| -12 (-5 *3 (-661 (-270))) (-5 *4 (-1198)) (-5 *2 (-51))
    (-5 *1 (-270))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-661 (-270))) (-5 *4 (-1206)) (-5 *1 (-272 *2))
-   (-4 *2 (-1246))))) 
+  (|partial| -12 (-5 *3 (-661 (-270))) (-5 *4 (-1198)) (-5 *1 (-272 *2))
+   (-4 *2 (-1238))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-391)) (-5 *1 (-270))))
  ((*1 *2 *3 *2) (-12 (-5 *2 (-391)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-946)) (-5 *1 (-270))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-946)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-270))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-938)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
 (((*1 *1) (-5 *1 (-146)))
- ((*1 *1 *2) (-12 (-5 *2 (-1162 (-229))) (-5 *1 (-270))))
- ((*1 *2 *3) (-12 (-5 *3 (-661 (-270))) (-5 *2 (-1162 (-229))) (-5 *1 (-271))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-946)) (-5 *1 (-270))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-946)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-946)) (-5 *1 (-270))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-946)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
-(((*1 *2 *3 *2) (-12 (-5 *2 (-896)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
-(((*1 *2 *3 *2) (-12 (-5 *2 (-896)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
+ ((*1 *1 *2) (-12 (-5 *2 (-1154 (-229))) (-5 *1 (-270))))
+ ((*1 *2 *3) (-12 (-5 *3 (-661 (-270))) (-5 *2 (-1154 (-229))) (-5 *1 (-271))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-270))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-938)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-270))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-938)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
+(((*1 *2 *3 *2) (-12 (-5 *2 (-888)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
+(((*1 *2 *3 *2) (-12 (-5 *2 (-888)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-270))))
  ((*1 *2 *3 *2) (-12 (-5 *2 (-114)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-270))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-1188)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-270))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1180)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
 (((*1 *2 *3 *2) (-12 (-5 *2 (-114)) (-5 *3 (-661 (-270))) (-5 *1 (-271))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-952))
+  (-12 (-5 *3 (-944))
    (-5 *2
-    (-2 (|:| |brans| (-661 (-661 (-970 (-229)))))
-     (|:| |xValues| (-1118 (-229))) (|:| |yValues| (-1118 (-229)))))
+    (-2 (|:| |brans| (-661 (-661 (-962 (-229)))))
+     (|:| |xValues| (-1110 (-229))) (|:| |yValues| (-1110 (-229)))))
    (-5 *1 (-155))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *3 (-952)) (-5 *4 (-419 (-558)))
+  (-12 (-5 *3 (-944)) (-5 *4 (-419 (-558)))
    (-5 *2
-    (-2 (|:| |brans| (-661 (-661 (-970 (-229)))))
-     (|:| |xValues| (-1118 (-229))) (|:| |yValues| (-1118 (-229)))))
+    (-2 (|:| |brans| (-661 (-661 (-962 (-229)))))
+     (|:| |xValues| (-1110 (-229))) (|:| |yValues| (-1110 (-229)))))
    (-5 *1 (-155))))
  ((*1 *2 *3)
   (-12
    (-5 *2
-    (-2 (|:| |brans| (-661 (-661 (-970 (-229)))))
-     (|:| |xValues| (-1118 (-229))) (|:| |yValues| (-1118 (-229)))))
-   (-5 *1 (-155)) (-5 *3 (-661 (-970 (-229))))))
+    (-2 (|:| |brans| (-661 (-661 (-962 (-229)))))
+     (|:| |xValues| (-1110 (-229))) (|:| |yValues| (-1110 (-229)))))
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    (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-661 (-791)))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1078)) (-4 *4 (-869))
+  (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1070)) (-4 *4 (-861))
    (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-114))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1078)) (-4 *4 (-869)) (-4 *5 (-815))
+  (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1070)) (-4 *4 (-861)) (-4 *5 (-815))
    (-4 *2 (-277 *4))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1078)) (-4 *3 (-869))
+  (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1070)) (-4 *3 (-861))
    (-4 *4 (-277 *3)) (-4 *5 (-815))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1078)) (-4 *3 (-869))
+  (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1070)) (-4 *3 (-861))
    (-4 *4 (-277 *3)) (-4 *5 (-815))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-345)) (-5 *1 (-257))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-141)) (-5 *1 (-142))))
@@ -14785,101 +14697,101 @@
  ((*1 *2 *1) (-12 (-5 *2 (-257)) (-5 *1 (-256))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-187 (-257))) (-5 *1 (-256))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-187 (-257))) (-5 *1 (-256))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1302)) (-5 *1 (-256))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1294)) (-5 *1 (-256))))) 
 (((*1 *2 *3 *3 *2)
   (|partial| -12 (-5 *2 (-791))
    (-4 *3 (-13 (-746) (-381) (-10 -7 (-15 ** (*3 *3 (-558))))))
    (-5 *1 (-253 *3))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-869)) (-5 *1 (-252 *3))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-251 *2)) (-4 *2 (-1246))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-251 *2)) (-4 *2 (-1246))))) 
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4503)) (-4 *1 (-251 *2)) (-4 *2 (-1246))))) 
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4503)) (-4 *1 (-251 *2)) (-4 *2 (-1246))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-558)) (-5 *1 (-248))))
- ((*1 *2 *3) (-12 (-5 *3 (-661 (-1188))) (-5 *2 (-558)) (-5 *1 (-248))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-1302)) (-5 *1 (-248))))
- ((*1 *2 *3) (-12 (-5 *3 (-661 (-1188))) (-5 *2 (-1302)) (-5 *1 (-248))))) 
-(((*1 *2 *3 *2) (-12 (-5 *2 (-1188)) (-5 *3 (-558)) (-5 *1 (-248))))) 
-(((*1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-248))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1296 *4)) (-4 *4 (-1246)) (-4 *1 (-245 *3 *4))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-305 (-973 (-558))))
-   (-5 *2
-    (-2 (|:| |varOrder| (-661 (-1206)))
-     (|:| |inhom| (-3 (-661 (-1296 (-791))) "failed"))
-     (|:| |hom| (-661 (-1296 (-791))))))
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-861)) (-5 *1 (-252 *3))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-251 *2)) (-4 *2 (-1238))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-251 *2)) (-4 *2 (-1238))))) 
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4426)) (-4 *1 (-251 *2)) (-4 *2 (-1238))))) 
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4426)) (-4 *1 (-251 *2)) (-4 *2 (-1238))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-558)) (-5 *1 (-248))))
+ ((*1 *2 *3) (-12 (-5 *3 (-661 (-1180))) (-5 *2 (-558)) (-5 *1 (-248))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-1294)) (-5 *1 (-248))))
+ ((*1 *2 *3) (-12 (-5 *3 (-661 (-1180))) (-5 *2 (-1294)) (-5 *1 (-248))))) 
+(((*1 *2 *3 *2) (-12 (-5 *2 (-1180)) (-5 *3 (-558)) (-5 *1 (-248))))) 
+(((*1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-248))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1288 *4)) (-4 *4 (-1238)) (-4 *1 (-245 *3 *4))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-305 (-965 (-558))))
+   (-5 *2
+    (-2 (|:| |varOrder| (-661 (-1198)))
+     (|:| |inhom| (-3 (-661 (-1288 (-791))) "failed"))
+     (|:| |hom| (-661 (-1288 (-791))))))
    (-5 *1 (-243))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1130)) (-4 *1 (-242 *3))))
- ((*1 *1) (-12 (-4 *1 (-242 *2)) (-4 *2 (-1130))))) 
-(((*1 *1) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1232)))))) 
-(((*1 *1 *2) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1232)))))) 
-(((*1 *1 *2) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1232)))))) 
-(((*1 *1 *2) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1232)))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1122)) (-4 *1 (-242 *3))))
+ ((*1 *1) (-12 (-4 *1 (-242 *2)) (-4 *2 (-1122))))) 
+(((*1 *1) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1224)))))) 
+(((*1 *1 *2) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1224)))))) 
+(((*1 *1 *2) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1224)))))) 
+(((*1 *1 *2) (-12 (-5 *1 (-231 *2)) (-4 *2 (-13 (-376) (-1224)))))) 
 (((*1 *2 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230))))
  ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230))))) 
 (((*1 *2 *2) (-12 (-5 *2 (-229)) (-5 *1 (-230))))
  ((*1 *2 *2) (-12 (-5 *2 (-171 (-229))) (-5 *1 (-230))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-229))))) 
 (((*1 *2 *3 *4 *5 *5 *2)
-  (|partial| -12 (-5 *2 (-114)) (-5 *3 (-973 *6)) (-5 *4 (-1206))
-   (-5 *5 (-863 *7)) (-4 *6 (-13 (-464) (-1067 (-558)) (-658 (-558))))
-   (-4 *7 (-13 (-1232) (-29 *6))) (-5 *1 (-228 *6 *7))))
+  (|partial| -12 (-5 *2 (-114)) (-5 *3 (-965 *6)) (-5 *4 (-1198))
+   (-5 *5 (-855 *7)) (-4 *6 (-13 (-464) (-1059 (-558)) (-658 (-558))))
+   (-4 *7 (-13 (-1224) (-29 *6))) (-5 *1 (-228 *6 *7))))
  ((*1 *2 *3 *4 *4 *2)
-  (|partial| -12 (-5 *2 (-114)) (-5 *3 (-1200 *6)) (-5 *4 (-863 *6))
-   (-4 *6 (-13 (-1232) (-29 *5)))
-   (-4 *5 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-228 *5 *6))))) 
+  (|partial| -12 (-5 *2 (-114)) (-5 *3 (-1192 *6)) (-5 *4 (-855 *6))
+   (-4 *6 (-13 (-1224) (-29 *5)))
+   (-4 *5 (-13 (-464) (-1059 (-558)) (-658 (-558)))) (-5 *1 (-228 *5 *6))))) 
 (((*1 *2 *3 *4 *2 *2 *5)
-  (|partial| -12 (-5 *2 (-863 *4)) (-5 *3 (-628 *4)) (-5 *5 (-114))
-   (-4 *4 (-13 (-1232) (-29 *6)))
-   (-4 *6 (-13 (-464) (-1067 (-558)) (-658 (-558)))) (-5 *1 (-228 *6 *4))))) 
+  (|partial| -12 (-5 *2 (-855 *4)) (-5 *3 (-628 *4)) (-5 *5 (-114))
+   (-4 *4 (-13 (-1224) (-29 *6)))
+   (-4 *6 (-13 (-464) (-1059 (-558)) (-658 (-558)))) (-5 *1 (-228 *6 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1188)) (-4 *4 (-13 (-464) (-1067 (-558)) (-658 (-558))))
-   (-5 *2 (-114)) (-5 *1 (-228 *4 *5)) (-4 *5 (-13 (-1232) (-29 *4)))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1078)) (-14 *3 (-661 (-1206)))))
+  (-12 (-5 *3 (-1180)) (-4 *4 (-13 (-464) (-1059 (-558)) (-658 (-558))))
+   (-5 *2 (-114)) (-5 *1 (-228 *4 *5)) (-4 *5 (-13 (-1224) (-29 *4)))))) 
+(((*1 *1 *1) (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1070)) (-14 *3 (-661 (-1198)))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-227 *2 *3)) (-4 *2 (-13 (-1078) (-869)))
-   (-14 *3 (-661 (-1206)))))) 
+  (-12 (-5 *1 (-227 *2 *3)) (-4 *2 (-13 (-1070) (-861)))
+   (-14 *3 (-661 (-1198)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-114)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1078))
-   (-14 *4 (-661 (-1206)))))
+  (-12 (-5 *2 (-114)) (-5 *1 (-50 *3 *4)) (-4 *3 (-1070))
+   (-14 *4 (-661 (-1198)))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-114)) (-5 *1 (-227 *3 *4)) (-4 *3 (-13 (-1078) (-869)))
-   (-14 *4 (-661 (-1206)))))) 
+  (-12 (-5 *2 (-114)) (-5 *1 (-227 *3 *4)) (-4 *3 (-13 (-1070) (-861)))
+   (-14 *4 (-661 (-1198)))))) 
 (((*1 *1 *2)
-  (-12 (-5 *2 (-326 *3)) (-4 *3 (-13 (-1078) (-869))) (-5 *1 (-227 *3 *4))
-   (-14 *4 (-661 (-1206)))))) 
+  (-12 (-5 *2 (-326 *3)) (-4 *3 (-13 (-1070) (-861))) (-5 *1 (-227 *3 *4))
+   (-14 *4 (-661 (-1198)))))) 
 (((*1 *1 *1)
-  (-12 (-5 *1 (-227 *2 *3)) (-4 *2 (-13 (-1078) (-869)))
-   (-14 *3 (-661 (-1206)))))) 
+  (-12 (-5 *1 (-227 *2 *3)) (-4 *2 (-13 (-1070) (-861)))
+   (-14 *3 (-661 (-1198)))))) 
 (((*1 *2 *3 *4 *5 *5 *6)
-  (-12 (-5 *4 (-1206)) (-5 *6 (-114))
-   (-4 *7 (-13 (-319) (-149) (-1067 (-558)) (-658 (-558))))
-   (-4 *3 (-13 (-1232) (-987) (-29 *7)))
+  (-12 (-5 *4 (-1198)) (-5 *6 (-114))
+   (-4 *7 (-13 (-319) (-149) (-1059 (-558)) (-658 (-558))))
+   (-4 *3 (-13 (-1224) (-979) (-29 *7)))
    (-5 *2
-    (-3 (|:| |f1| (-863 *3)) (|:| |f2| (-661 (-863 *3))) (|:| |fail| "failed")
+    (-3 (|:| |f1| (-855 *3)) (|:| |f2| (-661 (-855 *3))) (|:| |fail| "failed")
      (|:| |pole| "potentialPole")))
-   (-5 *1 (-223 *7 *3)) (-5 *5 (-863 *3))))) 
+   (-5 *1 (-223 *7 *3)) (-5 *5 (-855 *3))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-419 (-558))) (-5 *1 (-221))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-363)) (-5 *2 (-114)) (-5 *1 (-220 *4 *3)) (-4 *3 (-1272 *4))))) 
+  (-12 (-4 *4 (-363)) (-5 *2 (-114)) (-5 *1 (-220 *4 *3)) (-4 *3 (-1264 *4))))) 
 (((*1 *2 *2 *3 *2)
-  (-12 (-5 *3 (-791)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) (-4 *2 (-1272 *4))))) 
+  (-12 (-5 *3 (-791)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) (-4 *2 (-1264 *4))))) 
 (((*1 *2 *2 *3 *2)
-  (-12 (-5 *3 (-791)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) (-4 *2 (-1272 *4))))) 
+  (-12 (-5 *3 (-791)) (-4 *4 (-363)) (-5 *1 (-220 *4 *2)) (-4 *2 (-1264 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-363)) (-5 *2 (-661 (-2 (|:| |deg| (-791)) (|:| -3051 *3))))
-   (-5 *1 (-220 *4 *3)) (-4 *3 (-1272 *4))))) 
+  (-12 (-4 *4 (-363)) (-5 *2 (-661 (-2 (|:| |deg| (-791)) (|:| -2974 *3))))
+   (-5 *1 (-220 *4 *3)) (-4 *3 (-1264 *4))))) 
 (((*1 *2 *3 *4)
   (-12 (-5 *4 (-114)) (-4 *5 (-363))
    (-5 *2
     (-2 (|:| |cont| *5)
-     (|:| -1995 (-661 (-2 (|:| |irr| *3) (|:| -2634 (-558)))))))
-   (-5 *1 (-220 *5 *3)) (-4 *3 (-1272 *5))))) 
+     (|:| -1987 (-661 (-2 (|:| |irr| *3) (|:| -2626 (-558)))))))
+   (-5 *1 (-220 *5 *3)) (-4 *3 (-1264 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1 *2 *2)) (-4 *5 (-376)) (-4 *6 (-1272 (-419 *2)))
-   (-4 *2 (-1272 *5)) (-5 *1 (-219 *5 *2 *6 *3)) (-4 *3 (-355 *5 *2 *6))))) 
+  (-12 (-5 *4 (-1 *2 *2)) (-4 *5 (-376)) (-4 *6 (-1264 (-419 *2)))
+   (-4 *2 (-1264 *5)) (-5 *1 (-219 *5 *2 *6 *3)) (-4 *3 (-355 *5 *2 *6))))) 
 (((*1 *2 *1 *3 *2)
-  (-12 (-5 *3 (-791)) (-5 *1 (-216 *4 *2)) (-14 *4 (-946)) (-4 *2 (-1130))))) 
+  (-12 (-5 *3 (-791)) (-5 *1 (-216 *4 *2)) (-14 *4 (-938)) (-4 *2 (-1122))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
@@ -14889,7 +14801,7 @@
            (-2 (|:| |start| (-229)) (|:| |finish| (-229)) (|:| |grid| (-791))
             (|:| |boundaryType| (-558)) (|:| |dStart| (-709 (-229)))
             (|:| |dFinish| (-709 (-229))))))
-     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1188))
+     (|:| |f| (-661 (-661 (-326 (-229))))) (|:| |st| (-1180))
      (|:| |tol| (-229))))
    (-5 *2 (-114)) (-5 *1 (-213))))) 
 (((*1 *2 *3 *3 *4)
@@ -14900,7 +14812,7 @@
   (-12
    (-5 *3
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *2 (-391)) (-5 *1 (-208))))) 
@@ -14908,7 +14820,7 @@
   (-12
    (-5 *3
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *2 (-391)) (-5 *1 (-208))))) 
@@ -14916,7 +14828,7 @@
   (-12
    (-5 *3
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *2 (-391)) (-5 *1 (-208))))) 
@@ -14924,7 +14836,7 @@
   (-12
    (-5 *3
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *2 (-391)) (-5 *1 (-208))))) 
@@ -14932,7 +14844,7 @@
   (-12
    (-5 *3
     (-2 (|:| |xinit| (-229)) (|:| |xend| (-229))
-     (|:| |fn| (-1296 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
+     (|:| |fn| (-1288 (-326 (-229)))) (|:| |yinit| (-661 (-229)))
      (|:| |intvals| (-661 (-229))) (|:| |g| (-326 (-229)))
      (|:| |abserr| (-229)) (|:| |relerr| (-229))))
    (-5 *2 (-2 (|:| |stiffnessFactor| (-391)) (|:| |stabilityFactor| (-391))))
@@ -14947,37 +14859,37 @@
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *2 (-558)) (-5 *1 (-207))))) 
 (((*1 *2 *3)
   (|partial| -12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *2 (-661 (-229))) (-5 *1 (-207))))) 
 (((*1 *2 *3)
   (|partial| -12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
-   (-5 *2 (-2 (|:| -2978 (-115)) (|:| |w| (-229)))) (-5 *1 (-207))))) 
-(((*1 *2 *3 *3 *2) (-12 (-5 *2 (-1064)) (-5 *3 (-1206)) (-5 *1 (-195))))) 
+   (-5 *2 (-2 (|:| -2909 (-115)) (|:| |w| (-229)))) (-5 *1 (-207))))) 
+(((*1 *2 *3 *3 *2) (-12 (-5 *2 (-1056)) (-5 *3 (-1198)) (-5 *1 (-195))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *2 (-391)) (-5 *1 (-195))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *2
     (-3 (|:| |continuous| "Continuous at the end points")
@@ -14989,8 +14901,8 @@
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1206)) (|:| |fn| (-326 (-229)))
-     (|:| -1646 (-1118 (-863 (-229)))) (|:| |abserr| (-229))
+    (-2 (|:| |var| (-1198)) (|:| |fn| (-326 (-229)))
+     (|:| -1638 (-1110 (-855 (-229)))) (|:| |abserr| (-229))
      (|:| |relerr| (-229))))
    (-5 *2
     (-3 (|:| |finite| "The range is finite")
@@ -14999,162 +14911,162 @@
      (|:| |bothInfinite| "Both top and bottom points are infinite")
      (|:| |notEvaluated| "Range not yet evaluated")))
    (-5 *1 (-195))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-417 (-1200 (-558)))) (-5 *1 (-194)) (-5 *3 (-558))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-661 (-1200 (-558)))) (-5 *1 (-194)) (-5 *3 (-558))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-417 (-1192 (-558)))) (-5 *1 (-194)) (-5 *3 (-558))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-661 (-1192 (-558)))) (-5 *1 (-194)) (-5 *3 (-558))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-661 (-558))) (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
+  (-12 (-5 *3 (-661 (-558))) (-5 *2 (-1200 (-419 (-558)))) (-5 *1 (-193))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-661 (-946))) (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
+  (-12 (-5 *3 (-661 (-938))) (-5 *2 (-1200 (-419 (-558)))) (-5 *1 (-193))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-1200 (-419 (-558)))) (-5 *1 (-193))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-1200 (-419 (-558)))) (-5 *1 (-193))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-1208 (-419 (-558)))) (-5 *2 (-419 (-558))) (-5 *1 (-193))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-946)) (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-946)) (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-946)) (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-946)) (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-946)) (-5 *2 (-1208 (-419 (-558)))) (-5 *1 (-193))))) 
-(((*1 *2 *3)
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 (((*1 *1) (-12 (-4 *1 (-168 *2)) (-4 *2 (-175))))) 
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 (((*1 *2 *1)
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+  (-12 (-4 *1 (-168 *3)) (-4 *3 (-175)) (-4 *3 (-1081)) (-4 *3 (-1224))
    (-5 *2 (-2 (|:| |r| *3) (|:| |phi| *3)))))) 
 (((*1 *1 *1 *1) (-5 *1 (-163)))
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 (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-160 *3 *2)) (-4 *2 (-433 *3))))
  ((*1 *2 *2 *3)
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- ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1206))))
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+ ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1198))))
  ((*1 *1 *1) (-4 *1 (-162)))) 
 (((*1 *2 *2 *3)
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+  (-12 (-5 *3 (-1198)) (-4 *4 (-569)) (-5 *1 (-160 *4 *2)) (-4 *2 (-433 *4))))
  ((*1 *2 *2 *3)
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+  (-12 (-5 *3 (-1113 *2)) (-4 *2 (-433 *4)) (-4 *4 (-569))
    (-5 *1 (-160 *4 *2))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-1121 *1)) (-4 *1 (-162))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1206))))) 
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-1113 *1)) (-4 *1 (-162))))
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-162)) (-5 *2 (-1198))))) 
 (((*1 *2 *2 *2) (-12 (-5 *1 (-161 *2)) (-4 *2 (-557))))) 
 (((*1 *2 *2 *2) (-12 (-5 *1 (-161 *2)) (-4 *2 (-557))))) 
 (((*1 *1 *1 *1) (-4 *1 (-145)))
@@ -15184,56 +15096,56 @@
    (-4 *4 (-569))))) 
 (((*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-160 *3 *2)) (-4 *2 (-433 *3))))) 
 (((*1 *1) (-5 *1 (-159)))) 
-(((*1 *2) (-12 (-5 *2 (-946)) (-5 *1 (-159))))) 
+(((*1 *2) (-12 (-5 *2 (-938)) (-5 *1 (-159))))) 
 (((*1 *2 *3 *4 *4 *4 *4)
   (-12 (-5 *4 (-229))
    (-5 *2
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-     (|:| |yValues| (-1118 *4))))
-   (-5 *1 (-155)) (-5 *3 (-661 (-661 (-970 *4))))))) 
+    (-2 (|:| |brans| (-661 (-661 (-962 *4)))) (|:| |xValues| (-1110 *4))
+     (|:| |yValues| (-1110 *4))))
+   (-5 *1 (-155)) (-5 *3 (-661 (-661 (-962 *4))))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-952))
+  (-12 (-5 *3 (-944))
    (-5 *2
-    (-2 (|:| |brans| (-661 (-661 (-970 (-229)))))
-     (|:| |xValues| (-1118 (-229))) (|:| |yValues| (-1118 (-229)))))
+    (-2 (|:| |brans| (-661 (-661 (-962 (-229)))))
+     (|:| |xValues| (-1110 (-229))) (|:| |yValues| (-1110 (-229)))))
    (-5 *1 (-155))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *3 (-952)) (-5 *4 (-419 (-558)))
+  (-12 (-5 *3 (-944)) (-5 *4 (-419 (-558)))
    (-5 *2
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-     (|:| |xValues| (-1118 (-229))) (|:| |yValues| (-1118 (-229)))))
+    (-2 (|:| |brans| (-661 (-661 (-962 (-229)))))
+     (|:| |xValues| (-1110 (-229))) (|:| |yValues| (-1110 (-229)))))
    (-5 *1 (-155))))) 
 (((*1 *1 *2)
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+   (-14 *5 (-1014 *3 *4))))) 
 (((*1 *2 *3 *1)
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 (((*1 *1 *1)
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      (|:| |c2| (-419 *5)) (|:| |deg| (-791))))
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 (((*1 *2 *3 *4)
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+   (-5 *1 (-150 *5 *6 *7)) (-5 *4 (-791)) (-4 *7 (-1264 *3))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-4 *4 (-1251)) (-4 *5 (-1272 *4))
+  (|partial| -12 (-4 *4 (-1243)) (-4 *5 (-1264 *4))
    (-5 *2 (-2 (|:| |radicand| (-419 *5)) (|:| |deg| (-791))))
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+   (-5 *1 (-150 *4 *5 *3)) (-4 *3 (-1264 (-419 *5)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-1251)) (-4 *5 (-1272 *4))
-   (-5 *2 (-2 (|:| -4461 (-419 *5)) (|:| |poly| *3))) (-5 *1 (-150 *4 *5 *3))
-   (-4 *3 (-1272 (-419 *5)))))) 
+  (-12 (-4 *4 (-1243)) (-4 *5 (-1264 *4))
+   (-5 *2 (-2 (|:| -4384 (-419 *5)) (|:| |poly| *3))) (-5 *1 (-150 *4 *5 *3))
+   (-4 *3 (-1264 (-419 *5)))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-146))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-146))))
+(((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-146))))
  ((*1 *1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-146))))) 
 (((*1 *1) (-5 *1 (-146)))) 
 (((*1 *1) (-5 *1 (-146)))) 
@@ -15251,12 +15163,12 @@
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-146))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-661 (-146))) (-5 *1 (-143))))
- ((*1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-143))))) 
+ ((*1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-143))))) 
 (((*1 *1) (-5 *1 (-143)))) 
 (((*1 *1) (-5 *1 (-143)))) 
 (((*1 *1) (-5 *1 (-143)))) 
 (((*1 *1) (-5 *1 (-143)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-859))) (-5 *1 (-142))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-661 (-851))) (-5 *1 (-142))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-661 (-187 (-141)))) (-5 *1 (-142))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-661 (-187 (-141)))) (-5 *1 (-142))))) 
 (((*1 *1 *1 *2)
@@ -15276,7 +15188,7 @@
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-136))))) 
 (((*1 *2) (-12 (-5 *2 (-114)) (-5 *1 (-136))))) 
 (((*1 *2 *2) (-12 (-5 *2 (-114)) (-5 *1 (-136))))) 
-(((*1 *2 *1 *3) (-12 (-4 *1 (-134)) (-5 *3 (-791)) (-5 *2 (-1302))))) 
+(((*1 *2 *1 *3) (-12 (-4 *1 (-134)) (-5 *3 (-791)) (-5 *2 (-1294))))) 
 (((*1 *1 *1 *1) (|partial| -4 *1 (-133)))) 
 (((*1 *1) (-5 *1 (-132)))) 
 (((*1 *1) (-5 *1 (-132)))) 
@@ -15285,36 +15197,36 @@
 (((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-131))))) 
 (((*1 *2 *1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-131))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-130))))) 
-(((*1 *1 *1 *2 *1) (-12 (-5 *1 (-129 *2)) (-4 *2 (-1130))))
- ((*1 *1 *2) (-12 (-5 *1 (-129 *2)) (-4 *2 (-1130))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-869)) (-5 *1 (-128 *3))))) 
-(((*1 *1 *1 *2 *1) (-12 (-4 *1 (-127 *2)) (-4 *2 (-1130))))) 
+(((*1 *1 *1 *2 *1) (-12 (-5 *1 (-129 *2)) (-4 *2 (-1122))))
+ ((*1 *1 *2) (-12 (-5 *1 (-129 *2)) (-4 *2 (-1122))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-861)) (-5 *1 (-128 *3))))) 
+(((*1 *1 *1 *2 *1) (-12 (-4 *1 (-127 *2)) (-4 *2 (-1122))))) 
 (((*1 *1 *1 *1) (-5 *1 (-114))) ((*1 *1 *1 *1) (-4 *1 (-125)))) 
 (((*1 *1 *1 *1) (-5 *1 (-114))) ((*1 *1 *1 *1) (-4 *1 (-125)))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-869)) (-5 *1 (-123 *3))))) 
-(((*1 *1 *2 *1) (-12 (-5 *1 (-123 *2)) (-4 *2 (-869))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-114)) (-5 *1 (-122 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-122 *3)) (-4 *3 (-1272 (-558)))))
- ((*1 *2 *2) (-12 (-5 *2 (-791)) (-5 *1 (-122 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-114)) (-5 *1 (-122 *3)) (-4 *3 (-1272 (-558)))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-114)) (-5 *1 (-122 *3)) (-4 *3 (-1272 (-558)))))) 
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4503)) (-4 *1 (-121 *2)) (-4 *2 (-1246))))) 
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4503)) (-4 *1 (-121 *2)) (-4 *2 (-1246))))) 
-(((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-376) (-1067 (-419 *2)))) (-5 *2 (-558))
-   (-5 *1 (-117 *4 *3)) (-4 *3 (-1272 *4))))) 
-(((*1 *2 *3) (|partial| -12 (-5 *3 (-115)) (-5 *1 (-116 *2)) (-4 *2 (-1130))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-115)) (-5 *1 (-116 *3)) (-4 *3 (-1130))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-861)) (-5 *1 (-123 *3))))) 
+(((*1 *1 *2 *1) (-12 (-5 *1 (-123 *2)) (-4 *2 (-861))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-114)) (-5 *1 (-122 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2) (-12 (-5 *2 (-791)) (-5 *1 (-122 *3)) (-4 *3 (-1264 (-558)))))
+ ((*1 *2 *2) (-12 (-5 *2 (-791)) (-5 *1 (-122 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-114)) (-5 *1 (-122 *3)) (-4 *3 (-1264 (-558)))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-114)) (-5 *1 (-122 *3)) (-4 *3 (-1264 (-558)))))) 
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4426)) (-4 *1 (-121 *2)) (-4 *2 (-1238))))) 
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -4426)) (-4 *1 (-121 *2)) (-4 *2 (-1238))))) 
+(((*1 *2 *3)
+  (-12 (-4 *4 (-13 (-376) (-1059 (-419 *2)))) (-5 *2 (-558))
+   (-5 *1 (-117 *4 *3)) (-4 *3 (-1264 *4))))) 
+(((*1 *2 *3) (|partial| -12 (-5 *3 (-115)) (-5 *1 (-116 *2)) (-4 *2 (-1122))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-115)) (-5 *1 (-116 *3)) (-4 *3 (-1122))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-115)) (-5 *3 (-661 (-1 *4 (-661 *4)))) (-4 *4 (-1130))
+  (-12 (-5 *2 (-115)) (-5 *3 (-661 (-1 *4 (-661 *4)))) (-4 *4 (-1122))
    (-5 *1 (-116 *4))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1130)) (-5 *1 (-116 *4))))
+  (-12 (-5 *2 (-115)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1122)) (-5 *1 (-116 *4))))
  ((*1 *2 *3)
   (|partial| -12 (-5 *3 (-115)) (-5 *2 (-661 (-1 *4 (-661 *4))))
-   (-5 *1 (-116 *4)) (-4 *4 (-1130))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-661 (-992))) (-5 *1 (-109))))
- ((*1 *2 *1) (-12 (-5 *2 (-45 (-1188) (-793))) (-5 *1 (-115))))) 
+   (-5 *1 (-116 *4)) (-4 *4 (-1122))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-661 (-984))) (-5 *1 (-109))))
+ ((*1 *2 *1) (-12 (-5 *2 (-45 (-1180) (-793))) (-5 *1 (-115))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-115))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-115))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-115))))) 
@@ -15322,100 +15234,100 @@
 (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-114) (-115) (-115))) (-5 *1 (-115))))) 
 (((*1 *2 *1 *3) (-12 (-5 *3 (-518)) (-5 *2 (-114)) (-5 *1 (-115))))) 
 (((*1 *1 *1 *2) (-12 (-5 *2 (-518)) (-5 *1 (-115))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-1188)) (-5 *1 (-115))))) 
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-1180)) (-5 *1 (-115))))) 
 (((*1 *1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-793)) (-5 *1 (-115))))
- ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1188)) (-5 *3 (-793)) (-5 *1 (-115))))) 
-(((*1 *1 *1 *2) (-12 (-5 *2 (-45 (-1188) (-793))) (-5 *1 (-115))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-661 (-992))) (-5 *1 (-109))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1246)) (-4 *1 (-107 *3))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1246))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1246))))) 
-(((*1 *2) (-12 (-5 *2 (-661 (-1206))) (-5 *1 (-105))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-1206))
-   (-5 *2
-    (-2 (|:| |zeros| (-1184 (-229))) (|:| |ones| (-1184 (-229)))
-     (|:| |singularities| (-1184 (-229)))))
+ ((*1 *1 *1 *2 *3) (-12 (-5 *2 (-1180)) (-5 *3 (-793)) (-5 *1 (-115))))) 
+(((*1 *1 *1 *2) (-12 (-5 *2 (-45 (-1180) (-793))) (-5 *1 (-115))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-518)) (-5 *3 (-661 (-984))) (-5 *1 (-109))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1238)) (-4 *1 (-107 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1238))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1238))))) 
+(((*1 *2) (-12 (-5 *2 (-661 (-1198))) (-5 *1 (-105))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-1198))
+   (-5 *2
+    (-2 (|:| |zeros| (-1176 (-229))) (|:| |ones| (-1176 (-229)))
+     (|:| |singularities| (-1176 (-229)))))
    (-5 *1 (-105))))) 
 (((*1 *2 *3)
-  (-12 (|has| *2 (-6 (-4504 "*"))) (-4 *5 (-385 *2)) (-4 *6 (-385 *2))
-   (-4 *2 (-1078)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1272 *2))
+  (-12 (|has| *2 (-6 (-4427 "*"))) (-4 *5 (-385 *2)) (-4 *6 (-385 *2))
+   (-4 *2 (-1070)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1264 *2))
    (-4 *4 (-706 *2 *5 *6))))) 
 (((*1 *2 *3 *3)
-  (-12 (|has| *2 (-6 (-4504 "*"))) (-4 *5 (-385 *2)) (-4 *6 (-385 *2))
-   (-4 *2 (-1078)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1272 *2))
+  (-12 (|has| *2 (-6 (-4427 "*"))) (-4 *5 (-385 *2)) (-4 *6 (-385 *2))
+   (-4 *2 (-1070)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1264 *2))
    (-4 *4 (-706 *2 *5 *6))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-1078)) (-4 *2 (-706 *4 *5 *6)) (-5 *1 (-104 *4 *3 *2 *5 *6))
-   (-4 *3 (-1272 *4)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))))) 
+  (-12 (-4 *4 (-1070)) (-4 *2 (-706 *4 *5 *6)) (-5 *1 (-104 *4 *3 *2 *5 *6))
+   (-4 *3 (-1264 *4)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-1078)) (-4 *2 (-706 *4 *5 *6)) (-5 *1 (-104 *4 *3 *2 *5 *6))
-   (-4 *3 (-1272 *4)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-791)) (-5 *1 (-103 *3)) (-4 *3 (-1130))))) 
-(((*1 *1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1130)) (-5 *1 (-103 *3))))) 
+  (-12 (-4 *4 (-1070)) (-4 *2 (-706 *4 *5 *6)) (-5 *1 (-104 *4 *3 *2 *5 *6))
+   (-4 *3 (-1264 *4)) (-4 *5 (-385 *4)) (-4 *6 (-385 *4))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-791)) (-5 *1 (-103 *3)) (-4 *3 (-1122))))) 
+(((*1 *1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1122)) (-5 *1 (-103 *3))))) 
 (((*1 *1 *1 *1 *2)
-  (-12 (-5 *2 (-1 *3 *3 *3 *3 *3)) (-4 *3 (-1130)) (-5 *1 (-103 *3))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1 *2 *2 *2)) (-5 *1 (-103 *2)) (-4 *2 (-1130))))) 
+  (-12 (-5 *2 (-1 *3 *3 *3 *3 *3)) (-4 *3 (-1122)) (-5 *1 (-103 *3))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1 *2 *2 *2)) (-5 *1 (-103 *2)) (-4 *2 (-1122))))) 
 (((*1 *1 *1 *2 *3)
-  (-12 (-5 *3 (-1 (-661 *2) *2 *2 *2)) (-4 *2 (-1130)) (-5 *1 (-103 *2))))
+  (-12 (-5 *3 (-1 (-661 *2) *2 *2 *2)) (-4 *2 (-1122)) (-5 *1 (-103 *2))))
  ((*1 *1 *1 *2 *3)
-  (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1130)) (-5 *1 (-103 *2))))) 
+  (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1122)) (-5 *1 (-103 *2))))) 
 (((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-114))))) 
 (((*1 *2 *3 *3)
   (-12 (-4 *4 (-13 (-464) (-149))) (-5 *2 (-417 *3)) (-5 *1 (-100 *4 *3))
-   (-4 *3 (-1272 *4))))
+   (-4 *3 (-1264 *4))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1272 *5)) (-4 *5 (-13 (-464) (-149)))
+  (-12 (-5 *4 (-661 *3)) (-4 *3 (-1264 *5)) (-4 *5 (-13 (-464) (-149)))
    (-5 *2 (-417 *3)) (-5 *1 (-100 *5 *3))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 (-558))) (-4 *3 (-1078)) (-5 *1 (-99 *3))))
- ((*1 *1 *2 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1078)) (-5 *1 (-99 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1078)) (-5 *1 (-99 *3))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-391)) (-5 *1 (-97))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-391)) (-5 *1 (-97))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-391)) (-5 *1 (-97))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-391)) (-5 *1 (-97))))) 
-(((*1 *2 *3 *3) (-12 (-5 *3 (-1188)) (-5 *2 (-391)) (-5 *1 (-97))))) 
-(((*1 *2) (-12 (-5 *2 (-1302)) (-5 *1 (-97))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 (-558))) (-4 *3 (-1070)) (-5 *1 (-99 *3))))
+ ((*1 *1 *2 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1070)) (-5 *1 (-99 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1070)) (-5 *1 (-99 *3))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-391)) (-5 *1 (-97))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-391)) (-5 *1 (-97))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-391)) (-5 *1 (-97))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-391)) (-5 *1 (-97))))) 
+(((*1 *2 *3 *3) (-12 (-5 *3 (-1180)) (-5 *2 (-391)) (-5 *1 (-97))))) 
+(((*1 *2) (-12 (-5 *2 (-1294)) (-5 *1 (-97))))) 
 (((*1 *2 *2) (-12 (-5 *2 (-391)) (-5 *1 (-97))))) 
-(((*1 *2 *3 *3 *2) (-12 (-5 *2 (-391)) (-5 *3 (-1188)) (-5 *1 (-97))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-391)) (-5 *3 (-1188)) (-5 *1 (-97))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1130)) (-5 *1 (-91 *3))))) 
+(((*1 *2 *3 *3 *2) (-12 (-5 *2 (-391)) (-5 *3 (-1180)) (-5 *1 (-97))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-391)) (-5 *3 (-1180)) (-5 *1 (-97))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1122)) (-5 *1 (-91 *3))))) 
 (((*1 *2 *3 *4)
   (-12 (-4 *5 (-376)) (-4 *5 (-569))
    (-5 *2
-    (-2 (|:| |minor| (-661 (-946))) (|:| -3761 *3)
-     (|:| |minors| (-661 (-661 (-946)))) (|:| |ops| (-661 *3))))
-   (-5 *1 (-90 *5 *3)) (-5 *4 (-946)) (-4 *3 (-678 *5))))) 
+    (-2 (|:| |minor| (-661 (-938))) (|:| -3684 *3)
+     (|:| |minors| (-661 (-661 (-938)))) (|:| |ops| (-661 *3))))
+   (-5 *1 (-90 *5 *3)) (-5 *4 (-938)) (-4 *3 (-678 *5))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-569)) (-5 *2 (-1296 (-709 *4))) (-5 *1 (-90 *4 *5))
+  (-12 (-4 *4 (-569)) (-5 *2 (-1288 (-709 *4))) (-5 *1 (-90 *4 *5))
    (-5 *3 (-709 *4)) (-4 *5 (-678 *4))))) 
 (((*1 *2 *3 *4)
   (-12 (-4 *5 (-569))
-   (-5 *2 (-2 (|:| -1791 (-709 *5)) (|:| |vec| (-1296 (-661 (-946))))))
-   (-5 *1 (-90 *5 *3)) (-5 *4 (-946)) (-4 *3 (-678 *5))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-791)) (-5 *1 (-58 *3)) (-4 *3 (-1246))))
- ((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1246)) (-5 *1 (-58 *3))))) 
+   (-5 *2 (-2 (|:| -1783 (-709 *5)) (|:| |vec| (-1288 (-661 (-938))))))
+   (-5 *1 (-90 *5 *3)) (-5 *4 (-938)) (-4 *3 (-678 *5))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-791)) (-5 *1 (-58 *3)) (-4 *3 (-1238))))
+ ((*1 *1 *2) (-12 (-5 *2 (-661 *3)) (-4 *3 (-1238)) (-5 *1 (-58 *3))))) 
 (((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-558)) (-4 *1 (-57 *4 *3 *5)) (-4 *4 (-1246)) (-4 *3 (-385 *4))
+  (-12 (-5 *2 (-558)) (-4 *1 (-57 *4 *3 *5)) (-4 *4 (-1238)) (-4 *3 (-385 *4))
    (-4 *5 (-385 *4))))) 
 (((*1 *1 *1 *2 *3)
-  (-12 (-5 *2 (-558)) (-4 *1 (-57 *4 *5 *3)) (-4 *4 (-1246)) (-4 *5 (-385 *4))
+  (-12 (-5 *2 (-558)) (-4 *1 (-57 *4 *5 *3)) (-4 *4 (-1238)) (-4 *5 (-385 *4))
    (-4 *3 (-385 *4))))) 
 (((*1 *1) (-5 *1 (-55)))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-661 (-1206))) (-4 *4 (-1130))
-   (-4 *5 (-13 (-1078) (-909 *4) (-631 (-913 *4)))) (-5 *1 (-54 *4 *5 *2))
-   (-4 *2 (-13 (-433 *5) (-909 *4) (-631 (-913 *4))))))) 
+  (-12 (-5 *3 (-661 (-1198))) (-4 *4 (-1122))
+   (-4 *5 (-13 (-1070) (-901 *4) (-631 (-905 *4)))) (-5 *1 (-54 *4 *5 *2))
+   (-4 *2 (-13 (-433 *5) (-901 *4) (-631 (-905 *4))))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-661 (-1104 *4 *5 *2))) (-4 *4 (-1130))
-   (-4 *5 (-13 (-1078) (-909 *4) (-631 (-913 *4))))
-   (-4 *2 (-13 (-433 *5) (-909 *4) (-631 (-913 *4)))) (-5 *1 (-54 *4 *5 *2))))
+  (-12 (-5 *3 (-661 (-1096 *4 *5 *2))) (-4 *4 (-1122))
+   (-4 *5 (-13 (-1070) (-901 *4) (-631 (-905 *4))))
+   (-4 *2 (-13 (-433 *5) (-901 *4) (-631 (-905 *4)))) (-5 *1 (-54 *4 *5 *2))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *3 (-661 (-1104 *5 *6 *2))) (-5 *4 (-946)) (-4 *5 (-1130))
-   (-4 *6 (-13 (-1078) (-909 *5) (-631 (-913 *5))))
-   (-4 *2 (-13 (-433 *6) (-909 *5) (-631 (-913 *5)))) (-5 *1 (-54 *5 *6 *2))))) 
-(((*1 *1 *2 *3) (-12 (-5 *2 (-1132)) (-5 *3 (-793)) (-5 *1 (-51))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1132)) (-5 *1 (-51))))) 
+  (-12 (-5 *3 (-661 (-1096 *5 *6 *2))) (-5 *4 (-938)) (-4 *5 (-1122))
+   (-4 *6 (-13 (-1070) (-901 *5) (-631 (-905 *5))))
+   (-4 *2 (-13 (-433 *6) (-901 *5) (-631 (-905 *5)))) (-5 *1 (-54 *5 *6 *2))))) 
+(((*1 *1 *2 *3) (-12 (-5 *2 (-1124)) (-5 *3 (-793)) (-5 *1 (-51))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1124)) (-5 *1 (-51))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-51))))) 
 (((*1 *2)
   (-12 (-4 *3 (-569)) (-5 *2 (-661 *4)) (-5 *1 (-43 *3 *4)) (-4 *4 (-430 *3))))) 
@@ -15455,897 +15367,880 @@
 (((*1 *2 *3)
   (-12 (-4 *4 (-569)) (-5 *2 (-791)) (-5 *1 (-43 *4 *3)) (-4 *3 (-430 *4))))) 
 (((*1 *2 *3 *2 *4)
-  (-12 (-5 *3 (-115)) (-5 *4 (-791)) (-4 *5 (-13 (-464) (-1067 (-558))))
+  (-12 (-5 *3 (-115)) (-5 *4 (-791)) (-4 *5 (-13 (-464) (-1059 (-558))))
    (-4 *5 (-569)) (-5 *1 (-41 *5 *2)) (-4 *2 (-433 *5))
    (-4 *2
     (-13 (-376) (-310)
-     (-10 -8 (-15 -3476 ((-1154 *5 (-628 $)) $))
-      (-15 -3475 ((-1154 *5 (-628 $)) $))
-      (-15 -4453 ($ (-1154 *5 (-628 $)))))))))) 
+     (-10 -8 (-15 -3399 ((-1146 *5 (-628 $)) $))
+      (-15 -3398 ((-1146 *5 (-628 $)) $))
+      (-15 -4376 ($ (-1146 *5 (-628 $)))))))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-464) (-1067 (-558)))) (-4 *3 (-569)) (-5 *1 (-41 *3 *2))
+  (-12 (-4 *3 (-13 (-464) (-1059 (-558)))) (-4 *3 (-569)) (-5 *1 (-41 *3 *2))
    (-4 *2 (-433 *3))
    (-4 *2
     (-13 (-376) (-310)
-     (-10 -8 (-15 -3476 ((-1154 *3 (-628 $)) $))
-      (-15 -3475 ((-1154 *3 (-628 $)) $))
-      (-15 -4453 ($ (-1154 *3 (-628 $)))))))))) 
+     (-10 -8 (-15 -3399 ((-1146 *3 (-628 $)) $))
+      (-15 -3398 ((-1146 *3 (-628 $)) $))
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 (((*1 *2 *2)
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+ (-4404 . 174) (-4405 . 30)) 
\ No newline at end of file