* algebra/term.spad.pamphlet (is?$OperatorCategory): New.

* algebra/op.spad.pamphlet (BasicOperator): Don't export is? here. Inherit it from OperatorCategory Symbol. * algebra/catdef.spad.pamphlet (LeftLinearSet): New category. (RightLinearSet): Likewise. (LinearSet): Likewise. (AbelianGroup): Extend LeftLinearSet Integer. (LeftModule): Extend LeftLinearSet R. (Module): Extend LinearSet R. (RightModule): Extend RightLinearSet R. * algebra/exposed.lsp.pamphlet: Expose LeftLinearSet, RightLinearSet, and LinearSet. * algebra/Makefile.pamphlet: Tidy.
author: dos-reis <gdr@axiomatics.org> 2009-05-31 20:49:02 +0000
committer: dos-reis <gdr@axiomatics.org> 2009-05-31 20:49:02 +0000
commit: 803d7a62fb91bb4083a0aaaaa20749574292e967 (patch)
tree: 96fa55d12fe4f5e203c239e140f533b7a2824852
parent: 748e67afa492ccf46498cfa33541327aa11ad584 (diff)
download: open-axiom-803d7a62fb91bb4083a0aaaaa20749574292e967.tar.gz
19 files changed, 25321 insertions, 24804 deletions
diff --git a/configure b/configure
index 561d59a0..74fa25d4 100755
--- a/configure
+++ b/configure
@@ -1,6 +1,6 @@
 #! /bin/sh
 # Guess values for system-dependent variables and create Makefiles.
-# Generated by GNU Autoconf 2.63 for OpenAxiom 1.3.0-2009-05-29.
+# Generated by GNU Autoconf 2.63 for OpenAxiom 1.3.0-2009-05-31.
 #
 # Report bugs to <open-axiom-bugs@lists.sf.net>.
 #
@@ -745,8 +745,8 @@ SHELL=${CONFIG_SHELL-/bin/sh}
 # Identity of this package.
 PACKAGE_NAME='OpenAxiom'
 PACKAGE_TARNAME='openaxiom'
-PACKAGE_VERSION='1.3.0-2009-05-29'
-PACKAGE_STRING='OpenAxiom 1.3.0-2009-05-29'
+PACKAGE_VERSION='1.3.0-2009-05-31'
+PACKAGE_STRING='OpenAxiom 1.3.0-2009-05-31'
 PACKAGE_BUGREPORT='open-axiom-bugs@lists.sf.net'
 
 ac_unique_file="src/Makefile.pamphlet"
@@ -1500,7 +1500,7 @@ if test "$ac_init_help" = "long"; then
   # Omit some internal or obsolete options to make the list less imposing.
   # This message is too long to be a string in the A/UX 3.1 sh.
   cat <<_ACEOF
-\`configure' configures OpenAxiom 1.3.0-2009-05-29 to adapt to many kinds of systems.
+\`configure' configures OpenAxiom 1.3.0-2009-05-31 to adapt to many kinds of systems.
 
 Usage: $0 [OPTION]... [VAR=VALUE]...
 
@@ -1570,7 +1570,7 @@ fi
 
 if test -n "$ac_init_help"; then
   case $ac_init_help in
-     short | recursive ) echo "Configuration of OpenAxiom 1.3.0-2009-05-29:";;
+     short | recursive ) echo "Configuration of OpenAxiom 1.3.0-2009-05-31:";;
    esac
   cat <<\_ACEOF
 
@@ -1672,7 +1672,7 @@ fi
 test -n "$ac_init_help" && exit $ac_status
 if $ac_init_version; then
   cat <<\_ACEOF
-OpenAxiom configure 1.3.0-2009-05-29
+OpenAxiom configure 1.3.0-2009-05-31
 generated by GNU Autoconf 2.63
 
 Copyright (C) 1992, 1993, 1994, 1995, 1996, 1998, 1999, 2000, 2001,
@@ -1686,7 +1686,7 @@ cat >config.log <<_ACEOF
 This file contains any messages produced by compilers while
 running configure, to aid debugging if configure makes a mistake.
 
-It was created by OpenAxiom $as_me 1.3.0-2009-05-29, which was
+It was created by OpenAxiom $as_me 1.3.0-2009-05-31, which was
 generated by GNU Autoconf 2.63.  Invocation command line was
 
   $ $0 $@
@@ -17686,7 +17686,7 @@ exec 6>&1
 # report actual input values of CONFIG_FILES etc. instead of their
 # values after options handling.
 ac_log="
-This file was extended by OpenAxiom $as_me 1.3.0-2009-05-29, which was
+This file was extended by OpenAxiom $as_me 1.3.0-2009-05-31, which was
 generated by GNU Autoconf 2.63.  Invocation command line was
 
   CONFIG_FILES    = $CONFIG_FILES
@@ -17749,7 +17749,7 @@ Report bugs to <bug-autoconf@gnu.org>."
 _ACEOF
 cat >>$CONFIG_STATUS <<_ACEOF || ac_write_fail=1
 ac_cs_version="\\
-OpenAxiom config.status 1.3.0-2009-05-29
+OpenAxiom config.status 1.3.0-2009-05-31
 configured by $0, generated by GNU Autoconf 2.63,
   with options \\"`$as_echo "$ac_configure_args" | sed 's/^ //; s/[\\""\`\$]/\\\\&/g'`\\"
 
diff --git a/configure.ac b/configure.ac
index 3cdbdbb2..d7f48606 100644
--- a/configure.ac
+++ b/configure.ac
@@ -1,6 +1,6 @@
 sinclude(config/open-axiom.m4)
 sinclude(config/aclocal.m4)
-AC_INIT([OpenAxiom], [1.3.0-2009-05-29], 
+AC_INIT([OpenAxiom], [1.3.0-2009-05-31], 
         [open-axiom-bugs@lists.sf.net])
 
 AC_CONFIG_AUX_DIR(config)
diff --git a/configure.ac.pamphlet b/configure.ac.pamphlet
index b9fcb246..8676fb99 100644
--- a/configure.ac.pamphlet
+++ b/configure.ac.pamphlet
@@ -1131,7 +1131,7 @@ information:
 <<Autoconf init>>=
 sinclude(config/open-axiom.m4)
 sinclude(config/aclocal.m4)
-AC_INIT([OpenAxiom], [1.3.0-2009-05-29], 
+AC_INIT([OpenAxiom], [1.3.0-2009-05-31], 
         [open-axiom-bugs@lists.sf.net])
 
 @
diff --git a/src/ChangeLog b/src/ChangeLog
index 529cd053..5d6974e8 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,19 @@
+2009-05-31  Gabriel Dos Reis  <gdr@cs.tamu.edu>
+
+	* algebra/term.spad.pamphlet (is?$OperatorCategory): New.
+	* algebra/op.spad.pamphlet (BasicOperator): Don't export is? here.
+	Inherit it from OperatorCategory Symbol.
+	* algebra/catdef.spad.pamphlet (LeftLinearSet): New category.
+	(RightLinearSet): Likewise.
+	(LinearSet): Likewise.
+	(AbelianGroup): Extend LeftLinearSet Integer.
+	(LeftModule): Extend LeftLinearSet R.
+	(Module): Extend LinearSet R.
+	(RightModule): Extend RightLinearSet R.
+	* algebra/exposed.lsp.pamphlet: Expose LeftLinearSet,
+	RightLinearSet, and LinearSet.
+	* algebra/Makefile.pamphlet: Tidy.
+
 2009-05-29  Gabriel Dos Reis  <gdr@cs.tamu.edu>
 
 	* algebra/catdef.spad.pamphlet (SetCategory): Provide default
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index cee9ae4c..db050ac9 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -301,11 +301,11 @@ $(OUT)/LOGIC.$(FASLEXT): $(OUT)/BASTYPE.$(FASLEXT)
 
 $(OUT)/SGROUP.$(FASLEXT) $(OUT)/SGROUP-.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 $(OUT)/ABELSG.$(FASLEXT) $(OUT)/ABELSG-.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
-$(OUT)/LMODULE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
-$(OUT)/RMODULE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
+$(OUT)/LMODULE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/LLINSET.$(FASLEXT)
+$(OUT)/RMODULE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/RLINSET.$(FASLEXT)
 $(OUT)/BMODULE.$(FASLEXT): $(OUT)/LMODULE.$(FASLEXT) \
 	$(OUT)/RMODULE.$(FASLEXT) $(OUT)/SGROUP.$(FASLEXT)
-$(OUT)/MODULE.$(FASLEXT): $(OUT)/BMODULE.$(FASLEXT)
+$(OUT)/MODULE.$(FASLEXT): $(OUT)/BMODULE.$(FASLEXT) $(OUT)/LINSET.$(FASLEXT)
 $(OUT)/ALGEBRA.$(FASLEXT): $(OUT)/MODULE.$(FASLEXT)
 $(OUT)/OAGROUP.$(FASLEXT): $(OUT)/OCAMON.$(FASLEXT)
 $(OUT)/OCAMON.$(FASLEXT): $(OUT)/OAMON.$(FASLEXT)
@@ -313,10 +313,13 @@ $(OUT)/OAMON.$(FASLEXT): $(OUT)/OASGP.$(FASLEXT)
 $(OUT)/OASGP.$(FASLEXT): $(OUT)/ORDSET.$(FASLEXT) $(OUT)/ABELSG.$(FASLEXT)
 $(OUT)/RNG.$(FASLEXT): $(OUT)/SGROUP.$(FASLEXT)
 
+$(OUT)/LLINSET.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
+$(OUT)/RLINSET.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
+$(OUT)/LINSET.$(FASLEXT): $(OUT)/LLINSET.$(FASLEXT) $(OUT)/RLINSET.$(FASLEXT)
+
 $(OUT)/CTORKIND.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 $(OUT)/IOMODE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 
-$(OUT)/REF.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/IDENT.$(FASLEXT)
 $(OUT)/PRINT.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
 $(OUT)/RTVALUE.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
 
@@ -330,7 +333,7 @@ axiom_algebra_layer_0 = \
   RMODULE  ALGEBRA  ALGEBRA- SGROUP   SGROUP-  ABELSG   \
   ABELSG-  ORDSET   ORDSET-  OASGP    FILECAT  SEXCAT   \
   MODULE   MODULE-  PID      OAGROUP  OCAMON   OAMON    \
-  RNG      ORDFIN                                       \
+  RNG      ORDFIN   LLINSET  RLINSET  LINSET            \
   MKBCFUNC MKRECORD MKUCFUNC DROPT1   PLOT1    ITFUN2   \
   ITFUN3   STREAM1  STREAM2  STREAM3  ANY1     SEGBIND2 \
   COMBOPC  EQ2      NONE1    CONDUIT  IOMODE   CTORKIND \
@@ -374,7 +377,7 @@ $(OUT)/BYTEORD.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 $(OUT)/RING.$(FASLEXT): $(OUT)/RNG.$(FASLEXT) $(OUT)/MONOID.$(FASLEXT) \
 	$(OUT)/LMODULE.$(FASLEXT) $(OUT)/KOERCE.$(FASLEXT)
 $(OUT)/MONOID.$(FASLEXT): $(OUT)/SGROUP.$(FASLEXT)
-$(OUT)/ABELGRP.$(FASLEXT): $(OUT)/CABMON.$(FASLEXT)
+$(OUT)/ABELGRP.$(FASLEXT): $(OUT)/CABMON.$(FASLEXT) $(OUT)/LLINSET.$(FASLEXT)
 $(OUT)/ABELMON.$(FASLEXT): $(OUT)/ABELSG.$(FASLEXT)
 $(OUT)/ORDRING.$(FASLEXT): $(OUT)/OAGROUP.$(FASLEXT) $(OUT)/RING.$(FASLEXT) \
 	$(OUT)/MONOID.$(FASLEXT)
@@ -388,17 +391,17 @@ $(OUT)/GCDDOM.$(FASLEXT): $(OUT)/INTDOM.$(FASLEXT)
 $(OUT)/UFD.$(FASLEXT): $(OUT)/GCDDOM.$(FASLEXT) $(OUT)/ES.$(FASLEXT)
 $(OUT)/ES.$(FASLEXT): $(OUT)/RING.$(FASLEXT) $(OUT)/CACHSET.$(FASLEXT) \
 	$(OUT)/REF.$(FASLEXT) $(OUT)/ALIST.$(FASLEXT) \
-	$(OUT)/PATAB.$(FASLEXT)
+	$(OUT)/PATAB.$(FASLEXT) $(OUT)/PRIMARR.$(FASLEXT)
 $(OUT)/CACHSET.$(FASLEXT): $(OUT)/ORDSET.$(FASLEXT)
 $(OUT)/ALIST.$(FASLEXT): $(OUT)/ALAGG.$(FASLEXT)
 $(OUT)/PATAB.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
 $(OUT)/BOOLEAN.$(FASLEXT): $(OUT)/PROPLOG.$(FASLEXT)
-$(OUT)/ES.$(FASLEXT): $(OUT)/PRIMARR.$(FASLEXT)
 $(OUT)/VECTCAT.$(FASLEXT): $(OUT)/RADCAT.$(FASLEXT)
 $(OUT)/IARRAY1.$(FASLEXT): $(OUT)/PRIMARR.$(FASLEXT)
 $(OUT)/PROPERTY.$(FASLEXT): $(OUT)/IDENT.$(FASLEXT)
 $(OUT)/BINDING.$(FASLEXT): $(OUT)/PROPERTY.$(FASLEXT)
 $(OUT)/OPERCAT.$(FASLEXT): $(OUT)/ARITY.$(FASLEXT)
+$(OUT)/REF.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/IDENT.$(FASLEXT)
 
 axiom_algebra_layer_1 = \
   ABELGRP  ABELGRP- ABELMON  ABELMON- FORTCAT   ITUPLE   \
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index ad0818cf..1d0e4a83 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -255,11 +255,11 @@ $(OUT)/LOGIC.$(FASLEXT): $(OUT)/BASTYPE.$(FASLEXT)
 
 $(OUT)/SGROUP.$(FASLEXT) $(OUT)/SGROUP-.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 $(OUT)/ABELSG.$(FASLEXT) $(OUT)/ABELSG-.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
-$(OUT)/LMODULE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
-$(OUT)/RMODULE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
+$(OUT)/LMODULE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/LLINSET.$(FASLEXT)
+$(OUT)/RMODULE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/RLINSET.$(FASLEXT)
 $(OUT)/BMODULE.$(FASLEXT): $(OUT)/LMODULE.$(FASLEXT) \
 	$(OUT)/RMODULE.$(FASLEXT) $(OUT)/SGROUP.$(FASLEXT)
-$(OUT)/MODULE.$(FASLEXT): $(OUT)/BMODULE.$(FASLEXT)
+$(OUT)/MODULE.$(FASLEXT): $(OUT)/BMODULE.$(FASLEXT) $(OUT)/LINSET.$(FASLEXT)
 $(OUT)/ALGEBRA.$(FASLEXT): $(OUT)/MODULE.$(FASLEXT)
 $(OUT)/OAGROUP.$(FASLEXT): $(OUT)/OCAMON.$(FASLEXT)
 $(OUT)/OCAMON.$(FASLEXT): $(OUT)/OAMON.$(FASLEXT)
@@ -267,10 +267,13 @@ $(OUT)/OAMON.$(FASLEXT): $(OUT)/OASGP.$(FASLEXT)
 $(OUT)/OASGP.$(FASLEXT): $(OUT)/ORDSET.$(FASLEXT) $(OUT)/ABELSG.$(FASLEXT)
 $(OUT)/RNG.$(FASLEXT): $(OUT)/SGROUP.$(FASLEXT)
 
+$(OUT)/LLINSET.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
+$(OUT)/RLINSET.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
+$(OUT)/LINSET.$(FASLEXT): $(OUT)/LLINSET.$(FASLEXT) $(OUT)/RLINSET.$(FASLEXT)
+
 $(OUT)/CTORKIND.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 $(OUT)/IOMODE.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 
-$(OUT)/REF.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/IDENT.$(FASLEXT)
 $(OUT)/PRINT.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
 $(OUT)/RTVALUE.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
 
@@ -284,7 +287,7 @@ axiom_algebra_layer_0 = \
   RMODULE  ALGEBRA  ALGEBRA- SGROUP   SGROUP-  ABELSG   \
   ABELSG-  ORDSET   ORDSET-  OASGP    FILECAT  SEXCAT   \
   MODULE   MODULE-  PID      OAGROUP  OCAMON   OAMON    \
-  RNG      ORDFIN                                       \
+  RNG      ORDFIN   LLINSET  RLINSET  LINSET            \
   MKBCFUNC MKRECORD MKUCFUNC DROPT1   PLOT1    ITFUN2   \
   ITFUN3   STREAM1  STREAM2  STREAM3  ANY1     SEGBIND2 \
   COMBOPC  EQ2      NONE1    CONDUIT  IOMODE   CTORKIND \
@@ -333,7 +336,7 @@ $(OUT)/BYTEORD.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
 $(OUT)/RING.$(FASLEXT): $(OUT)/RNG.$(FASLEXT) $(OUT)/MONOID.$(FASLEXT) \
 	$(OUT)/LMODULE.$(FASLEXT) $(OUT)/KOERCE.$(FASLEXT)
 $(OUT)/MONOID.$(FASLEXT): $(OUT)/SGROUP.$(FASLEXT)
-$(OUT)/ABELGRP.$(FASLEXT): $(OUT)/CABMON.$(FASLEXT)
+$(OUT)/ABELGRP.$(FASLEXT): $(OUT)/CABMON.$(FASLEXT) $(OUT)/LLINSET.$(FASLEXT)
 $(OUT)/ABELMON.$(FASLEXT): $(OUT)/ABELSG.$(FASLEXT)
 $(OUT)/ORDRING.$(FASLEXT): $(OUT)/OAGROUP.$(FASLEXT) $(OUT)/RING.$(FASLEXT) \
 	$(OUT)/MONOID.$(FASLEXT)
@@ -347,17 +350,17 @@ $(OUT)/GCDDOM.$(FASLEXT): $(OUT)/INTDOM.$(FASLEXT)
 $(OUT)/UFD.$(FASLEXT): $(OUT)/GCDDOM.$(FASLEXT) $(OUT)/ES.$(FASLEXT)
 $(OUT)/ES.$(FASLEXT): $(OUT)/RING.$(FASLEXT) $(OUT)/CACHSET.$(FASLEXT) \
 	$(OUT)/REF.$(FASLEXT) $(OUT)/ALIST.$(FASLEXT) \
-	$(OUT)/PATAB.$(FASLEXT)
+	$(OUT)/PATAB.$(FASLEXT) $(OUT)/PRIMARR.$(FASLEXT)
 $(OUT)/CACHSET.$(FASLEXT): $(OUT)/ORDSET.$(FASLEXT)
 $(OUT)/ALIST.$(FASLEXT): $(OUT)/ALAGG.$(FASLEXT)
 $(OUT)/PATAB.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT)
 $(OUT)/BOOLEAN.$(FASLEXT): $(OUT)/PROPLOG.$(FASLEXT)
-$(OUT)/ES.$(FASLEXT): $(OUT)/PRIMARR.$(FASLEXT)
 $(OUT)/VECTCAT.$(FASLEXT): $(OUT)/RADCAT.$(FASLEXT)
 $(OUT)/IARRAY1.$(FASLEXT): $(OUT)/PRIMARR.$(FASLEXT)
 $(OUT)/PROPERTY.$(FASLEXT): $(OUT)/IDENT.$(FASLEXT)
 $(OUT)/BINDING.$(FASLEXT): $(OUT)/PROPERTY.$(FASLEXT)
 $(OUT)/OPERCAT.$(FASLEXT): $(OUT)/ARITY.$(FASLEXT)
+$(OUT)/REF.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT) $(OUT)/IDENT.$(FASLEXT)
 
 axiom_algebra_layer_1 = \
   ABELGRP  ABELGRP- ABELMON  ABELMON- FORTCAT   ITUPLE   \
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet
index ae0d4f50..c7263464 100644
--- a/src/algebra/catdef.spad.pamphlet
+++ b/src/algebra/catdef.spad.pamphlet
@@ -1,14 +1,77 @@
 \documentclass{article}
 \usepackage{axiom}
-\begin{document}
+
 \title{\$SPAD/src/algebra catdef.spad}
-\author{James Davenport, Lalo Gonzalez-Vega}
+\author{James Davenport, Lalo Gonzalez-Vega, Gabriel Dos~Reis}
+
+\begin{document}
+
 \maketitle
 \begin{abstract}
 \end{abstract}
-\eject
 \tableofcontents
 \eject
+
+\section{Linear sets}
+
+<<category LLINSET LeftLinearSet>>=
+)abbrev category LLINSET LeftLinearSet
+++ Author: Gabriel Dos Reis
+++ Date Created: May 31, 2009
+++ Date Last Modified: May 31, 2009
+++ Description:
+++   A set is an \spad{R}-left linear set if it is stable by left-dilation
+++   by elements in the ring \spad{R}.  This category differs from
+++   \spad{LeftModule} in that no other assumption (such as addition)
+++   is made about the underlying set.
+++ See Also: RightLinearSet.
+LeftLinearSet(R: Rng): Category == SetCategory with
+   0: %                
+     ++ \spad{0} represents the origin of the linear set
+   zero?: % -> Boolean 
+     ++ \spad{zero? x} holds is \spad{x} is the origin.
+   *: (R,%) -> %       
+     ++ \spad{r*x} is the left-dilation of \spad{x} by \spad{r}.
+
+@
+
+<<category RLINSET RightLinearSet>>=
+)abbrev category RLINSET RightLinearSet
+++ Author: Gabriel Dos Reis
+++ Date Created: May 31, 2009
+++ Date Last Modified: May 31, 2009
+++ Description:
+++   A set is an \spad{R}-right linear set if it is stable by right-dilation
+++   by elements in the ring \spad{R}.  This category differs from
+++   \spad{RightModule} in that no other assumption (such as addition)
+++   is made about the underlying set.
+++ See Also: LeftLinearSet.
+RightLinearSet(R: Rng): Category == SetCategory with
+   0: %                
+     ++ \spad{0} represents the origin of the linear set
+   zero?: % -> Boolean 
+     ++ \spad{zero? x} holds is \spad{x} is the origin.
+   *: (%,R) -> %       
+     ++ \spad{r*x} is the left-dilation of \spad{x} by \spad{r}.
+
+@
+
+<<category LINSET LinearSet>>=
+)abbrev category LINSET LinearSet
+++ Author: Gabriel Dos Reis
+++ Date Created: May 31, 2009
+++ Date Last Modified: May 31, 2009
+++ Description:
+++   A set is an \spad{R}-linear set if it is stable by dilation
+++   by elements in the ring \spad{R}.  This category differs from
+++   \spad{Module} in that no other assumption (such as addition)
+++   is made about the underlying set.
+++ See Also: LeftLinearSet, RightLinearSet.
+LinearSet(R: Rng): Category == Join(LeftLinearSet R, RightLinearSet R)
+
+@
+
+
 \section{category ABELGRP AbelianGroup}
 <<category ABELGRP AbelianGroup>>=
 )abbrev category ABELGRP AbelianGroup
@@ -29,13 +92,10 @@
 ++   \spad{-(-x) = x}
 ++   \spad{x+(-x) = 0}
 -- following domain must be compiled with subsumption disabled
-AbelianGroup(): Category == CancellationAbelianMonoid with
-    --operations
-      "-": % -> %                      ++ -x is the additive inverse of x.
-      "-": (%,%) -> %                  ++ x-y is the difference of x and y
-                                       ++ i.e. \spad{x + (-y)}.
-                       -- subsumes the partial subtraction from previous
-      "*": (Integer,%) -> %            ++ n*x is the product of x by the integer n.
+AbelianGroup(): Category == Join(CancellationAbelianMonoid, LeftLinearSet Integer) with
+      -: % -> %           ++ \spad{-x} is the additive inverse of \spad{x}    
+      "-": (%,%) -> %     ++ \spad{x-y} is the difference of \spad{x} 
+                          ++ and \spad{y} i.e. \spad{x + (-y)}.
     add
       (x:% - y:%):% == x+(-y)
       subtractIfCan(x:%, y:%):Union(%, "failed") == (x-y) :: Union(%,"failed")
@@ -923,12 +983,10 @@ IntegralDomain(): Category ==
 ++   \spad{ (a*b)*x = a*(b*x) }
 ++   \spad{ (a+b)*x = (a*x)+(b*x) }
 ++   \spad{ a*(x+y) = (a*x)+(a*y) }
-LeftModule(R:Rng):Category == AbelianGroup with
-    --operations
-      "*": (R,%) -> %     ++ r*x returns the left multiplication of the module element x
-                          ++ by the ring element r.
+LeftModule(R:Rng):Category == Join(AbelianGroup, LeftLinearSet R)
 
 @
+
 \section{category LINEXP LinearlyExplicitRingOver}
 <<category LINEXP LinearlyExplicitRingOver>>=
 )abbrev category LINEXP LinearlyExplicitRingOver
@@ -972,7 +1030,7 @@ LinearlyExplicitRingOver(R:Ring): Category == Ring with
 ++   \spad{(a*b)*x = a*(b*x)}
 ++   \spad{(a+b)*x = (a*x)+(b*x)}
 ++   \spad{a*(x+y) = (a*x)+(a*y)}
-Module(R:CommutativeRing): Category == BiModule(R,R)
+Module(R:CommutativeRing): Category == Join(BiModule(R,R), LinearSet R)
   add
     if not(R is %) then x:%*r:R == r*x
 
@@ -1502,12 +1560,10 @@ PrincipalIdealDomain(): Category == GcdDomain with
 ++   \spad{ x*(a*b) = (x*a)*b }
 ++   \spad{ x*(a+b) = (x*a)+(x*b) }
 ++   \spad{ (x+y)*x = (x*a)+(y*a) }
-RightModule(R:Rng):Category == AbelianGroup with
-    --operations
-      "*": (%,R) -> %  ++ x*r returns the right multiplication of the module element x
-                       ++ by the ring element r.
+RightModule(R:Rng):Category == Join(AbelianGroup, RightLinearSet R)
 
 @
+
 \section{category RING Ring}
 <<category RING Ring>>=
 )abbrev category RING Ring
@@ -1524,7 +1580,6 @@ RightModule(R:Rng):Category == AbelianGroup with
 ++ The category of rings with unity, always associative, but
 ++ not necessarily commutative.
 
---Ring(): Category == Join(Rng,Monoid,LeftModule(%:Rng)) with
 Ring(): Category == Join(Rng,Monoid,LeftModule(%),CoercibleFrom Integer) with
     --operations
       characteristic: NonNegativeInteger
@@ -1784,6 +1839,9 @@ VectorSpace(S:Field): Category ==  Module(S) with
 <<category CABMON CancellationAbelianMonoid>>
 <<category ABELGRP AbelianGroup>>
 <<category RNG Rng>>
+<<category LLINSET LeftLinearSet>>
+<<category RLINSET RightLinearSet>>
+<<category LINSET LinearSet>>
 <<category LMODULE LeftModule>>
 <<category RMODULE RightModule>>
 <<category RING Ring>>
diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet
index c1ca17ae..5247a755 100644
--- a/src/algebra/exposed.lsp.pamphlet
+++ b/src/algebra/exposed.lsp.pamphlet
@@ -679,11 +679,13 @@
   (|KeyedDictionary| . KDAGG)
   (|LazyStreamAggregate| . LZSTAGG)
   (|LeftAlgebra| . LALG)
+  (|LeftLinearSet| . LLINSET)
   (|LeftModule| . LMODULE)
   (|LieAlgebra| . LIECAT)
   (|LinearAggregate| . LNAGG)
   (|LinearlyExplicitRingOver| . LINEXP)
   (|LinearOrdinaryDifferentialOperatorCategory| . LODOCAT)
+  (|LinearSet| . LINSET)
   (|LiouvillianFunctionCategory| . LFCAT)
   (|ListAggregate| . LSAGG)
   (|Logic| . LOGIC)
@@ -752,6 +754,7 @@
   (|RetractableTo| . RETRACT)
   (|RGBColorModel| . RGBCMDL)
   (|RGBColorSpace| . RGBCSPC)
+  (|RightLinearSet| . RLINSET)
   (|RightModule| . RMODULE)
   (|Ring| . RING)
   (|Rng| . RNG)
diff --git a/src/algebra/op.spad.pamphlet b/src/algebra/op.spad.pamphlet
index a467dd0e..09fba256 100644
--- a/src/algebra/op.spad.pamphlet
+++ b/src/algebra/op.spad.pamphlet
@@ -78,8 +78,6 @@ BasicOperator(): Exports == Implementation where
     input      : $ -> Union(List SEX -> SEX, "failed")
       ++ input(op) returns the "%input" property of op if
       ++ it has one attached, "failed" otherwise.
-    is?        : ($, Symbol) -> Boolean
-      ++ is?(op, s) tests if the name of op is s.
     has?       : (%, Identifier) -> Boolean
       ++ \spad{has?(op,p)} tests if property \spad{s} is attached to \spad{op}.
     assert     : (%, Identifier) -> $
diff --git a/src/algebra/strap/ABELGRP.lsp b/src/algebra/strap/ABELGRP.lsp
index 467559ce..cd7922b8 100644
--- a/src/algebra/strap/ABELGRP.lsp
+++ b/src/algebra/strap/ABELGRP.lsp
@@ -4,14 +4,15 @@
 (DEFPARAMETER |AbelianGroup;AL| 'NIL) 
 
 (DEFUN |AbelianGroup;| ()
-  (PROG (#0=#:G1399)
+  (PROG (#0=#:G1400)
     (RETURN
       (PROG1 (LETT #0#
-                   (|Join| (|CancellationAbelianMonoid|)
-                           (|mkCategory| '|domain|
-                               '(((- ($ $)) T) ((- ($ $ $)) T)
-                                 ((* ($ (|Integer|) $)) T))
-                               NIL '((|Integer|)) NIL))
+                   (|sublisV| (PAIR '(#1=#:G1399) (LIST '(|Integer|)))
+                       (|Join| (|CancellationAbelianMonoid|)
+                               (|LeftLinearSet| '#1#)
+                               (|mkCategory| '|domain|
+                                   '(((- ($ $)) T) ((- ($ $ $)) T)) NIL
+                                   'NIL NIL)))
                    |AbelianGroup|)
         (|setShellEntry| #0# 0 '(|AbelianGroup|)))))) 
 
diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp
index 58577fe4..582076db 100644
--- a/src/algebra/strap/DFLOAT.lsp
+++ b/src/algebra/strap/DFLOAT.lsp
@@ -1031,7 +1031,7 @@
           (CONS (|makeByteWordVec2| 1
                     '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-                      0 0 0 0 0 0 0 0 0))
+                      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
                 (CONS '#(|FloatingPointSystem&| |RealNumberSystem&|
                          |Field&| |EuclideanDomain&| NIL
                          |UniqueFactorizationDomain&| |GcdDomain&|
@@ -1039,9 +1039,10 @@
                          |Algebra&| |DifferentialRing&| NIL
                          |OrderedRing&| |Module&| NIL NIL |Module&| NIL
                          NIL |Ring&| NIL NIL NIL NIL NIL NIL NIL
-                         |AbelianGroup&| NIL NIL NIL |AbelianMonoid&|
-                         |Monoid&| NIL |OrderedSet&|
-                         |AbelianSemiGroup&| |SemiGroup&|
+                         |AbelianGroup&| NIL NIL NIL NIL NIL
+                         |AbelianMonoid&| |Monoid&| NIL |OrderedSet&|
+                         NIL NIL NIL NIL |AbelianSemiGroup&|
+                         |SemiGroup&| NIL
                          |TranscendentalFunctionCategory&|
                          |RetractableTo&| |RetractableTo&| NIL
                          |SetCategory&| NIL
@@ -1072,9 +1073,15 @@
                                (|OrderedAbelianMonoid|)
                                (|CancellationAbelianMonoid|)
                                (|OrderedAbelianSemiGroup|)
+                               (|LinearSet| 112) (|LinearSet| $$)
                                (|AbelianMonoid|) (|Monoid|)
                                (|PatternMatchable| 109) (|OrderedSet|)
+                               (|LeftLinearSet| 112)
+                               (|RightLinearSet| 112)
+                               (|LeftLinearSet| $$)
+                               (|RightLinearSet| $$)
                                (|AbelianSemiGroup|) (|SemiGroup|)
+                               (|LeftLinearSet| 26)
                                (|TranscendentalFunctionCategory|)
                                (|RetractableTo| 112)
                                (|RetractableTo| 26) (|RealConstant|)
@@ -1150,8 +1157,8 @@
                                   20 1 0 0 0 105 1 0 0 0 1 2 0 0 0 113
                                   1 2 0 0 0 0 107 2 0 19 0 0 1 2 0 19 0
                                   0 1 2 0 19 0 0 62 2 0 19 0 0 1 2 0 19
-                                  0 0 54 2 0 0 0 26 63 2 0 0 0 0 45 1 0
-                                  0 0 55 2 0 0 0 0 57 2 0 0 0 0 56 2 0
+                                  0 0 54 2 0 0 0 26 63 2 0 0 0 0 45 2 0
+                                  0 0 0 57 1 0 0 0 55 2 0 0 0 0 56 2 0
                                   0 0 0 67 2 0 0 0 112 149 2 0 0 0 26
                                   66 2 0 0 0 113 1 2 0 0 0 24 1 2 0 0
                                   112 0 1 2 0 0 0 112 1 2 0 0 0 0 58 2
diff --git a/src/algebra/strap/INT.lsp b/src/algebra/strap/INT.lsp
index 2d9d4f7a..038285e5 100644
--- a/src/algebra/strap/INT.lsp
+++ b/src/algebra/strap/INT.lsp
@@ -623,17 +623,19 @@
             (|unitsKnown| . 0))
           (CONS (|makeByteWordVec2| 1
                     '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-                      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
+                      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+                      0 0))
                 (CONS '#(|IntegerNumberSystem&| |EuclideanDomain&|
                          |UniqueFactorizationDomain&| NIL NIL
                          |GcdDomain&| |IntegralDomain&| |Algebra&| NIL
                          NIL |DifferentialRing&| |OrderedRing&| NIL NIL
                          |Module&| NIL |Ring&| NIL NIL NIL NIL NIL
-                         |AbelianGroup&| NIL NIL NIL |AbelianMonoid&|
-                         |Monoid&| NIL NIL |OrderedSet&|
-                         |AbelianSemiGroup&| |SemiGroup&| NIL
-                         |RetractableTo&| |SetCategory&| NIL NIL NIL
-                         NIL NIL NIL NIL NIL NIL NIL |BasicType&| NIL)
+                         |AbelianGroup&| NIL NIL NIL NIL
+                         |AbelianMonoid&| |Monoid&| NIL NIL
+                         |OrderedSet&| NIL NIL |AbelianSemiGroup&|
+                         |SemiGroup&| NIL NIL |RetractableTo&|
+                         |SetCategory&| NIL NIL NIL NIL NIL NIL NIL NIL
+                         NIL NIL |BasicType&| NIL)
                       (CONS '#((|IntegerNumberSystem|)
                                (|EuclideanDomain|)
                                (|UniqueFactorizationDomain|)
@@ -653,10 +655,13 @@
                                (|OrderedAbelianMonoid|)
                                (|CancellationAbelianMonoid|)
                                (|OrderedAbelianSemiGroup|)
-                               (|AbelianMonoid|) (|Monoid|)
-                               (|StepThrough|) (|PatternMatchable| 17)
-                               (|OrderedSet|) (|AbelianSemiGroup|)
-                               (|SemiGroup|) (|RealConstant|)
+                               (|LinearSet| $$) (|AbelianMonoid|)
+                               (|Monoid|) (|StepThrough|)
+                               (|PatternMatchable| 17) (|OrderedSet|)
+                               (|LeftLinearSet| $$)
+                               (|RightLinearSet| $$)
+                               (|AbelianSemiGroup|) (|SemiGroup|)
+                               (|LeftLinearSet| 17) (|RealConstant|)
                                (|RetractableTo| 17) (|SetCategory|)
                                (|OpenMath|) (|ConvertibleTo| 14)
                                (|ConvertibleTo| 55)
@@ -713,7 +718,7 @@
                                   0 9 27 2 0 11 12 0 28 1 0 14 0 26 1 0
                                   0 0 1 2 0 0 0 7 1 2 0 9 0 0 1 2 0 9 0
                                   0 1 2 0 9 0 0 33 2 0 9 0 0 1 2 0 9 0
-                                  0 10 2 0 0 0 0 39 1 0 0 0 16 2 0 0 0
+                                  0 10 1 0 0 0 16 2 0 0 0 0 39 2 0 0 0
                                   0 37 2 0 0 0 7 81 2 0 0 0 137 1 2 0 0
                                   0 0 52 2 0 0 17 0 80 2 0 0 7 0 1 2 0
                                   0 137 0 1)))))
diff --git a/src/algebra/strap/SINT.lsp b/src/algebra/strap/SINT.lsp
index b3ec9c35..cf309a77 100644
--- a/src/algebra/strap/SINT.lsp
+++ b/src/algebra/strap/SINT.lsp
@@ -599,19 +599,19 @@
             (|leftUnitary| . 0) (|unitsKnown| . 0))
           (CONS (|makeByteWordVec2| 1
                     '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-                      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-                      0))
+                      0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+                      0 0 0 0))
                 (CONS '#(|IntegerNumberSystem&| |EuclideanDomain&|
                          |UniqueFactorizationDomain&| NIL NIL
                          |GcdDomain&| |IntegralDomain&| |Algebra&| NIL
                          NIL |DifferentialRing&| |OrderedRing&| NIL NIL
                          |Module&| NIL |Ring&| NIL NIL NIL NIL NIL
-                         |AbelianGroup&| NIL NIL NIL NIL
+                         |AbelianGroup&| NIL NIL NIL NIL NIL
                          |AbelianMonoid&| |Monoid&| NIL NIL NIL
-                         |OrderedSet&| |AbelianSemiGroup&| |SemiGroup&|
-                         |Logic&| NIL |RetractableTo&| |SetCategory&|
-                         NIL NIL NIL NIL NIL NIL NIL NIL NIL
-                         |BasicType&| NIL)
+                         |OrderedSet&| NIL NIL |AbelianSemiGroup&|
+                         |SemiGroup&| NIL |Logic&| NIL |RetractableTo&|
+                         |SetCategory&| NIL NIL NIL NIL NIL NIL NIL NIL
+                         NIL |BasicType&| NIL)
                       (CONS '#((|IntegerNumberSystem|)
                                (|EuclideanDomain|)
                                (|UniqueFactorizationDomain|)
@@ -632,12 +632,16 @@
                                (|CancellationAbelianMonoid|)
                                (|OrderedFinite|)
                                (|OrderedAbelianSemiGroup|)
-                               (|AbelianMonoid|) (|Monoid|) (|Finite|)
-                               (|StepThrough|) (|PatternMatchable| 5)
-                               (|OrderedSet|) (|AbelianSemiGroup|)
-                               (|SemiGroup|) (|Logic|) (|RealConstant|)
-                               (|RetractableTo| 5) (|SetCategory|)
-                               (|OpenMath|) (|ConvertibleTo| 98)
+                               (|LinearSet| $$) (|AbelianMonoid|)
+                               (|Monoid|) (|Finite|) (|StepThrough|)
+                               (|PatternMatchable| 5) (|OrderedSet|)
+                               (|LeftLinearSet| $$)
+                               (|RightLinearSet| $$)
+                               (|AbelianSemiGroup|) (|SemiGroup|)
+                               (|LeftLinearSet| 5) (|Logic|)
+                               (|RealConstant|) (|RetractableTo| 5)
+                               (|SetCategory|) (|OpenMath|)
+                               (|ConvertibleTo| 98)
                                (|ConvertibleTo| 96)
                                (|CombinatorialFunctionCategory|)
                                (|ConvertibleTo| 100)
diff --git a/src/algebra/term.spad.pamphlet b/src/algebra/term.spad.pamphlet
index 6a9071c7..da897986 100644
--- a/src/algebra/term.spad.pamphlet
+++ b/src/algebra/term.spad.pamphlet
@@ -72,12 +72,15 @@ Arity(): Public == Private where
 OperatorCategory(S: SetCategory): Category ==
     SetCategory with
       name: % -> S
-        ++ name(op) returns the externam name of `op'.
+        ++ \spad{name(op)} returns the externam name of \spad{op}.
       arity: % -> Arity
-        ++ arity(op) returns the arity of the operator `op'.
+        ++ \spad{arity(op)} returns the arity of the operator \spad{op}.
+      is?: (%,S) -> Boolean
+        ++ \spad{is?(op,n)} holds if the name of the operator \spad{op}
+        ++ is \spad{n}.
   add
     coerce(op: %): OutputForm == name(op)::OutputForm
-
+    is?(op,n) == name op = n
 @
 
 
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index d765e330..1fd81673 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,19 +1,19 @@
 
-(2282756 . 3452645032)       
+(2284136 . 3452782368)       
 (-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."))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
 (-20 S) 
-((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) 
+((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) 
 NIL 
 NIL 
 (-21) 
-((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) 
+((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) 
 NIL 
 NIL 
 (-22 S) 
@@ -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(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . 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(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4404 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4400 . T) (-4405 . T) (-4399 . T)) 
+((-4407 . T) (-4405 . T) (-4404 . T) ((-4412 "*") . T) (-4403 . T) (-4408 . T) (-4402 . T)) 
 NIL 
 (-30) 
 ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -2306) 
+(-32 R -2234) 
 ((|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 -1034) (QUOTE (-564))))) 
+((|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) 
 (-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 \\%")) (|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.")) (|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} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\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 -4407))) 
+((|HasAttribute| |#1| (QUOTE -4410))) 
 (-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 \\%")) (|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.")) (|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} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\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}."))) 
-((-4407 . T) (-4408 . T)) 
+((-4410 . T) (-4411 . 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"))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . 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 a1,{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -2306 UP UPUP -3056) 
+(-40 -2234 UP UPUP -1472) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2807 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2807 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2807 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) 
-(-41 R -2306) 
+((-4403 |has| (-407 |#2|) (-363)) (-4408 |has| (-407 |#2|) (-363)) (-4402 |has| (-407 |#2|) (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2706 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2706 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2706 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2706 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) 
+(-41 R -2234) 
 ((|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}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'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| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -106,31 +106,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-307)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) 
-((-4404 |has| |#1| (-556)) (-4402 . T) (-4401 . T)) 
+((-4407 |has| |#1| (-556)) (-4405 . T) (-4404 . T)) 
 ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) 
 (-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."))) 
-((-4407 . T) (-4408 . T)) 
-((-2807 (-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|))))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|))))))) 
+((-4410 . T) (-4411 . T)) 
+((-2706 (-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|))))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|))))))) 
 (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1036) (QUOTE (-564))))) 
 (-49) 
 ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) 
 NIL 
 NIL 
 (-50 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-51 S) 
 ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) 
@@ -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 -2306) 
+(-54 |Base| R -2234) 
 ((|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},{}...,{}\\spad{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},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) 
 NIL 
 NIL 
@@ -158,7 +158,7 @@ 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}\\spad{'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"))) 
-((-4407 . T) (-4408 . T)) 
+((-4410 . T) (-4411 . T)) 
 NIL 
 (-58 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),{}...]}."))) 
@@ -166,65 +166,65 @@ NIL
 NIL 
 (-59 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}"))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
 (-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\\spad{'s}."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-61 -2562) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-61 -2461) 
 ((|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 
-(-62 -2562) 
+(-62 -2461) 
 ((|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 
-(-63 -2562) 
+(-63 -2461) 
 ((|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 
-(-64 -2562) 
+(-64 -2461) 
 ((|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 
-(-65 -2562) 
+(-65 -2461) 
 ((|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 -2562) 
+(-66 -2461) 
 ((|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 -2562) 
+(-67 -2461) 
 ((|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 -2562) 
+(-68 -2461) 
 ((|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 -2562) 
+(-69 -2461) 
 ((|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 -2562) 
+(-70 -2461) 
 ((|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 -2562) 
+(-71 -2461) 
 ((|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 -2562) 
+(-72 -2461) 
 ((|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 -2562) 
+(-73 -2461) 
 ((|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 -2562) 
+(-74 -2461) 
 ((|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 
@@ -236,55 +236,55 @@ 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 \\spad{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 
-(-77 -2562) 
+(-77 -2461) 
 ((|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 
-(-78 -2562) 
+(-78 -2461) 
 ((|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 
-(-79 -2562) 
+(-79 -2461) 
 ((|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 -2562) 
+(-80 -2461) 
 ((|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 -2562) 
+(-81 -2461) 
 ((|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 -2562) 
+(-82 -2461) 
 ((|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 
-(-83 -2562) 
+(-83 -2461) 
 ((|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 
-(-84 -2562) 
+(-84 -2461) 
 ((|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 
-(-85 -2562) 
+(-85 -2461) 
 ((|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 
-(-86 -2562) 
+(-86 -2461) 
 ((|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 
-(-87 -2562) 
+(-87 -2461) 
 ((|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 
-(-88 -2562) 
+(-88 -2461) 
 ((|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 
-(-89 -2562) 
+(-89 -2461) 
 ((|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 (-363)))) 
 (-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}."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-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\"."))) 
-((-4407 . T)) 
+((-4410 . 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."))) 
-((-4407 . T) ((-4409 "*") . T) (-4408 . T) (-4404 . T) (-4402 . T) (-4401 . T) (-4400 . T) (-4405 . T) (-4399 . T) (-4398 . T) (-4397 . T) (-4396 . T) (-4395 . T) (-4403 . T) (-4406 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4394 . T)) 
+((-4410 . T) ((-4412 "*") . T) (-4411 . T) (-4407 . T) (-4405 . T) (-4404 . T) (-4403 . T) (-4408 . T) (-4402 . T) (-4401 . T) (-4400 . T) (-4399 . T) (-4398 . T) (-4406 . T) (-4409 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4397 . 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}."))) 
-((-4404 . T)) 
+((-4407 . 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{\\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 \\spad{pl} and \\spad{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{:=} \\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 \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-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 (-4409 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4412 "*")))) 
 (-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"))) 
-((-4407 . T)) 
+((-4410 . 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."))) 
-((-4408 . T)) 
+((-4411 . 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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2807 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2706 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) 
 (-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 \\spad{`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}"))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| (-112) (QUOTE (-1097))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-112) (QUOTE (-1097))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-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}"))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 NIL 
 (-112) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) 
@@ -385,25 +385,25 @@ NIL
 NIL 
 NIL 
 (-114) 
-((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op,{} p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,{}p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) 
+((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op,{} p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,{}p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) 
 NIL 
 NIL 
-(-115 -2306 UP) 
+(-115 -2234 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 
 (-116 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{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}."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-117 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{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}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2807 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-116 |#1|) (QUOTE (-907))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1020))) (|HasCategory| (-116 |#1|) (QUOTE (-818))) (-2706 (|HasCategory| (-116 |#1|) (QUOTE (-818))) (|HasCategory| (-116 |#1|) (QUOTE (-848)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1148))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1173)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-907)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) 
 (-118 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" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4408))) 
+((|HasAttribute| |#1| (QUOTE -4411))) 
 (-119 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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 
@@ -414,15 +414,15 @@ NIL
 NIL 
 (-121 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"))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-122 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-123) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
 (-124 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -430,20 +430,20 @@ NIL
 NIL 
 (-125 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-4407 . T) (-4408 . T)) 
+((-4410 . T) (-4411 . T)) 
 NIL 
 (-126 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-127 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."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-128) 
 ((|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 \\spad{`n'}. The array can then store up to \\spad{`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 \\spad{`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."))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2807 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2706 (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-129) (QUOTE (-1097)))) (|HasCategory| (-129) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-129) (QUOTE (-1097))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) 
 (-129) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) 
 NIL 
@@ -466,13 +466,13 @@ NIL
 NIL 
 (-134) 
 ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) 
-(((-4409 "*") . T)) 
+(((-4412 "*") . T)) 
 NIL 
-(-135 |minix| -3599 S T$) 
+(-135 |minix| -3554 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-136 |minix| -3599 R) 
+(-136 |minix| -3554 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 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 
@@ -494,8 +494,8 @@ NIL
 NIL 
 (-141) 
 ((|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}."))) 
-((-4407 . T) (-4397 . T) (-4408 . T)) 
-((-2807 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) 
+((-4410 . T) (-4400 . T) (-4411 . T)) 
+((-2706 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) 
 (-142 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{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
@@ -510,7 +510,7 @@ NIL
 NIL 
 (-145) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-146 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 \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) 
@@ -518,9 +518,9 @@ NIL
 NIL 
 (-147) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-148 -2306 UP UPUP) 
+(-148 -2234 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 
@@ -531,14 +531,14 @@ NIL
 (-150 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|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|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{==} [\\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 -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasAttribute| |#1| (QUOTE -4407))) 
+((|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasAttribute| |#1| (QUOTE -4410))) 
 (-151 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|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|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{==} [\\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 
 (-152 |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."))) 
-((-4402 . T) (-4401 . T) (-4404 . T)) 
+((-4405 . T) (-4404 . T) (-4407 . T)) 
 NIL 
 (-153) 
 ((|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."))) 
@@ -560,7 +560,7 @@ 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 
-(-158 R -2306) 
+(-158 R -2234) 
 ((|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})\\spad{/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.} \\spad{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.} \\spad{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.} \\spad{n!/}(\\spad{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 
@@ -591,10 +591,10 @@ NIL
 (-165 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 (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasAttribute| |#2| (QUOTE -4406)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556)))) 
+((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1000))) (|HasCategory| |#2| (QUOTE (-1197))) (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4406)) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556)))) 
 (-166 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})"))) 
-((-4400 -2807 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3654 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 -2706 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-907)))) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4409 |has| |#1| (-6 -4409)) (-3609 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-167 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."))) 
@@ -606,8 +606,8 @@ NIL
 NIL 
 (-169 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}."))) 
-((-4400 -2807 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-3654 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-824)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1194)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4403)) (|HasAttribute| |#1| (QUOTE -4406)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) 
+((-4403 -2706 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-907)))) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4406 |has| |#1| (-6 -4406)) (-4409 |has| |#1| (-6 -4409)) (-3609 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-826)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1197)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-907))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-907)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-907))))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-1057))) (-12 (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasAttribute| |#1| (QUOTE -4406)) (|HasAttribute| |#1| (QUOTE -4409)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-349))))) 
 (-170 R S CS) 
 ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) 
 NIL 
@@ -618,7 +618,7 @@ NIL
 NIL 
 (-172) 
 ((|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."))) 
-(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-173) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
@@ -626,7 +626,7 @@ NIL
 NIL 
 (-174 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) 
-(((-4409 "*") . T) (-4400 . T) (-4405 . T) (-4399 . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") . T) (-4403 . T) (-4408 . T) (-4402 . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-175) 
 ((|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|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -643,7 +643,7 @@ NIL
 (-178 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| (-948 |#2|) (LIST (QUOTE -882) (|devaluate| |#1|)))) 
+((|HasCategory| (-950 |#2|) (LIST (QUOTE -884) (|devaluate| |#1|)))) 
 (-179 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)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) 
 NIL 
@@ -680,7 +680,7 @@ NIL
 ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-188 R -2306) 
+(-188 R -2234) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -788,23 +788,23 @@ NIL
 ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) 
 NIL 
 NIL 
-(-215 -2306 UP UPUP R) 
+(-215 -2234 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 
-(-216 -2306 FP) 
+(-216 -2234 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 \\spad{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 
 (-217) 
 ((|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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2807 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2706 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) 
 (-218) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-219 R -2306) 
+(-219 R -2234) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -818,19 +818,19 @@ NIL
 NIL 
 (-222 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-223 |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}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-224 R -2306) 
+(-224 R -2234) 
 ((|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 
 (-225) 
 ((|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.")) (|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}."))) 
-((-3646 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-3601 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-226) 
 ((|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{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{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*\\%\\spad{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*\\%\\spad{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*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{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*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{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)}.}"))) 
@@ -838,23 +838,23 @@ NIL
 NIL 
 (-227 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}"))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-228 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 
 (-229 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."))) 
-((-4408 . T)) 
+((-4411 . T)) 
 NIL 
 (-230 S R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) 
+((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233)))) 
 (-231 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-232 S) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) 
@@ -862,36 +862,36 @@ NIL
 NIL 
 (-233) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-234 A S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4407))) 
+((|HasAttribute| |#1| (QUOTE -4410))) 
 (-235 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}."))) 
-((-4408 . T)) 
+((-4411 . T)) 
 NIL 
 (-236) 
 ((|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 
-(-237 S -3599 R) 
+(-237 S -3554 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|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 (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4404)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1094)))) 
-(-238 -3599 R) 
+((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (QUOTE (-846))) (|HasAttribute| |#3| (QUOTE -4407)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-724))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (QUOTE (-1097)))) 
+(-238 -3554 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#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}.")) (|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"))) 
-((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) 
+((-4404 |has| |#2| (-1047)) (-4405 |has| |#2| (-1047)) (-4407 |has| |#2| (-6 -4407)) ((-4412 "*") |has| |#2| (-172)) (-4410 . T)) 
 NIL 
-(-239 -3599 A B) 
+(-239 -3554 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 
-(-240 -3599 R) 
+(-240 -3554 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."))) 
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(|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173))))) (-2706 (|HasCategory| |#2| (QUOTE (-1047))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasAttribute| |#2| (QUOTE -4407)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) 
 (-241) 
 ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 
 NIL 
@@ -902,7 +902,7 @@ NIL
 NIL 
 (-243) 
 ((|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}."))) 
-((-4400 . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-244 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."))) 
@@ -910,16 +910,16 @@ NIL
 NIL 
 (-245 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}"))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
 (-246 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\\spad{'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 
 (-247 |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"))) 
-(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#2| (QUOTE (-905))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+(((-4412 "*") |has| |#2| (-172)) (-4403 |has| |#2| (-556)) (-4408 |has| |#2| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#2| (QUOTE (-907))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) 
 (-248) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\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|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`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 \\spad{`d'}."))) 
 NIL 
@@ -930,23 +930,23 @@ NIL
 NIL 
 (-250 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-4404 -2807 (-2358 (|has| |#4| (-1045)) (|has| |#4| (-233))) (-2358 (|has| |#4| (-1045)) (|has| |#4| (-896 (-1170)))) (|has| |#4| (-6 -4404)) (-2358 (|has| |#4| (-1045)) (|has| |#4| (-637 (-564))))) (-4401 |has| |#4| (-1045)) (-4402 |has| |#4| (-1045)) ((-4409 "*") |has| |#4| (-172)) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-233))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-722))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-789))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-844))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1045))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#4| (QUOTE (-363))) (-2807 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (QUOTE (-1045)))) (-2807 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (QUOTE (-363)))) (|HasCategory| |#4| (QUOTE (-1045))) (|HasCategory| |#4| (QUOTE (-789))) (-2807 (|HasCategory| |#4| (QUOTE (-789))) (|HasCategory| |#4| (QUOTE (-844)))) (|HasCategory| |#4| (QUOTE (-844))) (|HasCategory| |#4| (QUOTE (-722))) (|HasCategory| |#4| (QUOTE (-172))) (-2807 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (QUOTE (-1045)))) (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#4| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2807 (|HasCategory| |#4| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#4| (LIST (QUOTE 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(|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-2807 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (|HasCategory| |#3| (QUOTE (-722))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-2807 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (-2807 (|HasAttribute| |#3| (QUOTE -4404)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) 
+((-4407 -2706 (-2275 (|has| |#3| (-1047)) (|has| |#3| (-233))) (-2275 (|has| |#3| (-1047)) (|has| |#3| (-898 (-1173)))) (|has| |#3| (-6 -4407)) (-2275 (|has| |#3| (-1047)) (|has| |#3| (-637 (-564))))) (-4404 |has| |#3| (-1047)) (-4405 |has| |#3| (-1047)) ((-4412 "*") |has| |#3| (-172)) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-724))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#3| (QUOTE (-363))) (-2706 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1047)))) (-2706 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-791))) (-2706 (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (QUOTE (-846)))) (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (QUOTE (-724))) (-2706 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-1047)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (-2706 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-172)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-233)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-363)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-368)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-724)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-791)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-846)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1097))))) (-2706 (-12 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-724))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1047))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-724))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-848))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (-2706 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (|HasCategory| |#3| (QUOTE (-724))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-2706 (|HasCategory| |#3| (QUOTE (-1047))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1097)))) (-2706 (|HasAttribute| |#3| (QUOTE -4407)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) 
 (-252 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} \\spad{:=} 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 (-233)))) 
 (-253 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} \\spad{:=} 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."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
 NIL 
 (-254 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}."))) 
-((-4407 . T) (-4408 . T)) 
+((-4410 . T) (-4411 . T)) 
 NIL 
 (-255) 
 ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(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)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}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)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}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)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}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)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(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)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}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)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}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)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}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)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
@@ -986,8 +986,8 @@ NIL
 NIL 
 (-264 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"))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
 (-265 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}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|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 
@@ -1032,11 +1032,11 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'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 
-(-276 R -2306) 
+(-276 R -2234) 
 ((|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{\\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 
-(-277 R -2306) 
+(-277 R -2234) 
 ((|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{\\spad{ki}} was rewritten as \\spad{\\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 
@@ -1055,10 +1055,10 @@ NIL
 (-281 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 (-846))) (|HasCategory| |#2| (QUOTE (-1094)))) 
+((|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097)))) 
 (-282 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}."))) 
-((-4408 . T)) 
+((-4411 . T)) 
 NIL 
 (-283 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}."))) 
@@ -1079,18 +1079,18 @@ NIL
 (-287 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 -4408))) 
+((|HasAttribute| |#1| (QUOTE -4411))) 
 (-288 |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 
-(-289 S R |Mod| -1812 -3669 |exactQuo|) 
+(-289 S R |Mod| -1790 -2740 |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}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-290) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-4400 . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-291) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Identifier|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}.")) (|setProperty!| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `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 `e'. Otherwise,{} `nothing.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) 
@@ -1106,21 +1106,21 @@ NIL
 NIL 
 (-294 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| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and 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."))) 
-((-4404 -2807 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-1045)) (-4402 |has| |#1| (-1045))) 
-((|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2807 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722)))) (|HasCategory| |#1| (QUOTE (-473))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2807 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-302))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-2807 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722)))) (-2807 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-172)))) 
+((-4407 -2706 (|has| |#1| (-1047)) (|has| |#1| (-473))) (-4404 |has| |#1| (-1047)) (-4405 |has| |#1| (-1047))) 
+((|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1047)))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-1047)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1047)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1047)))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-1047)))) (-2706 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-724)))) (|HasCategory| |#1| (QUOTE (-473))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1097)))) (-2706 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-302))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-2706 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724)))) (-2706 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-724)))) 
 (-295 |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."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-296) 
 ((|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 
 NIL 
-(-297 -2306 S) 
+(-297 -2234 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 
-(-298 E -2306) 
+(-298 E -2234) 
 ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\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 
@@ -1135,7 +1135,7 @@ NIL
 (-301 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| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|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| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\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|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|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 -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1045)))) 
+((|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1047)))) 
 (-302) 
 ((|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| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|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| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\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|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|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 
@@ -1158,7 +1158,7 @@ NIL
 NIL 
 (-307) 
 ((|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 \\spad{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| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-308 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) 
@@ -1168,7 +1168,7 @@ NIL
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} 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 
-(-310 -2306) 
+(-310 -2234) 
 ((|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 
@@ -1182,8 +1182,8 @@ NIL
 NIL 
 (-313 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))}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2807 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2807 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
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 (-314 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 
@@ -1194,9 +1194,9 @@ NIL
 NIL 
 (-316 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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-(-317 R -2306) 
+((-4407 -2706 (-2275 (|has| |#1| (-1047)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2706 (-2275 (|has| |#1| (-1047)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1047)) (|has| |#1| (-473)))) (|has| |#1| (-1047)) (|has| |#1| (-473))) (-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) ((-4412 "*") |has| |#1| (-556)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-556)) (-4402 |has| |#1| (-556))) 
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+(-317 R -2234) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'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{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{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 
@@ -1206,8 +1206,8 @@ NIL
 NIL 
 (-319 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."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) 
 (-320 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},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
@@ -1218,8 +1218,8 @@ NIL
 NIL 
 (-322 S) 
 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) 
-((-4402 . T) (-4401 . T)) 
-((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-788)))) 
+((-4405 . T) (-4404 . T)) 
+((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-790)))) 
 (-323 S E) 
 ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|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}\\spad{'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|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
@@ -1227,26 +1227,26 @@ NIL
 (-324 S) 
 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-767) (QUOTE (-788)))) 
+((|HasCategory| (-769) (QUOTE (-790)))) 
 (-325 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\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!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\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| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172)))) 
 (-326 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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 \\spad{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."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-327 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."))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
-(-328 S -2306) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+(-328 S -2234) 
 ((|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})\\spad{\\$}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})\\spad{\\$}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**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{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},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-368)))) 
-(-329 -2306) 
+(-329 -2234) 
 ((|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})\\spad{\\$}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})\\spad{\\$}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**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{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},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-330) 
 ((|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."))) 
@@ -1264,54 +1264,54 @@ 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 
-(-334 S -2306 UP UPUP R) 
+(-334 S -2234 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 \\spad{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 \\spad{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 
-(-335 -2306 UP UPUP R) 
+(-335 -2234 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 \\spad{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 \\spad{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 
-(-336 -2306 UP UPUP R) 
+(-336 -2234 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
 (-337 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-338 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-339 |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{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\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.}"))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-379)))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-379)))) (|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1036) (QUOTE (-564))))) 
 (-340 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}."))) 
 NIL 
 NIL 
-(-341 S -2306 UP UPUP) 
+(-341 S -2234 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 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(\\spad{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 (-368))) (|HasCategory| |#2| (QUOTE (-363)))) 
-(-342 -2306 UP UPUP) 
+(-342 -2234 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 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(\\spad{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."))) 
-((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 |has| (-407 |#2|) (-363)) (-4408 |has| (-407 |#2|) (-363)) (-4402 |has| (-407 |#2|) (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-343 |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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#1|) (QUOTE (-145)))) 
 (-344 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-345 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-346 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(\\spad{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 
@@ -1326,33 +1326,33 @@ NIL
 NIL 
 (-349) 
 ((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-350 R UP -2306) 
+(-350 R UP -2234) 
 ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-351 |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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#1|) (QUOTE (-145)))) 
 (-352 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-353 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-354 |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}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| (-908 |#1|) (QUOTE (-145))) (|HasCategory| (-908 |#1|) (QUOTE (-368)))) (|HasCategory| (-908 |#1|) (QUOTE (-147))) (|HasCategory| (-908 |#1|) (QUOTE (-368))) (|HasCategory| (-908 |#1|) (QUOTE (-145)))) 
 (-355 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
-(-356 -2306 GF) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
+(-356 -2234 GF) 
 ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{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 
@@ -1360,21 +1360,21 @@ NIL
 ((|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(\\spad{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(\\spad{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(\\spad{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(\\spad{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(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{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 
-(-358 -2306 FP FPP) 
+(-358 -2234 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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
 (-359 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{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}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-360 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{\\spad{ls}}."))) 
 NIL 
 NIL 
 (-361 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-362 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1382,7 +1382,7 @@ NIL
 NIL 
 (-363) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-364 |Name| S) 
 ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) 
@@ -1398,7 +1398,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-556)))) 
 (-367 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\\spad{'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\\spad{'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\\spad{'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(\\spad{\"*\"})} 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\\spad{'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\\spad{'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\\spad{'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\\spad{'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{\\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{\\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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-4404 |has| |#1| (-556)) (-4402 . T) (-4401 . T)) 
+((-4407 |has| |#1| (-556)) (-4405 . T) (-4404 . T)) 
 NIL 
 (-368) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) 
@@ -1410,7 +1410,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-363)))) 
 (-370 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 ( \\spad{Tr}(\\spad{vi} * \\spad{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}\\spad{'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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-371 S A R B) 
 ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) 
@@ -1419,14 +1419,14 @@ NIL
 (-372 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{>=} \\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|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094)))) 
+((|HasAttribute| |#1| (QUOTE -4411)) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097)))) 
 (-373 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{>=} \\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|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-4407 . T)) 
+((-4410 . T)) 
 NIL 
 (-374 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#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) (-4402 . T) (-4401 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4405 . T) (-4404 . T)) 
 NIL 
 (-375 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."))) 
@@ -1438,7 +1438,7 @@ NIL
 ((|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) 
 (-377 R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-378 |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 \\spad{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}."))) 
@@ -1446,7 +1446,7 @@ NIL
 NIL 
 (-379) 
 ((|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{\\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}."))) 
-((-4390 . T) (-4398 . T) (-3646 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4393 . T) (-4401 . T) (-3601 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-380 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) 
@@ -1454,11 +1454,11 @@ NIL
 NIL 
 (-381 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.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172)))) 
 (-382 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.\\spad{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}."))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 NIL 
 (-383) 
 ((|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}."))) 
@@ -1470,15 +1470,15 @@ NIL
 NIL 
 (-385 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."))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172)))) 
 (-386 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\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| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-846)))) 
+((|HasCategory| |#1| (QUOTE (-848)))) 
 (-387) 
 ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-388) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
@@ -1490,13 +1490,13 @@ NIL
 NIL 
 (-390 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 NIL 
 (-391) 
 ((|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 
-(-392 -2306 UP UPUP R) 
+(-392 -2234 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 
@@ -1520,11 +1520,11 @@ NIL
 ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-398 -2562 |returnType| -2838 |symbols|) 
+(-398 -2461 |returnType| -2737 |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 
-(-399 -2306 UP) 
+(-399 -2234 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
@@ -1538,15 +1538,15 @@ NIL
 NIL 
 (-402) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-403 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\\spad{'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\\spad{'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 -4390)) (|HasAttribute| |#1| (QUOTE -4398))) 
+((|HasAttribute| |#1| (QUOTE -4393)) (|HasAttribute| |#1| (QUOTE -4401))) 
 (-404) 
 ((|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(\\spad{\"+\"}) 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\\spad{'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\\spad{'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\"."))) 
-((-3646 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-3601 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-405 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."))) 
@@ -1558,20 +1558,20 @@ NIL
 NIL 
 (-407 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 \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
-((-4394 -12 (|has| |#1| (-6 -4405)) (|has| |#1| (-452)) (|has| |#1| (-6 -4394))) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2807 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4394)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+((-4397 -12 (|has| |#1| (-6 -4408)) (|has| |#1| (-452)) (|has| |#1| (-6 -4397))) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-818))) (-2706 (|HasCategory| |#1| (QUOTE (-818))) (|HasCategory| |#1| (QUOTE (-848)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1148))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826))))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-826)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
 (-408 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'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{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
 NIL 
 (-409 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{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},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'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."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-410 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\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) 
+((|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) 
 (-411 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\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
@@ -1580,14 +1580,14 @@ NIL
 ((|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 
-(-413 R -2306 UP A) 
+(-413 R -2234 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)}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-414 R -2306 UP A |ibasis|) 
+(-414 R -2234 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) 
 NIL 
-((|HasCategory| |#4| (LIST (QUOTE -1034) (|devaluate| |#2|)))) 
+((|HasCategory| |#4| (LIST (QUOTE -1036) (|devaluate| |#2|)))) 
 (-415 AR R AS S) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
@@ -1598,12 +1598,12 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-363)))) 
 (-417 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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\\spad{'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{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to 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{\\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."))) 
-((-4404 |has| |#1| (-556)) (-4402 . T) (-4401 . T)) 
+((-4407 |has| |#1| (-556)) (-4405 . T) (-4404 . T)) 
 NIL 
 (-418 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 \\spad{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| "nil" "sqfr" "irred" "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| "nil" "sqfr" "irred" "prime") $ (|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| "nil" "sqfr" "irred" "prime")) (|:| |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| "nil" "sqfr" "irred" "prime")) (|:| |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."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1216))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1216)))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) 
 (-419 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)}."))) 
 NIL 
@@ -1627,40 +1627,40 @@ NIL
 (-424 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 (-846))) (|HasCategory| |#2| (QUOTE (-368)))) 
+((|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-368)))) 
 (-425 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-4407 . T) (-4397 . T) (-4408 . T)) 
+((-4410 . T) (-4400 . T) (-4411 . T)) 
 NIL 
-(-426 R -2306) 
+(-426 R -2234) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
 (-427 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) 
-((-4394 -12 (|has| |#1| (-6 -4394)) (|has| |#2| (-6 -4394))) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -4394)) (|HasAttribute| |#2| (QUOTE -4394)))) 
-(-428 R -2306) 
+((-4397 -12 (|has| |#1| (-6 -4397)) (|has| |#2| (-6 -4397))) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -4397)) (|HasAttribute| |#2| (QUOTE -4397)))) 
+(-428 R -2234) 
 ((|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 
 (-429 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| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'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 -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) 
+((|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) 
 (-430 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| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'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}."))) 
-((-4404 -2807 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4399 |has| |#1| (-556))) 
+((-4407 -2706 (|has| |#1| (-1047)) (|has| |#1| (-473))) (-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) ((-4412 "*") |has| |#1| (-556)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-556)) (-4402 |has| |#1| (-556))) 
 NIL 
-(-431 R -2306) 
+(-431 R -2234) 
 ((|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 
-(-432 R -2306) 
+(-432 R -2234) 
 ((|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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve 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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-27)))) 
-(-433 R -2306) 
+(-433 R -2234) 
 ((|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 
@@ -1668,10 +1668,10 @@ 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 
-(-435 R -2306 UP) 
+(-435 R -2234 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 -1034) (QUOTE (-48))))) 
+((|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-48))))) 
 (-436) 
 ((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) 
 NIL 
@@ -1700,7 +1700,7 @@ 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\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'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\\spad{'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 
-(-443 R UP -2306) 
+(-443 R UP -2234) 
 ((|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 \\spad{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\\spad{'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\\spad{'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\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'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 
@@ -1738,16 +1738,16 @@ NIL
 NIL 
 (-452) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{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| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-453 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"))) 
-((-4404 |has| (-407 (-948 |#1|)) (-556)) (-4402 . T) (-4401 . T)) 
-((|HasCategory| (-407 (-948 |#1|)) (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-407 (-948 |#1|)) (QUOTE (-556)))) 
+((-4407 |has| (-407 (-950 |#1|)) (-556)) (-4405 . T) (-4404 . T)) 
+((|HasCategory| (-407 (-950 |#1|)) (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-407 (-950 |#1|)) (QUOTE (-556)))) 
 (-454 |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"))) 
-(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#2| (QUOTE (-905))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+(((-4412 "*") |has| |#2| (-172)) (-4403 |has| |#2| (-556)) (-4408 |has| |#2| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#2| (QUOTE (-907))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) 
 (-455 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\\spad{'s} conditional."))) 
 NIL 
@@ -1774,7 +1774,7 @@ NIL
 NIL 
 (-461 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 NIL 
 (-462 E V R P Q) 
 ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1782,8 +1782,8 @@ NIL
 NIL 
 (-463 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-464 S R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} 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 
@@ -1812,7 +1812,7 @@ NIL
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-471 |lv| -2306 R) 
+(-471 |lv| -2234 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1822,23 +1822,23 @@ NIL
 NIL 
 (-473) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-474 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|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."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) 
 (-475 |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."))) 
-((-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094)))) 
+((-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-848))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097)))) 
 (-476 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)}"))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-477) 
 ((|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{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-478) 
 ((|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'."))) 
@@ -1846,29 +1846,29 @@ NIL
 NIL 
 (-479 |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."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-480) 
 ((|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\\spad{'s} book Lie Groups \\spad{--} 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{<=} \\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 
 (-481 |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 total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#2| (QUOTE (-905))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) 
-(-482 -3599 S) 
+(((-4412 "*") |has| |#2| (-172)) (-4403 |has| |#2| (-556)) (-4408 |has| |#2| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#2| (QUOTE (-907))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+(-482 -3554 S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
-((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (-2807 (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-363))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-789))) (-2807 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-172))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1045)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1045)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-172)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-233)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-844)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 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 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) 
 NIL 
 NIL 
 (-484 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}."))) 
-((-4407 . T) (-4408 . T)) 
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-(-485 -2306 UP UPUP R) 
+((-4410 . T) (-4411 . T)) 
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+(-485 -2234 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 
@@ -1878,12 +1878,12 @@ NIL
 NIL 
 (-487) 
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-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
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+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2706 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) 
 (-488 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 -4407)) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((|HasAttribute| |#1| (QUOTE -4410)) (|HasAttribute| |#1| (QUOTE -4411)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-489 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1904,34 +1904,34 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-494 -2306 UP |AlExt| |AlPol|) 
+(-494 -2234 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-495) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1036) (QUOTE (-564))))) 
 (-496 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
 (-497 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\\spad{'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."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-498 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 
-(-499 R UP -2306) 
+(-499 R UP -2234) 
 ((|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{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\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{\\spad{mi}} is given by \\spad{\\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{\\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{\\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 \\spad{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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-500 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| (-112) (QUOTE (-1097))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-112) (QUOTE (-1097))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-501 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 
@@ -1944,10 +1944,10 @@ 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{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
 NIL 
-(-504 -2306 |Expon| |VarSet| |DPoly|) 
+(-504 -2234 |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 -612) (QUOTE (-1170))))) 
+((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1173))))) 
 (-505 |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 
@@ -1991,39 +1991,39 @@ NIL
 (-515 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-788)))) 
+((|HasCategory| |#2| (QUOTE (-790)))) 
 (-516 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} 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}"))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
 (-517) 
 ((|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 
 (-518 |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}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((-2807 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((-2706 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) 
 (-519 R |mnRow| |mnCol| |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-520 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."))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
 (-521 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,{} \\spad{m*h} and \\spad{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 -4408))) 
+((|HasAttribute| |#3| (QUOTE -4411))) 
 (-522 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 -4408))) 
+((|HasAttribute| |#7| (QUOTE -4411))) 
 (-523 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."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-524) 
 ((|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 
@@ -2056,7 +2056,7 @@ NIL
 ((|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 
 NIL 
-(-532 K -2306 |Par|) 
+(-532 K -2234 |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 \\spad{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 
@@ -2080,7 +2080,7 @@ 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 
-(-538 K -2306 |Par|) 
+(-538 K -2234 |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 
@@ -2110,7 +2110,7 @@ NIL
 NIL 
 (-545) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\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."))) 
-((-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4408 . T) (-4409 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-546) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
@@ -2130,13 +2130,13 @@ NIL
 NIL 
 (-550 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-551 R -2306) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-551 R -2234) 
 ((|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 
-(-552 R0 -2306 UP UPUP R) 
+(-552 R0 -2234 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 
@@ -2146,7 +2146,7 @@ NIL
 NIL 
 (-554 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{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-3646 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-3601 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-555 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."))) 
@@ -2154,9 +2154,9 @@ NIL
 NIL 
 (-556) 
 ((|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."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-557 R -2306) 
+(-557 R -2234) 
 ((|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|)) "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},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#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 
@@ -2168,39 +2168,39 @@ NIL
 ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |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"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |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")))) (|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| "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"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |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"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "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"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |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"))))))) "\\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| "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"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |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")))))))) "\\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 
-(-560 R -2306 L) 
+(-560 R -2234 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| "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| "failed")) (|:| |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| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#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| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#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|))))) "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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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|)) "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|)) "failed") |#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 -652) (|devaluate| |#2|)))) 
+((|HasCategory| |#3| (LIST (QUOTE -654) (|devaluate| |#2|)))) 
 (-561) 
 ((|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 
-(-562 -2306 UP UPUP R) 
+(-562 -2234 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 
-(-563 -2306 UP) 
+(-563 -2234 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 
 (-564) 
 ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) 
-((-4389 . T) (-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4392 . T) (-4398 . T) (-4402 . T) (-4397 . T) (-4408 . T) (-4409 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-565) 
 ((|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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\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 {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\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 {\\spad{\\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,{} {\\spad{\\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,{} {\\spad{\\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,{} {\\spad{\\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,{} {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\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,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\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 
-(-566 R -2306 L) 
+(-566 R -2234 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| "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| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -652) (|devaluate| |#2|)))) 
-(-567 R -2306) 
+((|HasCategory| |#3| (LIST (QUOTE -654) (|devaluate| |#2|)))) 
+(-567 R -2234) 
 ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) 
-(-568 -2306 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1136)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) 
+(-568 -2234 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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{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 
@@ -2208,27 +2208,27 @@ 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 
-(-570 -2306) 
+(-570 -2234) 
 ((|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,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 
 (-571 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."))) 
-((-3646 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-3601 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-572) 
 ((|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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
-(-573 R -2306) 
+(-573 R -2234) 
 ((|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| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) 
-(-574 -2306 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) 
+(-574 -2234 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|)) "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' + +/[\\spad{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(+,{}[\\spad{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|)) "failed") |#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(+,{}[\\spad{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|)) "failed") |#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|)) "failed") |#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 
-(-575 R -2306) 
+(-575 R -2234) 
 ((|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 
@@ -2250,28 +2250,28 @@ NIL
 NIL 
 (-580 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 (-581 |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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) 
 (-582) 
 ((|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 
-(-583 R -2306) 
+(-583 R -2234) 
 ((|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},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) 
 NIL 
 NIL 
-(-584 E -2306) 
+(-584 E -2234) 
 ((|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 
-(-585 -2306) 
+(-585 -2234) 
 ((|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 \\spad{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}."))) 
-((-4402 . T) (-4401 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170))))) 
+((-4405 . T) (-4404 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-1173))))) 
 (-586 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) 
 NIL 
@@ -2298,19 +2298,19 @@ NIL
 NIL 
 (-592 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2807 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2706 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097)))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) 
 (-593 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 
 (-594 |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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) 
 (-595 |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}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} 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.}"))) 
-((-4402 |has| |#1| (-556)) (-4401 |has| |#1| (-556)) ((-4409 "*") |has| |#1| (-556)) (-4400 |has| |#1| (-556)) (-4404 . T)) 
+((-4405 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) ((-4412 "*") |has| |#1| (-556)) (-4403 |has| |#1| (-556)) (-4407 . T)) 
 ((|HasCategory| |#1| (QUOTE (-556)))) 
 (-596 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) 
@@ -2320,7 +2320,7 @@ 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 
-(-598 R -2306 FG) 
+(-598 R -2234 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{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{\\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{\\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 
@@ -2330,12 +2330,12 @@ NIL
 NIL 
 (-600 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
 (-601 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 -4408)) (|HasCategory| |#2| (QUOTE (-846))) (|HasAttribute| |#1| (QUOTE -4407)) (|HasCategory| |#3| (QUOTE (-1094)))) 
+((|HasAttribute| |#1| (QUOTE -4411)) (|HasCategory| |#2| (QUOTE (-848))) (|HasAttribute| |#1| (QUOTE -4410)) (|HasCategory| |#3| (QUOTE (-1097)))) 
 (-602 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
@@ -2350,19 +2350,19 @@ NIL
 NIL 
 (-605 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4404 -2807 (-2358 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) 
-((-2807 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) 
+((-4407 -2706 (-2275 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4405 . T) (-4404 . T)) 
+((-2706 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) 
 (-606 |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."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| (-1155) (QUOTE (-848))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -611) (QUOTE (-860))))) 
 (-607 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 
 (-608 |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}."))) 
-((-4408 . T)) 
+((-4411 . T)) 
 NIL 
 (-609 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"))) 
@@ -2371,7 +2371,7 @@ NIL
 (-610 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.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) 
 NIL 
-((|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) 
+((|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) 
 (-611 S) 
 ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
@@ -2380,7 +2380,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-613 -2306 UP) 
+(-613 -2234 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
@@ -2402,20 +2402,20 @@ NIL
 NIL 
 (-618 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."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-619 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}."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-844)))) 
-(-620 R -2306) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-846)))) 
+(-620 R -2234) 
 ((|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 
 (-621 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"))) 
-((-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4400 . T) (-4404 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) 
+((-4405 . T) (-4404 . T) ((-4412 "*") . T) (-4403 . T) (-4407 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) 
 (-622 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(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) 
 NIL 
@@ -2430,7 +2430,7 @@ NIL
 NIL 
 (-625 |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.\\spad{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(\\spad{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}}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
 (-626 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(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{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{\\spad{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(\\spad{lp},{} norm?)} 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{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(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{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(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) 
@@ -2440,30 +2440,30 @@ NIL
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-628 R -2306) 
+(-628 R -2234) 
 ((|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{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\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 
-(-629 |lv| -2306) 
+(-629 |lv| -2234) 
 ((|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 
 (-630) 
 ((|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}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|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."))) 
-((-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3813) (QUOTE (-52))))))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 (-52))) (QUOTE (-1094)))) 
+((-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3778) (QUOTE (-52))))))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1155) (QUOTE (-848))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 (-52))) (QUOTE (-1097)))) 
 (-631 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{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-363)))) 
 (-632 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4402 . T) (-4401 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4405 . T) (-4404 . T)) 
 NIL 
 (-633 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4404 -2807 (-2358 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4402 . T) (-4401 . T)) 
-((-2807 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) 
+((-4407 -2706 (-2275 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4405 . T) (-4404 . T)) 
+((-2706 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) 
 (-634 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|) "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|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) 
 NIL 
@@ -2475,2610 +2475,2622 @@ NIL
 (-636 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}\\spad{'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}\\spad{'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}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((-2351 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) 
+((-2268 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) 
 (-637 R) 
 ((|constructor| (NIL "An extension ring 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}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-638 A B) 
-((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) 
+(-638 R) 
+((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) 
 NIL 
 NIL 
 (-639 A B) 
+((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) 
+NIL 
+NIL 
+(-640 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 
 NIL 
-(-640 A B C) 
+(-641 A B C) 
 ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) 
 NIL 
 NIL 
-(-641 S) 
+(-642 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()} returns the empty list."))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
-(-642 T$) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+(-643 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-643 S) 
-((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
 (-644 R) 
-((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) 
+((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{LeftModule} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{r*x} is the left-dilation of \\spad{x} by \\spad{r}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds is \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
+NIL 
+NIL 
+(-645 S) 
+((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-646 R) 
+((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
 NIL 
-(-645 S E |un|) 
+(-647 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,{}y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x,{} y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s,{} e,{} x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s,{} a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a,{} s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l,{} n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l,{} n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s,{} e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l,{} fop,{} fexp,{} unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a,{} b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a,{} n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) 
 NIL 
 NIL 
-(-646 A S) 
+(-648 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{:=} \\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{:=} \\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}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|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| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4408))) 
-(-647 S) 
+((|HasAttribute| |#1| (QUOTE -4411))) 
+(-649 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{:=} \\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{:=} \\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}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|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| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
-(-648 R -2306 L) 
+(-650 R -2234 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 
-(-649 A) 
+(-651 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}}"))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) 
-(-650 A M) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) 
+(-652 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) 
-(-651 S A) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) 
+(-653 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-363)))) 
-(-652 A) 
+(-654 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}."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-653 -2306 UP) 
+(-655 -2234 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)))) 
-(-654 A -4234) 
+(-656 A -2297) 
 ((|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}}"))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) 
-(-655 A L) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) 
+(-657 A L) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} 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}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} 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}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} 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}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-656 S) 
+(-658 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-657) 
+(-659) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-658 M R S) 
+(-660 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}."))) 
-((-4402 . T) (-4401 . T)) 
-((|HasCategory| |#1| (QUOTE (-787)))) 
-(-659 R) 
+((-4405 . T) (-4404 . T)) 
+((|HasCategory| |#1| (QUOTE (-789)))) 
+(-661 R) 
 ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) 
 NIL 
 NIL 
-(-660 |VarSet| R) 
+(-662 |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.\\spad{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) (-4402 . T) (-4401 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4405 . T) (-4404 . T)) 
 ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-172)))) 
-(-661 A S) 
+(-663 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}."))) 
 NIL 
 NIL 
-(-662 S) 
+(-664 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}."))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-663 -2306) 
+(-665 -2234) 
 ((|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\\spad{'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|) "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|) "failed")) (|:| |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|) "failed")) (|:| |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|) "failed")) (|:| |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|) "failed")) (|:| |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 
-(-664 -2306 |Row| |Col| M) 
+(-666 -2234 |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| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |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| "failed")) (|:| |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 
-(-665 R E OV P) 
+(-667 R E OV P) 
 ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,{}lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) 
 NIL 
 NIL 
-(-666 |n| R) 
+(-668 |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."))) 
-((-4404 . T) (-4407 . T) (-4401 . T) (-4402 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2807 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) 
-(-667) 
+((-4407 . T) (-4410 . T) (-4404 . T) (-4405 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2706 (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) 
+(-669) 
 ((|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 
 NIL 
-(-668 |VarSet|) 
+(-670 |VarSet|) 
 ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-669 A S) 
+(-671 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-670 S) 
+(-672 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-671 R) 
+(-673 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 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
-(-672) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+(-674) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-673 |VarSet|) 
+(-675 |VarSet|) 
 ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) 
 NIL 
 NIL 
-(-674 A) 
+(-676 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,{}g,{}x)} is \\spad{g(n,{}g(n-1,{}..g(1,{}x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,{}n,{}x)} applies \\spad{f n} times to \\spad{x}."))) 
 NIL 
 NIL 
-(-675 A C) 
+(-677 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,{}c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,{}c)} selects its first argument."))) 
 NIL 
 NIL 
-(-676 A B C) 
+(-678 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,{}g,{}x)} is \\spad{f(g x)}."))) 
 NIL 
 NIL 
-(-677) 
+(-679) 
 ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for \\spad{`s'}.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of \\spad{`s'}.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,{}t)} builds the mapping AST \\spad{s} \\spad{->} \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) 
 NIL 
 NIL 
-(-678 A) 
+(-680 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,{}x)= g(n,{}g(n-1,{}..g(1,{}x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,{}n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) 
 NIL 
 NIL 
-(-679 A C) 
+(-681 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,{}a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) 
 NIL 
 NIL 
-(-680 A B C) 
+(-682 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}"))) 
 NIL 
 NIL 
-(-681 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+(-683 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}."))) 
 NIL 
 NIL 
-(-682 S R |Row| |Col|) 
+(-684 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| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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 (-4409 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556)))) 
-(-683 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556)))) 
+(-685 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| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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"))) 
-((-4407 . T) (-4408 . T)) 
+((-4410 . T) (-4411 . T)) 
 NIL 
-(-684 R |Row| |Col| M) 
+(-686 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|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")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|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}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|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."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556)))) 
-(-685 R) 
+(-687 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."))) 
-((-4407 . T) (-4408 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
-(-686 R) 
+((-4410 . T) (-4411 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4412 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+(-688 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{**} \\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 
 NIL 
-(-687 T$) 
+(-689 T$) 
 ((|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 \\spad{`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 \\spad{`x'} into \\%."))) 
 NIL 
 NIL 
-(-688 S -2306 FLAF FLAS) 
+(-690 S -2234 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,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row 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 
-(-689 R Q) 
+(-691 R Q) 
 ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) 
 NIL 
 NIL 
-(-690) 
+(-692) 
 ((|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"))) 
-((-4400 . T) (-4405 |has| (-695) (-363)) (-4399 |has| (-695) (-363)) (-3654 . T) (-4406 |has| (-695) (-6 -4406)) (-4403 |has| (-695) (-6 -4403)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
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-(-691 S) 
+((-4403 . T) (-4408 |has| (-697) (-363)) (-4402 |has| (-697) (-363)) (-3609 . T) (-4409 |has| (-697) (-6 -4409)) (-4406 |has| (-697) (-6 -4406)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
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+(-693 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}."))) 
-((-4408 . T)) 
+((-4411 . T)) 
 NIL 
-(-692 U) 
+(-694 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 \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) 
 NIL 
 NIL 
-(-693) 
+(-695) 
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} 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|)) "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|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) 
 NIL 
 NIL 
-(-694 OV E -2306 PG) 
+(-696 OV E -2234 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 
-(-695) 
+(-697) 
 ((|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}"))) 
-((-3646 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-3601 . T) (-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-696 R) 
+(-698 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."))) 
 NIL 
 NIL 
-(-697) 
+(-699) 
 ((|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}"))) 
-((-4406 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4409 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-698 S D1 D2 I) 
+(-700 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"))) 
 NIL 
 NIL 
-(-699 S) 
+(-701 S) 
 ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x,{} y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) 
 NIL 
 NIL 
-(-700 S) 
+(-702 S) 
 ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e,{} foo,{} [x1,{}...,{}xn])} creates a function \\spad{foo(x1,{}...,{}xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x,{} y)} creates a function \\spad{foo(x,{} y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e,{} foo)} creates a function \\spad{foo() == e}."))) 
 NIL 
 NIL 
-(-701 S T$) 
+(-703 S T$) 
 ((|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 part1 is \\spad{a} and part2 is \\spad{b}."))) 
 NIL 
 NIL 
-(-702 S -4063 I) 
+(-704 S -4044 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 
-(-703 E OV R P) 
+(-705 E OV R P) 
 ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,{}lv,{}lu,{}lr,{}lp,{}lt,{}ln,{}t,{}r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,{}lv,{}lu,{}lr,{}lp,{}ln,{}r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,{}lv,{}lr,{}ln,{}lu,{}t,{}r)} \\undocumented"))) 
 NIL 
 NIL 
-(-704 R) 
+(-706 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)}.}"))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-705 R1 UP1 UPUP1 R2 UP2 UPUP2) 
+(-707 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}."))) 
 NIL 
 NIL 
-(-706) 
+(-708) 
 ((|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 
-(-707 R |Mod| -1812 -3669 |exactQuo|) 
+(-709 R |Mod| -1790 -2740 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-708 R |Rep|) 
+(-710 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
-(-709 IS E |ff|) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1148))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-711 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-710 R M) 
+(-712 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) 
+((-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) (-4407 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) 
-(-711 R |Mod| -1812 -3669 |exactQuo|) 
+(-713 R |Mod| -1790 -2740 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-712 S R) 
+(-714 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-713 R) 
+(-715 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 NIL 
-(-714 -2306) 
+(-716 -2234) 
 ((|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]]}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-715 S) 
+(-717 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-716) 
+(-718) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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."))) 
 NIL 
 NIL 
-(-717 S) 
+(-719 S) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'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 such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\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,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\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,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-718) 
+(-720) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'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 such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\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,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\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,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-719 S R UP) 
+(-721 S R UP) 
 ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368)))) 
-(-720 R UP) 
+(-722 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."))) 
-((-4400 |has| |#1| (-363)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 |has| |#1| (-363)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-721 S) 
+(-723 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."))) 
 NIL 
 NIL 
-(-722) 
+(-724) 
 ((|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 
-(-723 -2306 UP) 
+(-725 -2234 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 
-(-724 |VarSet| E1 E2 R S PR PS) 
+(-726 |VarSet| E1 E2 R S PR PS) 
 ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (\\spad{PG})")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,{}p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,{}p)} \\undocumented"))) 
 NIL 
 NIL 
-(-725 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
+(-727 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,{}x)} \\undocumented"))) 
 NIL 
 NIL 
-(-726 E OV R PPR) 
+(-728 E OV R PPR) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|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 
-(-727 |vl| R) 
+(-729 |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."))) 
-(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#2| (QUOTE (-905))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2807 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) 
-(-728 E OV R PRF) 
+(((-4412 "*") |has| |#2| (-172)) (-4403 |has| |#2| (-556)) (-4408 |has| |#2| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#2| (QUOTE (-907))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-862 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+(-730 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 
 NIL 
-(-729 E OV R P) 
+(-731 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) 
 NIL 
 NIL 
-(-730 R S M) 
+(-732 R S M) 
 ((|constructor| (NIL "MonoidRingFunctions2 implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,{}u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) 
 NIL 
 NIL 
-(-731 R M) 
+(-733 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}."))) 
-((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-846)))) 
-(-732 S) 
+((-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) (-4407 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-848)))) 
+(-734 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-4397 . T) (-4408 . T)) 
+((-4400 . T) (-4411 . T)) 
 NIL 
-(-733 S) 
+(-735 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}."))) 
-((-4407 . T) (-4397 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-734) 
+((-4410 . T) (-4400 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-736) 
 ((|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."))) 
 NIL 
 NIL 
-(-735 S) 
+(-737 S) 
 ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,{}l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) 
 NIL 
 NIL 
-(-736 |Coef| |Var|) 
+(-738 |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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4402 . T) (-4401 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4405 . T) (-4404 . T) (-4407 . T)) 
 NIL 
-(-737 OV E R P) 
+(-739 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"))) 
 NIL 
 NIL 
-(-738 E OV R P) 
+(-740 E OV R P) 
 ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-739 S R) 
+(-741 S R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{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}."))) 
 NIL 
 NIL 
-(-740 R) 
+(-742 R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{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}."))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 NIL 
-(-741) 
+(-743) 
 ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{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\\spad{'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\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) 
 NIL 
 NIL 
-(-742) 
+(-744) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.) See \\downlink{Manual Page}{manpageXXc05}.")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,{}ldfjac,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,{}b,{}eps,{}eta,{}ifail,{}f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation,{} extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}."))) 
 NIL 
 NIL 
-(-743) 
+(-745) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values,{} and applies it to calculate convolutions and correlations. See \\downlink{Manual Page}{manpageXXc06}.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,{}n,{}x,{}ifail)} takes \\spad{m} Hermitian sequences,{} each containing \\spad{n} data values,{} and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,{}n,{}x,{}ifail)} forms the complex conjugates,{} each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,{}y,{}ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,{}x,{}ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,{}n,{}init,{}x,{}y,{}trigm,{}trign,{}ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,{}n,{}init,{}x,{}y,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,{}n,{}x,{}y,{}ifail)} calculates the circular convolution of two real vectors of period \\spad{n}. No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,{}x,{}y,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}."))) 
 NIL 
 NIL 
-(-744) 
+(-746) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules. See \\downlink{Manual Page}{manpageXXd01}.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,{}a,{}b,{}maxcls,{}eps,{}lenwrk,{}mincls,{}wrkstr,{}ifail,{}functn)} returns an approximation to the integral of a function over a hyper-rectangular region,{} using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,{}y,{}n,{}ifail)} integrates a function which is specified numerically at four or more points,{} over the whole of its specified range,{} using third-order finite-difference formulae with error estimates,{} according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,{}a,{}b,{}maxpts,{}eps,{}lenwrk,{}minpts,{}ifail,{}functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions),{} with constant and finite limits,{} to a specified relative accuracy,{} using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,{}b,{}itype,{}n,{}gtype,{}ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre,{} Gauss-Rational,{} Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,{}omega,{}key,{}epsabs,{}limlst,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,{}b,{}c,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the Hilbert transform of a function \\spad{g}(\\spad{x}) over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,{}b,{}alfa,{}beta,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} is an adaptive integrator which calculates an approximation to the integral of a function \\spad{g}(\\spad{x})\\spad{w}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,{}b,{}omega,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,{}inf,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over an infinite or semi-infinite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,{}b,{}npts,{}points,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is an adaptive integrator,{} especially suited to oscillating,{} non-singular integrands,{} which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general-purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01ajf}."))) 
 NIL 
 NIL 
-(-745) 
+(-747) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem,{} those in which all boundary conditions are specified at one point (initial-value problems),{} and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems,{} two-point boundary-value problems and Sturm-Liouville eigenvalue problems. See \\downlink{Manual Page}{manpageXXd02}.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "\\spad{d02raf(n,{}mnp,{}numbeg,{}nummix,{}tol,{}init,{}iy,{}ijac,{}lwork,{}liwork,{}np,{}x,{}y,{}deleps,{}ifail,{}fcn,{}g)} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations,{} using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval,{}monit,{}report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains Asp12 and Asp33 are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,{}b,{}n,{}tol,{}mnp,{}lw,{}liw,{}c,{}d,{}gam,{}x,{}np,{}ifail,{}fcnf,{}fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,{}v,{}n,{}a,{}b,{}tol,{}mnp,{}lw,{}liw,{}x,{}np,{}ifail,{}fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations,{} using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,{}m,{}n,{}relabs,{}iw,{}x,{}y,{}tol,{}ifail,{}g,{}fcn,{}pederv,{}output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a variable-order,{} variable-step method implementing the Backward Differentiation Formulae (\\spad{BDF}),{} until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,{}m,{}n,{}tol,{}relabs,{}x,{}y,{}ifail,{}g,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions,{} using a variable-order,{} variable-step Adams method until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,{}n,{}irelab,{}hmax,{}x,{}y,{}tol,{}ifail,{}g,{}fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,{}m,{}n,{}irelab,{}x,{}y,{}tol,{}ifail,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}."))) 
 NIL 
 NIL 
-(-746) 
+(-748) 
 ((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations. See \\downlink{Manual Page}{manpageXXd03}.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03faf(xs,{}xf,{}l,{}lbdcnd,{}bdxs,{}bdxf,{}ys,{}yf,{}m,{}mbdcnd,{}bdys,{}bdyf,{}zs,{}zf,{}n,{}nbdcnd,{}bdzs,{}bdzf,{}lambda,{}ldimf,{}mdimf,{}lwrk,{}f,{}ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,{}xmax,{}ymin,{}ymax,{}ngx,{}ngy,{}lda,{}scheme,{}ifail,{}pdef,{}bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,{}ngy,{}lda,{}maxit,{}acc,{}iout,{}a,{}rhs,{}ub,{}ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}."))) 
 NIL 
 NIL 
-(-747) 
+(-749) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(\\spad{s}),{} the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions,{} there are supporting routines to evaluate,{} differentiate or integrate them. See \\downlink{Manual Page}{manpageXXe01}.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,{}x,{}y,{}f,{}rnw,{}fnodes,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,{}x,{}y,{}f,{}nw,{}nq,{}rnw,{}rnq,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,{}x,{}y,{}f,{}triang,{}grads,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,{}x,{}y,{}f,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,{}my,{}x,{}y,{}f,{}ifail)} computes a bicubic spline interpolating surface through a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,{}x,{}f,{}d,{}a,{}b,{}ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,{}\\spad{b}]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,{}x,{}f,{}ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,{}x,{}y,{}lck,{}lwrk,{}ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}."))) 
 NIL 
 NIL 
-(-748) 
+(-750) 
 ((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors,{} as of experimental measurement,{} which need to be smoothed out. To seek an approximation to the data,{} it is first necessary to specify for the approximating function a mathematical form (a polynomial,{} for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function,{} since these cover the most common needs. However,{} fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating,{} differentiating and integrating polynomial and spline curves and surfaces,{} once the numerical values of their coefficients have been determined. See \\downlink{Manual Page}{manpageXXe02}.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,{}py,{}lamda,{}mu,{}m,{}x,{}y,{}npoint,{}nadres,{}ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,{}la,{}nplus2,{}toler,{}a,{}b,{}ifail)} calculates an \\spad{l} solution to an over-determined system of \\indented{22}{1} linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,{}my,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}lwrk,{}liwrk,{}ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,{}m,{}x,{}y,{}f,{}w,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,{}mx,{}x,{}my,{}y,{}f,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}iwrk,{}ifail)} computes a bicubic spline approximation to a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. The knots of the spline are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,{}px,{}py,{}x,{}y,{}f,{}w,{}mu,{}point,{}npoint,{}nc,{}nws,{}eps,{}lamda,{}ifail)} forms a minimal,{} weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,{}m,{}x,{}y,{}w,{}s,{}nest,{}lwrk,{}n,{}lamda,{}ifail,{}wrk,{}iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,{}lamda,{}c,{}ifail)} computes the definite integral from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,{}lamda,{}c,{}x,{}left,{}ifail)} evaluates a cubic spline and its first three derivatives from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,{}lamda,{}c,{}x,{}ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,{}ncap7,{}x,{}y,{}w,{}lamda,{}ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}x,{}ifail)} evaluates a polynomial from its Chebyshev-series representation,{} allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}qatm1,{}iaint1,{}laint,{}ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}iadif1,{}ladif,{}ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,{}kplus1,{}nrows,{}xmin,{}xmax,{}x,{}y,{}w,{}mf,{}xf,{}yf,{}lyf,{}ip,{}lwrk,{}liwrk,{}ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,{}a,{}xcap,{}ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,{}kplus1,{}nrows,{}x,{}y,{}w,{}ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}."))) 
 NIL 
 NIL 
-(-749) 
+(-751) 
 ((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables,{} possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only,{} since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1}. See \\downlink{Manual Page}{manpageXXe04}.")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,{}m,{}n,{}fsumsq,{}s,{}lv,{}v,{}ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function \\spad{f}(\\spad{x}) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04ucf(n,{}nclin,{}ncnln,{}nrowa,{}nrowj,{}nrowr,{}a,{}bl,{}bu,{}liwork,{}lwork,{}sta,{}cra,{}der,{}fea,{}fun,{}hes,{}infb,{}infs,{}linf,{}lint,{}list,{}maji,{}majp,{}mini,{}minp,{}mon,{}nonf,{}opt,{}ste,{}stao,{}stac,{}stoo,{}stoc,{}ve,{}istate,{}cjac,{}clamda,{}r,{}x,{}ifail,{}confun,{}objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables,{} linear constraints. (E04UCF may be used for unconstrained,{} bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense,{} and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "\\spad{e04naf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}nrowh,{}ncolh,{}bigbnd,{}a,{}bl,{}bu,{}cvec,{}featol,{}hess,{}cold,{}lpp,{}orthog,{}liwork,{}lwork,{}x,{}istate,{}ifail,{}qphess)} is a comprehensive programming (\\spad{QP}) or linear programming (\\spad{LP}) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04mbf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}a,{}bl,{}bu,{}cvec,{}linobj,{}liwork,{}lwork,{}x,{}ifail)} is an easy-to-use routine for solving linear programming problems,{} or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,{}ibound,{}liw,{}lw,{}bl,{}bu,{}x,{}ifail,{}funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F}(\\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ),{} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}\\spad{n}} lower bounds of the independent variables \\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ,{} using \\indented{43}{1\\space{2}2\\space{6}\\spad{n}} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,{}es,{}fu,{}it,{}lin,{}list,{}ma,{}op,{}pr,{}sta,{}sto,{}ve,{}x,{}ifail,{}objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned,{} limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}."))) 
 NIL 
 NIL 
-(-750) 
+(-752) 
 ((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations. See \\downlink{Manual Page}{manpageXXf01}.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,{}m,{}n,{}ncolq,{}lda,{}theta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}theta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the complex \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,{}m,{}n,{}ncolq,{}lda,{}zeta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}zeta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the real \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,{}avals,{}lal,{}nrow,{}ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,{}nz,{}licn,{}lirn,{}abort,{}avals,{}irn,{}icn,{}droptl,{}densw,{}ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01bsf(n,{}nz,{}licn,{}ivect,{}jvect,{}icn,{}ikeep,{}grow,{}eta,{}abort,{}idisp,{}avals,{}ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,{}nz,{}licn,{}lirn,{}pivot,{}lblock,{}grow,{}abort,{}a,{}irn,{}icn,{}ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix,{} or,{} optionally,{} first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}."))) 
 NIL 
 NIL 
-(-751) 
+(-753) 
 ((|constructor| (NIL "This package uses the NAG Library to compute \\begin{items} \\item eigenvalues and eigenvectors of a matrix \\item eigenvalues and eigenvectors of generalized matrix eigenvalue problems \\item singular values and singular vectors of a matrix. \\end{items} See \\downlink{Manual Page}{manpageXXf02}.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldph,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldpt,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image,{}monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,{}ia,{}ib,{}eps1,{}matv,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues and,{} if required,{} all the eigenvectors of the generalized eigenproblem Ax=(lambda)\\spad{Bx} where A and \\spad{B} are real,{} square matrices,{} using the \\spad{QZ} algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,{}n,{}alb,{}ub,{}m,{}iv,{}a,{}ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form,{} bisection and inverse iteration,{} where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,{}iar,{}\\spad{ai},{}iai,{}n,{}ivr,{}ivi,{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,{}iai,{}n,{}ivr,{}ivi,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,{}n,{}ivr,{}ivi,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,{}n,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,{}ib,{}n,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,{}ib,{}n,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,{}ia,{}n,{}iv,{}ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,{}n,{}a,{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}."))) 
 NIL 
 NIL 
-(-752) 
+(-754) 
 ((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\axiom{AX=B},{} where \\axiom{\\spad{B}} may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real,{} complex,{} symmetric,{} Hermitian positive- definite,{} or sparse. It may also be rectangular,{} in which case a least-squares solution is obtained. See \\downlink{Manual Page}{manpageXXf04}.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "\\spad{f04qaf(m,{}n,{}damp,{}atol,{}btol,{}conlim,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}b,{}ifail,{}aprod)} solves sparse unsymmetric equations,{} sparse linear least- squares problems and sparse damped linear least-squares problems,{} using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,{}al,{}lal,{}d,{}nrow,{}ir,{}b,{}nrb,{}iselct,{}nrx,{}ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides,{} AX=B,{} where A is a symmetric positive-definite variable-bandwidth matrix,{} which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,{}b,{}precon,{}shift,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}rtol,{}ifail,{}aprod,{}msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f04maf(n,{}nz,{}avals,{}licn,{}irn,{}lirn,{}icn,{}wkeep,{}ikeep,{}inform,{}b,{}acc,{}noits,{}ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations,{} Ax=b,{} using a pre-conditioned conjugate gradient method,{} where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,{}n,{}nra,{}tol,{}lwork,{}a,{}b,{}ifail)} finds the solution of a linear least-squares problem,{} Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank,{} then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,{}n,{}d,{}e,{}b,{}ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,{}a,{}licn,{}icn,{}ikeep,{}mtype,{}idisp,{}rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side,{} Ax=b or \\indented{1}{\\spad{T}} A \\spad{x=b},{} where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,{}ia,{}b,{}n,{}iaa,{}ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting,{} and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,{}b,{}n,{}a,{}ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side,{} Ax=b,{} using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,{}b,{}n,{}a,{}ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,{}b,{}ib,{}n,{}m,{}ic,{}a,{}ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}."))) 
 NIL 
 NIL 
-(-753) 
+(-755) 
 ((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations,{} and to solve systems of linear equations following the matrix factorizations. See \\downlink{Manual Page}{manpageXXf07}.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,{}n,{}nrhs,{}a,{}lda,{}ldb,{}b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides,{} AX=B,{} where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,{}n,{}lda,{}a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,{}n,{}nrhs,{}a,{}lda,{}ipiv,{}ldb,{}b)} (DGETRS) solves a real system of linear equations with \\indented{36}{\\spad{T}} multiple right-hand sides,{} AX=B or A \\spad{X=B},{} where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,{}n,{}lda,{}a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}."))) 
 NIL 
 NIL 
-(-754) 
+(-756) 
 ((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions. See \\downlink{Manual Page}{manpageXXs}.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,{}y,{}z,{}r,{}ifail)} returns a value of the symmetrised elliptic integral of the third kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the second kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,{}y,{}ifail)} returns a value of an elementary integral,{} which occurs as a degenerate case of an elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{C}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{S}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,{}ifail)} returns a value for the Kelvin function kei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,{}ifail)} returns a value for the Kelvin function ker(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,{}ifail)} returns a value for the Kelvin function bei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,{}ifail)} returns a value for the Kelvin function ber(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{I}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{K}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,{}ifail)} returns a value for the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,{}fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{\\spad{H}\\space{6}(\\spad{z}) or \\spad{H}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}\\space{8}(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Bi}(\\spad{z}) or its derivative Bi'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Ai}(\\spad{z}) or its derivative Ai'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{J}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{Y}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,{}ifail)} returns a value for the derivative of the Airy function \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,{}ifail)} returns a value of the derivative of the Airy function \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,{}ifail)} returns a value of the Airy function,{} \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,{}ifail)} returns a value for the Airy function,{} \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,{}ifail)} returns the value of the error function erf(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,{}ifail)} returns the value of the complementary error function,{} erfc(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,{}x,{}tol,{}ifail)} computes values for the incomplete gamma functions \\spad{P}(a,{}\\spad{x}) and \\spad{Q}(a,{}\\spad{x}). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,{}ifail)} returns a value for the log,{} \\spad{ln}(Gamma(\\spad{x})),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,{}ifail)} returns the value of the Gamma function (Gamma)(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,{}ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,{}ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,{}ifail)} returns the value of the exponential integral \\indented{1}{\\spad{E} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,{}ifail)} S01EAF evaluates the exponential function exp(\\spad{z}) ,{} for complex \\spad{z}. See \\downlink{Manual Page}{manpageXXs01eaf}."))) 
 NIL 
 NIL 
-(-755) 
+(-757) 
 ((|constructor| (NIL "Support functions for the NAG Library Link functions")) (|restorePrecision| (((|Void|)) "\\spad{restorePrecision()} \\undocumented{}")) (|checkPrecision| (((|Boolean|)) "\\spad{checkPrecision()} \\undocumented{}")) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}")) (|aspFilename| (((|String|) (|String|)) "\\spad{aspFilename(\"f\")} returns a String consisting of \\spad{\"f\"} suffixed with \\indented{1}{an extension identifying the current AXIOM session.}")) (|fortranLinkerArgs| (((|String|)) "\\spad{fortranLinkerArgs()} returns the current linker arguments")) (|fortranCompilerName| (((|String|)) "\\spad{fortranCompilerName()} returns the name of the currently selected \\indented{1}{Fortran compiler}"))) 
 NIL 
 NIL 
-(-756 S) 
+(-758 S) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-757) 
+(-759) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-758 S) 
+(-760 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-759) 
+(-761) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-760 |Par|) 
+(-762 |Par|) 
 ((|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 
-(-761 -2306) 
+(-763 -2234) 
 ((|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 
-(-762 P -2306) 
+(-764 P -2234) 
 ((|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\\spad{''}."))) 
 NIL 
 NIL 
-(-763 T$) 
+(-765 T$) 
 NIL 
 NIL 
 NIL 
-(-764 UP -2306) 
+(-766 UP -2234) 
 ((|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{\\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{\\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{\\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{\\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{\\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{\\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 
-(-765) 
+(-767) 
 ((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-766 R) 
+(-768 R) 
 ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) 
 NIL 
 NIL 
-(-767) 
+(-769) 
 ((|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."))) 
-(((-4409 "*") . T)) 
+(((-4412 "*") . T)) 
 NIL 
-(-768 R -2306) 
+(-770 R -2234) 
 ((|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 
-(-769 S) 
+(-771 S) 
 ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) 
 NIL 
 NIL 
-(-770) 
+(-772) 
 ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) 
 NIL 
 NIL 
-(-771 R |PolR| E |PolE|) 
+(-773 R |PolR| E |PolE|) 
 ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) 
 NIL 
 NIL 
-(-772 R E V P TS) 
+(-774 R E V P TS) 
 ((|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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{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},{}\\spad{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 
-(-773 -2306 |ExtF| |SUEx| |ExtP| |n|) 
+(-775 -2234 |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 
-(-774 BP E OV R P) 
+(-776 BP E OV R P) 
 ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) 
 NIL 
 NIL 
-(-775 |Par|) 
+(-777 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,{}eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with variable \\spad{x}. Fraction \\spad{P} \\spad{RN}.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with a new symbol as variable."))) 
 NIL 
 NIL 
-(-776 R |VarSet|) 
+(-778 R |VarSet|) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2351 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2351 (|HasCategory| |#1| (QUOTE (-545)))) (-2351 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2351 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564))))) (-2351 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2351 (|HasCategory| |#1| (LIST (QUOTE -988) (QUOTE (-564))))))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
-(-777 R S) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173)))) (-2268 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173)))) (-2268 (|HasCategory| |#1| (QUOTE (-545)))) (-2268 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173)))) (-2268 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564))))) (-2268 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1173)))) (-2268 (|HasCategory| |#1| (LIST (QUOTE -990) (QUOTE (-564))))))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-779 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 
 NIL 
-(-778 R) 
+(-780 R) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|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)}"))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
-(-779 R) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1148))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-781 R) 
 ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) 
-(-780 R E V P) 
+(-782 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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.}"))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-781 S) 
+(-783 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 
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-(-782) 
+((-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (QUOTE (-172)))) 
+(-784) 
 ((|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 
 NIL 
-(-783) 
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 ((|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|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.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|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 
-(-784) 
+(-786) 
 ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,{}y,{}x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})\\spad{**}(-1/5)}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try ,{} did ,{} next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is the same as \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation\\spad{'s} right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) 
 NIL 
 NIL 
-(-785) 
+(-787) 
 ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) 
 NIL 
 NIL 
-(-786 |Curve|) 
+(-788 |Curve|) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,{}r,{}n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-787) 
+(-789) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-788) 
+(-790) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-789) 
+(-791) 
 ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,{}y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-790) 
+(-792) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-791) 
+(-793) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-792 S R) 
+(-794 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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,{}\\spad{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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-368)))) 
-(-793 R) 
+((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-368)))) 
+(-795 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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,{}\\spad{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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-794 -2807 R OS S) 
+(-796 -2706 R OS S) 
 ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
-(-795 R) 
+(-797 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2807 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) 
-(-796) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2706 (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-997 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) 
+(-798) 
 ((|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 
-(-797 R -2306 L) 
+(-799 R -2234 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{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-798 R -2306) 
+(-800 R -2234) 
 ((|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| "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| "failed") (|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| "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| "failed") (|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 
-(-799) 
+(-801) 
 ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'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 
-(-800 R -2306) 
+(-802 R -2234) 
 ((|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 
-(-801) 
+(-803) 
 ((|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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) 
 NIL 
 NIL 
-(-802 -2306 UP UPUP R) 
+(-804 -2234 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."))) 
 NIL 
 NIL 
-(-803 -2306 UP L LQ) 
+(-805 -2234 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}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'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."))) 
 NIL 
 NIL 
-(-804) 
+(-806) 
 ((|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{}"))) 
 NIL 
 NIL 
-(-805 -2306 UP L LQ) 
+(-807 -2234 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^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}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'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}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\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}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\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 \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{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 {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) 
 NIL 
 NIL 
-(-806 -2306 UP) 
+(-808 -2234 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|) "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}\\spad{'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|) "failed")) (|:| |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}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) 
 NIL 
 NIL 
-(-807 -2306 L UP A LO) 
+(-809 -2234 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}."))) 
 NIL 
 NIL 
-(-808 -2306 UP) 
+(-810 -2234 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}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\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 \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\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)))) 
-(-809 -2306 LO) 
+(-811 -2234 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 
-(-810 -2306 LODO) 
+(-812 -2234 LODO) 
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 NIL 
 NIL 
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 ((|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| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-791))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1047))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-724))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-791))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-848))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1047)))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173))))) (-2706 (|HasCategory| |#2| (QUOTE (-1047))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasAttribute| |#2| (QUOTE -4407)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) 
+(-814 R) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
-(-813 |Kernels| R |var|) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-816 (-1173)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-815 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-4409 "*") |has| |#2| (-363)) (-4400 |has| |#2| (-363)) (-4405 |has| |#2| (-363)) (-4399 |has| |#2| (-363)) (-4404 . T) (-4402 . T) (-4401 . T)) 
+(((-4412 "*") |has| |#2| (-363)) (-4403 |has| |#2| (-363)) (-4408 |has| |#2| (-363)) (-4402 |has| |#2| (-363)) (-4407 . T) (-4405 . T) (-4404 . T)) 
 ((|HasCategory| |#2| (QUOTE (-363)))) 
-(-814 S) 
+(-816 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}))."))) 
 NIL 
 NIL 
-(-815 S) 
+(-817 S) 
 ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'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}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the \\spad{n-th} monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the \\spad{n-th} monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m} and \\spad{y = m * r} hold and such that \\spad{l} and \\spad{r} have no overlap,{} that is \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|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}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x,{} s)} returns the exact right quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} that is \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x,{} s)} returns the exact left quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} \\indented{1}{by \\spad{y} that is \\spad{q} such that \\spad{x = y * q},{}} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (|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| $) "\\spad{first(x)} returns the first letter of \\spad{x}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\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."))) 
 NIL 
 NIL 
-(-816) 
+(-818) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-817) 
+(-819) 
 ((|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 
-(-818) 
+(-820) 
 ((|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 \\spad{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 \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) 
 NIL 
 NIL 
-(-819) 
+(-821) 
 ((|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| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\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 
-(-820) 
+(-822) 
 ((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{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 \\spad{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 
-(-821) 
+(-823) 
 ((|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|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) 
 NIL 
 NIL 
-(-822 R) 
+(-824 R) 
 ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) 
 NIL 
 NIL 
-(-823 P R) 
+(-825 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
 ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-233)))) 
-(-824) 
+(-826) 
 ((|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 \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) 
 NIL 
 NIL 
-(-825) 
+(-827) 
 ((|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 \\spad{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 \\spad{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 
-(-826 S) 
+(-828 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-4407 . T) (-4397 . T) (-4408 . T)) 
+((-4410 . T) (-4400 . T) (-4411 . T)) 
 NIL 
-(-827) 
+(-829) 
 ((|constructor| (NIL "\\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 \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) 
 NIL 
 NIL 
-(-828 R S) 
+(-830 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 
-(-829 R) 
+(-831 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."))) 
-((-4404 |has| |#1| (-844))) 
-((|HasCategory| |#1| (QUOTE (-844))) (-2807 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2807 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) 
-(-830 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.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) 
+((-4407 |has| |#1| (-846))) 
+((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-21))) (-2706 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545)))) 
+(-832 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 
-(-831 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.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of `op'."))) 
+(-833 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-832 R) 
+(-834 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) 
+((-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) (-4407 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) 
-(-833) 
+(-835) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) 
 NIL 
 NIL 
-(-834) 
+(-836) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 \\spad{`x'}."))) 
 NIL 
 NIL 
-(-835) 
+(-837) 
 ((|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 
-(-836) 
+(-838) 
 ((|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 
-(-837) 
+(-839) 
 ((|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 
-(-838 R S) 
+(-840 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 
-(-839 R) 
+(-841 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-4404 |has| |#1| (-844))) 
-((|HasCategory| |#1| (QUOTE (-844))) (-2807 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2807 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) 
-(-840) 
+((-4407 |has| |#1| (-846))) 
+((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-21))) (-2706 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545)))) 
+(-842) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-841 -3599 S) 
+(-843 -3554 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-842) 
+(-844) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-843 S) 
+(-845 S) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
 NIL 
 NIL 
-(-844) 
+(-846) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-845 S) 
+(-847 S) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) 
 NIL 
 NIL 
-(-846) 
+(-848) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) 
 NIL 
 NIL 
-(-847 S R) 
+(-849 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\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 \\spad{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\\spad{''}.")) (|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\\spad{''}.")) (|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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172)))) 
-(-848 R) 
+(-850 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\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 \\spad{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\\spad{''}.")) (|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\\spad{''}.")) (|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)}.}"))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-849 R C) 
+(-851 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{''}. \\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{''}. \\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{''}. \\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{''}. \\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 (-363))) (|HasCategory| |#1| (QUOTE (-556)))) 
-(-850 R |sigma| -1924) 
+(-852 R |sigma| -1926) 
 ((|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."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) 
-(-851 |x| R |sigma| -1924) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) 
+(-853 |x| R |sigma| -1926) 
 ((|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}."))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) 
-(-852 R) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) 
+(-854 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 -407) (QUOTE (-564)))))) 
-(-853) 
+(-855) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-854) 
+(-856) 
 ((|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 
-(-855 S) 
+(-857 S) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`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 \\spad{`v'} on the conduit \\spad{`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 \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-856) 
+(-858) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`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 \\spad{`v'} on the conduit \\spad{`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 \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-857) 
+(-859) 
 ((|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 \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) 
 NIL 
 NIL 
-(-858) 
+(-860) 
 ((|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| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|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'''},{} \\spad{\"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 
-(-859) 
+(-861) 
 ((|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\\spad{''} 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\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) 
 NIL 
 NIL 
-(-860 |VariableList|) 
+(-862 |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 
-(-861) 
+(-863) 
 ((|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 
-(-862 R |vl| |wl| |wtlevel|) 
+(-864 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: \\spad{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)"))) 
-((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) 
+((-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) (-4407 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) 
-(-863 R PS UP) 
+(-865 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 
-(-864 R |x| |pt|) 
+(-866 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 
-(-865 |p|) 
+(-867 |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}."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-866 |p|) 
+(-868 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{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)."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-867 |p|) 
+(-869 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{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)."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2807 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) 
-(-868 |p| PADIC) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-868 |#1|) (QUOTE (-907))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-868 |#1|) (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-147))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-868 |#1|) (QUOTE (-1020))) (|HasCategory| (-868 |#1|) (QUOTE (-818))) (-2706 (|HasCategory| (-868 |#1|) (QUOTE (-818))) (|HasCategory| (-868 |#1|) (QUOTE (-848)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (QUOTE (-1148))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-868 |#1|) (QUOTE (-233))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -514) (QUOTE (-1173)) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -868) (|devaluate| |#1|)) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| (-868 |#1|) (QUOTE (-307))) (|HasCategory| (-868 |#1|) (QUOTE (-545))) (|HasCategory| (-868 |#1|) (QUOTE (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-868 |#1|) (QUOTE (-907)))) (|HasCategory| (-868 |#1|) (QUOTE (-145))))) 
+(-870 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of \\spad{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)}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2807 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) 
-(-869 S T$) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-818))) (-2706 (|HasCategory| |#2| (QUOTE (-818))) (|HasCategory| |#2| (QUOTE (-848)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1148))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-848))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+(-871 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 \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#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 \\spad{`s'} and \\spad{`t'}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) 
-(-870) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))))) 
+(-872) 
 ((|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\\spad{'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\\spad{'s} lowest value."))) 
 NIL 
 NIL 
-(-871) 
+(-873) 
 ((|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 
-(-872 CF1 CF2) 
+(-874 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) 
 NIL 
 NIL 
-(-873 |ComponentFunction|) 
+(-875 |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 
-(-874 CF1 CF2) 
+(-876 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) 
 NIL 
 NIL 
-(-875 |ComponentFunction|) 
+(-877 |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 
-(-876) 
+(-878) 
 ((|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 
-(-877 CF1 CF2) 
+(-879 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) 
 NIL 
 NIL 
-(-878 |ComponentFunction|) 
+(-880 |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 
-(-879) 
+(-881) 
 ((|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\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'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}\\spad{'s},{} and 4 \\spad{5}\\spad{'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| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l,{}n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}"))) 
 NIL 
 NIL 
-(-880 R) 
+(-882 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 
-(-881 R S L) 
+(-883 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 
-(-882 S) 
+(-884 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 
-(-883 |Base| |Subject| |Pat|) 
+(-885 |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 (-2351 (|HasCategory| |#2| (QUOTE (-1045)))) (-2351 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2351 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) 
-(-884 R A B) 
+((-12 (-2268 (|HasCategory| |#2| (QUOTE (-1047)))) (-2268 (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (-2268 (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173))))) 
+(-886 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}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) 
 NIL 
 NIL 
-(-885 R S) 
+(-887 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\\spad{'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},{}e1),{}...,{}(\\spad{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 
-(-886 R -4063) 
+(-888 R -4044) 
 ((|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 \\spad{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 
-(-887 R S) 
+(-889 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 
-(-888 R) 
+(-890 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 \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{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 \\spad{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 \\spad{'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 
-(-889 |VarSet|) 
+(-891 |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.\\spad{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 
-(-890 UP R) 
+(-892 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented"))) 
 NIL 
 NIL 
-(-891) 
+(-893) 
 ((|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 
-(-892 UP -2306) 
+(-894 UP -2234) 
 ((|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 
-(-893) 
+(-895) 
 ((|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\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|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\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|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\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|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\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) 
 NIL 
 NIL 
-(-894) 
+(-896) 
 ((|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 
-(-895 A S) 
+(-897 A S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|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}-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)}.") (($ $ |#2|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-896 S) 
+(-898 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|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}-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)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-897 S) 
+(-899 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})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-898 |n| R) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-900 |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,{} \\spad{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 \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{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 
-(-899 S) 
+(-901 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}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under 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."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-900 S) 
+(-902 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}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
 NIL 
 NIL 
-(-901 S) 
+(-903 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|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."))) 
-((-4404 . T)) 
-((-2807 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) 
-(-902 R E |VarSet| S) 
+((-4407 . T)) 
+((-2706 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-848)))) 
+(-904 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 \\spad{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 
-(-903 R S) 
+(-905 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 \\spad{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 
-(-904 S) 
+(-906 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| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" 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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{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 (-145)))) 
-(-905) 
+(-907) 
 ((|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| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" 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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{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}."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-906 |p|) 
+(-908 |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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) 
-(-907 R0 -2306 UP UPUP R) 
+(-909 R0 -2234 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 
-(-908 UP UPUP R) 
+(-910 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 
-(-909 UP UPUP) 
+(-911 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 
-(-910 R) 
+(-912 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\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} 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} \\spad{``p}-adically\\spad{''} 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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-911 R) 
+(-913 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 
-(-912 E OV R P) 
+(-914 E OV R P) 
 ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-913) 
+(-915) 
 ((|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\\spad{'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\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'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\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\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(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{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 \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{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(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{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 
-(-914 -2306) 
+(-916 -2234) 
 ((|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 \\spad{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 
-(-915 R) 
+(-917 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 
-(-916) 
+(-918) 
 ((|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| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-917) 
+(-919) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4409 "*") . T)) 
+(((-4412 "*") . T)) 
 NIL 
-(-918 -2306 P) 
+(-920 -2234 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-919 |xx| -2306) 
+(-921 |xx| -2234) 
 ((|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 
-(-920 R |Var| |Expon| GR) 
+(-922 R |Var| |Expon| GR) 
 ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{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{>=} \\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} \\spad{~=} 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{>=} \\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{>=} \\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{>=} \\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{>=} \\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{>=} \\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{>=} \\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 
-(-921 S) 
+(-923 S) 
 ((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{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 
-(-922) 
+(-924) 
 ((|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 
-(-923) 
+(-925) 
 ((|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*\\%\\spad{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 
-(-924) 
+(-926) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-925 R -2306) 
+(-927 R -2234) 
 ((|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 \\spad{'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 
-(-926) 
+(-928) 
 ((|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 \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) 
 NIL 
 NIL 
-(-927 S A B) 
+(-929 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 
-(-928 S R -2306) 
+(-930 S R -2234) 
 ((|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 
-(-929 I) 
+(-931 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 
-(-930 S E) 
+(-932 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 
-(-931 S R L) 
+(-933 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 
-(-932 S E V R P) 
+(-934 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 -882) (|devaluate| |#1|)))) 
-(-933 R -2306 -4063) 
+((|HasCategory| |#3| (LIST (QUOTE -884) (|devaluate| |#1|)))) 
+(-935 R -2234 -4044) 
 ((|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 \\spad{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 
-(-934 -4063) 
+(-936 -4044) 
 ((|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 \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
-(-935 S R Q) 
+(-937 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 
-(-936 S) 
+(-938 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 
-(-937 S R P) 
+(-939 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 
-(-938) 
+(-940) 
 ((|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 
-(-939 R) 
+(-941 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
-(-940 |lv| R) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+(-942 |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 
-(-941 |TheField| |ThePols|) 
+(-943 |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},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@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},{}\\spad{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 (-844)))) 
-(-942 R S) 
+((|HasCategory| |#1| (QUOTE (-846)))) 
+(-944 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 
-(-943 |x| R) 
+(-945 |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 
-(-944 S R E |VarSet|) 
+(-946 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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 (-905))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) 
-(-945 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-907))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#4| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) 
+(-947 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 \\spad{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 \\spad{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 \\spad{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 \\spad{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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
 NIL 
-(-946 E V R P -2306) 
+(-948 E V R P -2234) 
 ((|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},{}...,{}\\spad{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 
-(-947 E |Vars| R P S) 
+(-949 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 
-(-948 R) 
+(-950 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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
-(-949 E V R P -2306) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1173) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-951 E V R P -2234) 
 ((|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| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-452)))) 
-(-950) 
+(-952) 
 ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) 
 NIL 
 NIL 
-(-951) 
+(-953) 
 ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-952 R L) 
+(-954 R L) 
 ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) 
 NIL 
 NIL 
-(-953 A B) 
+(-955 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-954 S) 
+(-956 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
-(-955) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+(-957) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) 
 NIL 
 NIL 
-(-956 -2306) 
+(-958 -2234) 
 ((|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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'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}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) 
 NIL 
 NIL 
-(-957 I) 
+(-959 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'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\\spad{'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 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 
-(-958) 
+(-960) 
 ((|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 
-(-959 R E) 
+(-961 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}"))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4405))) 
-(-960 A B) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4408))) 
+(-962 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"))) 
-((-4404 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) 
-(-961) 
+((-4407 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791)))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-848))))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#2| (QUOTE (-724))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#2| (QUOTE (-724)))) (-12 (|HasCategory| |#1| (QUOTE (-791))) (|HasCategory| |#2| (QUOTE (-791))))) (-12 (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#2| (QUOTE (-724)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-848))))) 
+(-963) 
 ((|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 \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-962 T$) 
+(-964 T$) 
 ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|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.")) (|isTerm| (((|Maybe| |#1|) $) "\\spad{isTerm f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-963) 
+(-965) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-964 S) 
+(-966 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-4407 . T) (-4408 . T)) 
+((-4410 . T) (-4411 . T)) 
 NIL 
-(-965 R |polR|) 
+(-967 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{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{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.\\spad{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{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\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{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{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} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + 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{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} 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{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} 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}) \\spad{>=} 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 = \\spad{+/-} 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 \\spad{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}) \\spad{>=} 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}) \\spad{>=} 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}) \\spad{>=} 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{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} 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 (-452)))) 
-(-966) 
+(-968) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-967) 
+(-969) 
 ((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition"))) 
 NIL 
 NIL 
-(-968 S |Coef| |Expon| |Var|) 
+(-970 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 
-(-969 |Coef| |Expon| |Var|) 
+(-971 |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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-970) 
+(-972) 
 ((|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 \\spad{x-},{} \\spad{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 
-(-971 S R E |VarSet| P) 
+(-973 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?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{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,{}\\spad{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{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{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{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{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?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-556)))) 
-(-972 R E |VarSet| P) 
+(-974 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?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{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,{}\\spad{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{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{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{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{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?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((-4407 . T)) 
+((-4410 . T)) 
 NIL 
-(-973 R E V P) 
+(-975 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(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*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 \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*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(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{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(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{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},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{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(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{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(\\spad{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(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{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?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{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 \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-307)))) (|HasCategory| |#1| (QUOTE (-452)))) 
-(-974 K) 
+(-976 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 
-(-975 |VarSet| E RC P) 
+(-977 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{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 
-(-976 R) 
+(-978 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}."))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-977 R1 R2) 
+(-979 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) 
 NIL 
 NIL 
-(-978 R) 
+(-980 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 
-(-979 K) 
+(-981 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 \\spad{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 
-(-980 R E OV PPR) 
+(-982 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 
-(-981 K R UP -2306) 
+(-983 K R UP -2234) 
 ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) 
 NIL 
 NIL 
-(-982 |vl| |nv|) 
+(-984 |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 
-(-983 R |Var| |Expon| |Dpoly|) 
+(-985 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\\spad{'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|) "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\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|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} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-307))))) 
-(-984 R E V P TS) 
+(-986 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,{}\\spad{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(\\spad{lp},{}\\spad{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?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{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?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{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{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{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 
-(-985) 
+(-987) 
 ((|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 
-(-986 A B R S) 
+(-988 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 
-(-987 A S) 
+(-989 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 (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145)))) 
-(-988 S) 
+((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-818))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1148)))) 
+(-990 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}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-989 |n| K) 
+(-991 |n| K) 
 ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|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 
-(-990) 
+(-992) 
 ((|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 
-(-991 S) 
+(-993 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|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\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."))) 
-((-4407 . T) (-4408 . T)) 
+((-4410 . T) (-4411 . T)) 
 NIL 
-(-992 S R) 
+(-994 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 (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-290)))) 
-(-993 R) 
+((|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-290)))) 
+(-995 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}."))) 
-((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 |has| |#1| (-290)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-994 QR R QS S) 
+(-996 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 
-(-995 R) 
+(-997 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.}"))) 
-((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) 
-(-996 S) 
+((-4403 |has| |#1| (-290)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1173)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-545)))) 
+(-998 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}."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-997 S) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-999 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-998) 
+(-1000) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 
-(-999 -2306 UP UPUP |radicnd| |n|) 
+(-1001 -2234 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2807 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2807 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2807 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) 
-(-1000 |bb|) 
+((-4403 |has| (-407 |#2|) (-363)) (-4408 |has| (-407 |#2|) (-363)) (-4402 |has| (-407 |#2|) (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2706 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2706 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2706 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2706 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) 
+(-1002 |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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2807 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) 
-(-1001) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-564) (QUOTE (-907))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-1173)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1020))) (|HasCategory| (-564) (QUOTE (-818))) (-2706 (|HasCategory| (-564) (QUOTE (-818))) (|HasCategory| (-564) (QUOTE (-848)))) (|HasCategory| (-564) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1148))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1173)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-907)))) (|HasCategory| (-564) (QUOTE (-145))))) 
+(-1003) 
 ((|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 
-(-1002) 
+(-1004) 
 ((|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 
-(-1003 RP) 
+(-1005 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 
-(-1004 S) 
+(-1006 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 
-(-1005 A S) 
+(-1007 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{:=} \\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 -4408)) (|HasCategory| |#2| (QUOTE (-1094)))) 
-(-1006 S) 
+((|HasAttribute| |#1| (QUOTE -4411)) (|HasCategory| |#2| (QUOTE (-1097)))) 
+(-1008 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{:=} \\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 
-(-1007 S) 
+(-1009 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} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (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 
-(-1008) 
+(-1010) 
 ((|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} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (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}}"))) 
-((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) 
+((-4403 . T) (-4408 . T) (-4402 . T) (-4405 . T) (-4404 . T) ((-4412 "*") . T) (-4407 . T)) 
 NIL 
-(-1009 R -2306) 
+(-1011 R -2234) 
 ((|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 
-(-1010 R -2306) 
+(-1012 R -2234) 
 ((|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 
-(-1011 -2306 UP) 
+(-1013 -2234 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 
-(-1012 -2306 UP) 
+(-1014 -2234 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 
-(-1013 S) 
+(-1015 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 
-(-1014 F1 UP UPUP R F2) 
+(-1016 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 
-(-1015) 
+(-1017) 
 ((|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 
-(-1016 |Pol|) 
+(-1018 |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 
-(-1017 |Pol|) 
+(-1019 |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 
-(-1018) 
+(-1020) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-1019) 
+(-1021) 
 ((|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 
-(-1020 |TheField|) 
+(-1022 |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"))) 
-((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T)) 
-((-2807 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) 
-(-1021 -2306 L) 
+((-4403 . T) (-4408 . T) (-4402 . T) (-4405 . T) (-4404 . T) ((-4412 "*") . T) (-4407 . T)) 
+((-2706 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1036) (QUOTE (-564))))) 
+(-1023 -2234 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{\\spad{fi}} must satisfy \\spad{op \\spad{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 
-(-1022 S) 
+(-1024 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 (-1094)))) 
-(-1023 R E V P) 
+((|HasCategory| |#1| (QUOTE (-1097)))) 
+(-1025 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(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{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(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{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},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1024 R) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1026 R) 
 ((|constructor| (NIL "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(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{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 \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\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 \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\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 
-((|HasAttribute| |#1| (QUOTE (-4409 "*")))) 
-(-1025 R) 
+((|HasAttribute| |#1| (QUOTE (-4412 "*")))) 
+(-1027 R) 
 ((|constructor| (NIL "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\\spad{'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\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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 
 ((-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307)))) 
-(-1026 S) 
+(-1028 S) 
 ((|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 
-(-1027) 
+(-1029) 
 ((|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 
-(-1028 S) 
+(-1030 S) 
 ((|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 
-(-1029 S) 
+(-1031 S) 
 ((|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 
-(-1030 -2306 |Expon| |VarSet| |FPol| |LFPol|) 
+(-1032 -2234 |Expon| |VarSet| |FPol| |LFPol|) 
 ((|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"))) 
-(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1031) 
+(-1033) 
 ((|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.}"))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3813) (QUOTE (-52))))))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1032) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1173))) (LIST (QUOTE |:|) (QUOTE -3778) (QUOTE (-52))))))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-1173) (QUOTE (-848))) (|HasCategory| (-52) (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1034) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-1033 A S) 
+(-1035 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 
-(-1034 S) 
+(-1036 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 
-(-1035 Q R) 
+(-1037 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 
-(-1036) 
+(-1038) 
 ((|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 
-(-1037 UP) 
+(-1039 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 
-(-1038 R) 
+(-1040 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 
-(-1039 R) 
+(-1041 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}\\spad{'s} appearing inside the \\spad{gi}\\spad{'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}\\spad{'s} appearing inside the \\spad{gi}\\spad{'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 
-(-1040 T$) 
+(-1042 T$) 
 ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) 
 NIL 
 NIL 
-(-1041 T$) 
+(-1043 T$) 
 ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) 
 NIL 
 NIL 
-(-1042 R |ls|) 
+(-1044 R |ls|) 
 ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{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}."))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1094))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -776) (|devaluate| |#1|) (LIST (QUOTE -860) (|devaluate| |#2|)))))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-860 |#2|) (QUOTE (-368))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1043) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| (-778 |#1| (-862 |#2|)) (QUOTE (-1097))) (|HasCategory| (-778 |#1| (-862 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -778) (|devaluate| |#1|) (LIST (QUOTE -862) (|devaluate| |#2|)))))) (|HasCategory| (-778 |#1| (-862 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-778 |#1| (-862 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-862 |#2|) (QUOTE (-368))) (|HasCategory| (-778 |#1| (-862 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1045) 
 ((|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 
-(-1044 S) 
+(-1046 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 
-(-1045) 
+(-1047) 
 ((|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."))) 
-((-4404 . T)) 
+((-4407 . T)) 
 NIL 
-(-1046 |xx| -2306) 
+(-1048 |xx| -2234) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-1047 S |m| |n| R |Row| |Col|) 
+(-1049 R) 
+((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{RightModule} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{r*x} is the left-dilation of \\spad{x} by \\spad{r}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds is \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
+NIL 
+NIL 
+(-1050 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 (-307))) (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (QUOTE (-556))) (|HasCategory| |#4| (QUOTE (-172)))) 
-(-1048 |m| |n| R |Row| |Col|) 
+(-1051 |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"))) 
-((-4407 . T) (-4402 . T) (-4401 . T)) 
+((-4410 . T) (-4405 . T) (-4404 . T)) 
 NIL 
-(-1049 |m| |n| R) 
+(-1052 |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}."))) 
-((-4407 . T) (-4402 . T) (-4401 . T)) 
-((-2807 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1050 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-4410 . T) (-4405 . T) (-4404 . T)) 
+((|HasCategory| |#3| (QUOTE (-172))) (-2706 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1053 |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 
-(-1051 R) 
-((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) 
+(-1054 R) 
+((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
 NIL 
-(-1052) 
+(-1055) 
 ((|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 
-(-1053 S) 
+(-1056 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.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-1054) 
+(-1057) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1055 |TheField| |ThePolDom|) 
+(-1058 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-1056) 
+(-1059) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) 
-((-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4398 . T) (-4402 . T) (-4397 . T) (-4408 . T) (-4409 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1057) 
+(-1060) 
 ((|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| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3813) (QUOTE (-52))))))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1170)) (|:| -3813 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1058 S R E V) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1173))) (LIST (QUOTE |:|) (QUOTE -3778) (QUOTE (-52))))))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-52) (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1097))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (QUOTE (-1097))) (|HasCategory| (-1173) (QUOTE (-848))) (|HasCategory| (-52) (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1173)) (|:| -3778 (-52))) (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1061 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| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{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 \\spad{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{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)\\spad{*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)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -988) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-1170))))) 
-(-1059 R E V) 
+((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -990) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-1173))))) 
+(-1062 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{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 \\spad{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{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)\\spad{*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)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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}}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
 NIL 
-(-1060) 
+(-1063) 
 ((|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 
-(-1061 S |TheField| |ThePols|) 
+(-1064 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 
-(-1062 |TheField| |ThePols|) 
+(-1065 |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 
-(-1063 R E V P TS) 
+(-1066 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\\spad{'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},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{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{\\spad{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 
-(-1064 S R E V P) 
+(-1067 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,{}...,{}\\spad{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,{}...,{}\\spad{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(\\spad{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}{\\spad{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 \\spad{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 \\spad{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 \\spad{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 
-(-1065 R E V P) 
+(-1068 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,{}...,{}\\spad{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,{}...,{}\\spad{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(\\spad{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}{\\spad{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 \\spad{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 \\spad{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 \\spad{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}."))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-1066 R E V P TS) 
+(-1069 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{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},{}\\spad{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},{}\\spad{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},{}\\spad{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},{}\\spad{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 
-(-1067) 
+(-1070) 
 ((|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 
-(-1068) 
+(-1071) 
 ((|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 
-(-1069 |f|) 
+(-1072 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1070 |Base| R -2306) 
+(-1073 |Base| R -2234) 
 ((|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},{}...,{}\\spad{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 
-(-1071 |Base| R -2306) 
+(-1074 |Base| R -2234) 
 ((|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 
-(-1072 R |ls|) 
+(-1075 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 
-(-1073 UP SAE UPA) 
+(-1076 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 
-(-1074 R UP M) 
+(-1077 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."))) 
-((-4400 |has| |#1| (-363)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) 
-(-1075 UP SAE UPA) 
+((-4403 |has| |#1| (-363)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) 
+(-1078 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 
-(-1076) 
+(-1079) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-1077) 
+(-1080) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-1078 S) 
+(-1081 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 
-(-1079) 
+(-1082) 
 ((|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 \\spad{`b'}.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,{}s)} returns the first binding of \\spad{`n'} in \\spad{`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 
-(-1080 R) 
+(-1083 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 
-(-1081 R) 
+(-1084 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"))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
-(-1082 S) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1085 (-1173)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-1085 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 
-(-1083 R S) 
+(-1086 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 (-844)))) 
-(-1084) 
+((|HasCategory| |#1| (QUOTE (-846)))) 
+(-1087) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1085 R S) 
+(-1088 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 
-(-1086 S) 
+(-1089 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.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1094)))) 
-(-1087 S) 
+((|HasCategory| |#1| (QUOTE (-1097)))) 
+(-1090 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{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\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 
-(-1088 S) 
+(-1091 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1094)))) 
-(-1089 S L) 
+((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1097)))) 
+(-1092 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 
-(-1090) 
+(-1093) 
 ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) 
 NIL 
 NIL 
-(-1091 A S) 
+(-1094 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1092 S) 
+(-1095 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-4397 . T)) 
+((-4400 . T)) 
 NIL 
-(-1093 S) 
+(-1096 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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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 
-(-1094) 
+(-1097) 
 ((|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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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 
-(-1095 |m| |n|) 
+(-1098 |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 \\spad{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 {a_1,{}...,{}a_m}. Error if {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| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{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| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{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 
-(-1096 S) 
+(-1099 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)}}"))) 
-((-4407 . T) (-4397 . T) (-4408 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
-(-1097 |Str| |Sym| |Int| |Flt| |Expr|) 
+((-4410 . T) (-4400 . T) (-4411 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+(-1100 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns 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 \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{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 \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{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 \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{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|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) 
 NIL 
 NIL 
-(-1098) 
+(-1101) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1099 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1102 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1100 R FS) 
+(-1103 R FS) 
 ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 
-(-1101 R E V P TS) 
+(-1104 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,{}\\spad{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(\\spad{lp},{}\\spad{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?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{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?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{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{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{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 
-(-1102 R E V P TS) 
+(-1105 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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 
-(-1103 R E V P) 
+(-1106 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 \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{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.}"))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-1104) 
+(-1107) 
 ((|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| (|Integer|)) (|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| (|Integer|)) (|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| (|Integer|))) "\\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 \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{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,{}\\spad{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 \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) 
 NIL 
 NIL 
-(-1105 S) 
+(-1108 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1106) 
+(-1109) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 
-(-1107 |dimtot| |dim1| S) 
+(-1110 |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 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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-(-1108 R |x|) 
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-309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))))) (-2706 (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1097)))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#3| (QUOTE (-363))) (-2706 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1047)))) (-2706 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-791))) (-2706 (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (QUOTE (-846)))) (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (QUOTE (-724))) (-2706 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-1047)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (-2706 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1047)))) (-2706 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1047)))) (-2706 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1047)))) (-2706 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (|HasCategory| |#3| (QUOTE (-233))) (-2706 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-724))) (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (QUOTE (-1097)))) (|HasCategory| |#3| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-25)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-131)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-172)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-233)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-363)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-368)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-724)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-791)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-846)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1097))))) (-2706 (-12 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-724))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1047))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-724))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-791))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-846))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-848))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-1173))))) (-2706 (|HasCategory| |#3| (QUOTE (-1047))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -1036) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1097)))) (|HasAttribute| |#3| (QUOTE -4407)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) 
+(-1111 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 \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If 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 \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If 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 (-452)))) 
-(-1109) 
+(-1112) 
 ((|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 \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) 
 NIL 
 NIL 
-(-1110 R -2306) 
+(-1113 R -2234) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "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|) "failed") |#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|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1111 R) 
+(-1114 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "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|) "failed") (|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|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1112) 
+(-1115) 
 ((|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 \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) 
 NIL 
 NIL 
-(-1113) 
+(-1116) 
 ((|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 
-(-1114) 
+(-1117) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|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."))) 
-((-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4398 . T) (-4402 . T) (-4397 . T) (-4408 . T) (-4409 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1115 S) 
+(-1118 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}) = \\spad{#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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-4407 . T) (-4408 . T)) 
+((-4410 . T) (-4411 . T)) 
 NIL 
-(-1116 S |ndim| R |Row| |Col|) 
+(-1119 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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}\\spad{'s} on the diagonal and zeroes elsewhere."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-363))) (|HasAttribute| |#3| (QUOTE (-4409 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) 
-(-1117 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-363))) (|HasAttribute| |#3| (QUOTE (-4412 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) 
+(-1120 |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}\\spad{'s} on the diagonal and zeroes elsewhere."))) 
-((-4407 . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4410 . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1118 R |Row| |Col| M) 
+(-1121 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 
-(-1119 R |VarSet|) 
+(-1122 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."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-905))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) 
-(-1120 |Coef| |Var| SMP) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-907))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-1123 |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 \\spad{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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) 
-(-1121 R E V P) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) 
+(-1124 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}"))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-1122 UP -2306) 
+(-1125 UP -2234) 
 ((|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 
-(-1123 R) 
+(-1126 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 
-(-1124 R) 
+(-1127 R) 
 ((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function 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 func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) 
 NIL 
 NIL 
-(-1125 R) 
+(-1128 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 
-(-1126 S A) 
+(-1129 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 (-846)))) 
-(-1127 R) 
+((|HasCategory| |#1| (QUOTE (-848)))) 
+(-1130 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 
-(-1128 R) 
+(-1131 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 \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and 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); 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 \\spad{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 \\spad{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 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 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 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 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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 
-(-1129) 
+(-1132) 
 ((|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 
-(-1130) 
+(-1133) 
 ((|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 
-(-1131) 
+(-1134) 
 ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) 
 NIL 
 NIL 
-(-1132) 
+(-1135) 
 ((|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 
-(-1133) 
+(-1136) 
 ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) 
 NIL 
 NIL 
-(-1134 V C) 
+(-1137 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},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{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},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{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 
-(-1135 V C) 
+(-1138 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,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{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,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{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|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{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},{}\\spad{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 \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{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 \\spad{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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2807 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1136 |ndim| R) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1137) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097))) (-2706 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1137) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1137 |#1| |#2|) (QUOTE (-1097))))) (|HasCategory| (-1137 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1139 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) 
-((-4404 . T) (-4396 |has| |#2| (-6 (-4409 "*"))) (-4407 . T) (-4401 . T) (-4402 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2807 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2807 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) 
-(-1137 S) 
+((-4407 . T) (-4399 |has| |#2| (-6 (-4412 "*"))) (-4410 . T) (-4404 . T) (-4405 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-363))) (-2706 (|HasAttribute| |#2| (QUOTE (-4412 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) 
+(-1140 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{>=} \\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{>=} \\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\",{}\\spad{\"*\"})} 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}) \\spad{==} 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1138) 
+(-1141) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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{>=} \\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{>=} \\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\",{}\\spad{\"*\"})} 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}) \\spad{==} 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-1139 R E V P TS) 
+(-1142 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\\spad{'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{\\spad{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 
-(-1140 R E V P) 
+(-1143 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(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{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(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{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},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1141 S) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1144 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}."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1142 A S) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1145 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}.")) (|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 
-(-1143 S) 
+(-1146 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}.")) (|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 
-(-1144 |Key| |Ent| |dent|) 
+(-1147 |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."))) 
-((-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094)))) 
-(-1145) 
+((-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-848))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097)))) 
+(-1148) 
 ((|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}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
 NIL 
-(-1146 |Coef|) 
+(-1149 |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 
-(-1147 S) 
+(-1150 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 
-(-1148 A B) 
+(-1151 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 
-(-1149 A B C) 
+(-1152 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 
-(-1150 S) 
+(-1153 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."))) 
-((-4408 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1151) 
+((-4411 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1154) 
 ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-1152) 
+(-1155) 
 NIL 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) 
-(-1153 |Entry|) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| (-144) (QUOTE (-1097))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) 
+(-1156 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#1|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 (-1152)) (|:| -3813 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1154 A) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#1|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (QUOTE (-1097))) (|HasCategory| (-1155) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 (-1155)) (|:| -3778 |#1|)) (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1157 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 1.")) (|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 \\spad{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 \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{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 (-363))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) 
-(-1155 |Coef|) 
+(-1158 |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 
-(-1156 |Coef|) 
+(-1159 |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 
-(-1157 R UP) 
+(-1160 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 (-307)))) 
-(-1158 |n| R) 
+(-1161 |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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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\\spad{'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,{}\\spad{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\\spad{'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 
-(-1159 S1 S2) 
+(-1162 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 \\spad{s:t}"))) 
 NIL 
 NIL 
-(-1160) 
+(-1163) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1161 |Coef| |var| |cen|) 
+(-1164 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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+(-1165 R -2234) 
 ((|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}(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 
-(-1163 R) 
+(-1166 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 
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 ((|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 
-(-1165 E OV R P) 
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 ((|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 
-(-1166 R) 
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 ((|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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-(-1167 |Coef| |var| |cen|) 
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+((|HasCategory| |#1| (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1148))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-907)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-1170 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) 
-(-1168 |Coef| |var| |cen|) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) 
+(-1171 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) 
-(-1169) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (|HasCategory| (-769) (QUOTE (-1109))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) 
+(-1172) 
 ((|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 
-(-1170) 
+(-1173) 
 ((|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}([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 
-(-1171 R) 
+(-1174 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{\\spad{ri}'s}: \\spad{[r1 + ... + rn,{} r1 r2 + ... + r(n-1) rn,{} ...,{} r1 r2 ... rn]}."))) 
 NIL 
 NIL 
-(-1172 R) 
+(-1175 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-6 -4405)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2807 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4405))) 
-(-1173) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-6 -4408)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2706 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-969) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4408))) 
+(-1176) 
 ((|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| "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| "void"))) "\\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| "void"))) "\\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| "void")) $) "\\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 
-(-1174) 
+(-1177) 
 ((|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 
-(-1175) 
+(-1178) 
 ((|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 \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`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 \\spad{`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 \\spad{`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 \\spad{`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 \\spad{`s'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1176 N) 
+(-1179 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1177 N) 
+(-1180 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| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) 
 NIL 
 NIL 
-(-1178 R) 
+(-1181 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 
-(-1179) 
+(-1182) 
 ((|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 
-(-1180 S) 
+(-1183 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 \\spad{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}{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{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 bat1 is the inverse of 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 
-(-1181 S) 
+(-1184 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 
-(-1182 |Key| |Entry|) 
+(-1185 |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}"))) 
-((-4407 . T) (-4408 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1901) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3813) (|devaluate| |#2|)))))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2807 (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -1901 |#1|) (|:| -3813 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1183 R) 
+((-4410 . T) (-4411 . T)) 
+((-12 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3778) (|devaluate| |#2|)))))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1097))) (-2706 (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-860)))) (|HasCategory| (-2 (|:| -1907 |#1|) (|:| -3778 |#2|)) (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1186 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{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) 
 NIL 
 NIL 
-(-1184 S |Key| |Entry|) 
+(-1187 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{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
 NIL 
 NIL 
-(-1185 |Key| |Entry|) 
+(-1188 |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{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
-((-4408 . T)) 
+((-4411 . T)) 
 NIL 
-(-1186 |Key| |Entry|) 
+(-1189 |Key| |Entry|) 
 ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} 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 
-(-1187) 
+(-1190) 
 ((|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 
-(-1188 S) 
+(-1191 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 
-(-1189) 
+(-1192) 
 ((|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 \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} 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 
-(-1190) 
+(-1193) 
 ((|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 
-(-1191 R) 
+(-1194 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 
-(-1192) 
+(-1195) 
 ((|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 
-(-1193 S) 
+(-1196 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1194) 
+(-1197) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1195 S) 
+(-1198 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1196 S) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1097))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1199 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1197) 
+(-1200) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1198 R -2306) 
+(-1201 R -2234) 
 ((|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 
-(-1199 R |Row| |Col| M) 
+(-1202 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 
-(-1200 R -2306) 
+(-1203 R -2234) 
 ((|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 \\spad{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 \\spad{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 -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) 
-(-1201 S R E V P) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -890) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -884) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -884) (|devaluate| |#1|))))) 
+(-1204 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} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{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|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{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{\\spad{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(\\spad{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{\\spad{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(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{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},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{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{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{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},{}\\spad{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{\\spad{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},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff 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{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{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{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{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{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{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 (-368)))) 
-(-1202 R E V P) 
+(-1205 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} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{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|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{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{\\spad{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(\\spad{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{\\spad{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(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{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},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{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{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{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},{}\\spad{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{\\spad{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},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff 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{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{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{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{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{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-1203 |Coef|) 
+(-1206 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) 
-(-1204 |Curve|) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) 
+(-1207 |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 
-(-1205) 
+(-1208) 
 ((|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 
-(-1206 S) 
+(-1209 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'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 (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1207 -2306) 
+((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1210 -2234) 
 ((|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 
-(-1208) 
+(-1211) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1209) 
+(-1212) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1210 S) 
+(-1213 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 \\spad{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 \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-846)))) 
-(-1211) 
+((|HasCategory| |#1| (QUOTE (-848)))) 
+(-1214) 
 ((|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 
-(-1212 S) 
+(-1215 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 
-(-1213) 
+(-1216) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1214) 
+(-1217) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1215) 
+(-1218) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1216) 
+(-1219) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1217) 
+(-1220) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1218 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1221 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1219 |Coef|) 
+(-1222 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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{<=} \\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."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1220 S |Coef| UTS) 
+(-1223 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 (-363)))) 
-(-1221 |Coef| UTS) 
+(-1224 |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)}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1222 |Coef| UTS) 
+(-1225 |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)}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
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(LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-816)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-846)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (-12 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|#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (QUOTE (-905))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-307)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-905)))) (-2807 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-905)))) 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-(-1223 |Coef| |var| |cen|) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
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(QUOTE -1036) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-818))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-363)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-907))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1254 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-1227 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 
-(-1225 R S) 
+(-1228 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 (-844)))) 
-(-1226 S) 
+((|HasCategory| |#1| (QUOTE (-846)))) 
+(-1229 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 (-844))) (|HasCategory| |#1| (QUOTE (-1094)))) 
-(-1227 |x| R |y| S) 
+((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1097)))) 
+(-1230 |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 
-(-1228 R Q UP) 
+(-1231 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 \\spad{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 
-(-1229 R UP) 
+(-1232 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},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{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 
-(-1230 R UP) 
+(-1233 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 
-(-1231 R U) 
+(-1234 R U) 
 ((|constructor| (NIL "This package implements Karatsuba\\spad{'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\\spad{'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\\spad{'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\\spad{'s} trick at all."))) 
 NIL 
 NIL 
-(-1232 |x| R) 
+(-1235 |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}"))) 
-(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-556)) (-4403 |has| |#2| (-363)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
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-(-1233 R PR S PS) 
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+((|HasCategory| |#2| (QUOTE (-907))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-379))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -884) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -884) (QUOTE (-564))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-379)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -890) (QUOTE (-564)))))) (-12 (|HasCategory| (-1079) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (QUOTE (-564)))) (-2706 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (-2706 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1148))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (-2706 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-907)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+(-1236 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 
-(-1234 S R) 
+(-1237 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 \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{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|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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\\spad{'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 -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1145)))) 
-(-1235 R) 
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1148)))) 
+(-1238 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 \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{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|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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\\spad{'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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4406 |has| |#1| (-363)) (-4408 |has| |#1| (-6 -4408)) (-4405 . T) (-4404 . T) (-4407 . T)) 
 NIL 
-(-1236 S |Coef| |Expon|) 
+(-1239 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{<=} \\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}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|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 -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2423) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) 
-(-1237 |Coef| |Expon|) 
+((|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2327) (LIST (|devaluate| |#2|) (QUOTE (-1173)))))) 
+(-1240 |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{<=} \\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}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1238 RC P) 
+(-1241 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1239 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1242 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1240 |Coef|) 
+(-1243 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1241 S |Coef| ULS) 
+(-1244 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 
-(-1242 |Coef| ULS) 
+(-1245 |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)}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1243 |Coef| ULS) 
+(-1246 |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)}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) 
-(-1244 |Coef| |var| |cen|) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) 
+(-1247 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2807 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) 
-(-1245 R FE |var| |cen|) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4402 |has| |#1| (-363)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2706 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) 
+(-1248 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))}."))) 
-(((-4409 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4400 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-2807 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) 
-(-1246 A S) 
+(((-4412 "*") |has| (-1247 |#2| |#3| |#4|) (-172)) (-4403 |has| (-1247 |#2| |#3| |#4|) (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-172))) (-2706 (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1247 |#2| |#3| |#4|) (LIST (QUOTE -1036) (QUOTE (-564)))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1247 |#2| |#3| |#4|) (QUOTE (-556)))) 
+(-1249 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{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\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{:=} \\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} \\spad{>=} 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} \\spad{>=} 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} \\spad{>=} 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4408))) 
-(-1247 S) 
+((|HasAttribute| |#1| (QUOTE -4411))) 
+(-1250 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\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{:=} \\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} \\spad{>=} 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} \\spad{>=} 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} \\spad{>=} 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1248 |Coef1| |Coef2| UTS1 UTS2) 
+(-1251 |Coef1| |Coef2| UTS1 UTS2) 
 ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) 
 NIL 
 NIL 
-(-1249 S |Coef|) 
+(-1252 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2070) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) 
-(-1250 |Coef|) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-957))) (|HasCategory| |#2| (QUOTE (-1197))) (|HasSignature| |#2| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4107) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1173))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) 
+(-1253 |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."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1251 |Coef| |var| |cen|) 
+(-1254 |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|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|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| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{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}."))) 
-(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-556)) (-4401 . T) (-4402 . T) (-4404 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2807 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2423) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2070) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3836) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) 
-(-1252 |Coef| UTS) 
+(((-4412 "*") |has| |#1| (-172)) (-4403 |has| |#1| (-556)) (-4404 . T) (-4405 . T) (-4407 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2706 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-1173)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (|HasCategory| (-769) (QUOTE (-1109))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -2327) (LIST (|devaluate| |#1|) (QUOTE (-1173)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasCategory| |#1| (QUOTE (-363))) (-2706 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-957))) (|HasCategory| |#1| (QUOTE (-1197))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4107) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1173))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (LIST (QUOTE -642) (QUOTE (-1173))) (|devaluate| |#1|))))))) 
+(-1255 |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 
-(-1253 -2306 UP L UTS) 
+(-1256 -2234 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 (-556)))) 
-(-1254) 
+(-1257) 
 ((|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 
-(-1255 |sym|) 
+(-1258 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1256 S R) 
+(-1259 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})\\spad{*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 (-998))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1257 R) 
+((|HasCategory| |#2| (QUOTE (-1000))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-724))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1260 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})\\spad{*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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-4408 . T) (-4407 . T)) 
+((-4411 . T) (-4410 . T)) 
 NIL 
-(-1258 A B) 
+(-1261 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-1259 R) 
+(-1262 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-4408 . T) (-4407 . T)) 
-((-2807 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2807 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2807 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
-(-1260) 
+((-4411 . T) (-4410 . T)) 
+((-2706 (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2706 (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2706 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-564) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-724))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1000))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) 
+(-1263) 
 ((|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,{}\\spad{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{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\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\\spad{'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(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\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 
-(-1261) 
+(-1264) 
 ((|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 
-(-1262) 
+(-1265) 
 ((|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 
-(-1263) 
+(-1266) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 
-(-1264) 
+(-1267) 
 ((|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| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1265 A S) 
+(-1268 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1266 S) 
+(-1269 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}."))) 
-((-4402 . T) (-4401 . T)) 
+((-4405 . T) (-4404 . T)) 
 NIL 
-(-1267 R) 
+(-1270 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]\\spad{*v} + A[2]*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 
-(-1268 K R UP -2306) 
+(-1271 K R UP -2234) 
 ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) 
 NIL 
 NIL 
-(-1269) 
+(-1272) 
 ((|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 
-(-1270) 
+(-1273) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1271 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1274 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: \\spad{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)"))) 
-((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T)) 
+((-4405 |has| |#1| (-172)) (-4404 |has| |#1| (-172)) (-4407 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) 
-(-1272 R E V P) 
+(-1275 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}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{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{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) 
-((-4408 . T) (-4407 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-858))))) 
-(-1273 R) 
+((-4411 . T) (-4410 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-860))))) 
+(-1276 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.\\spad{fr})"))) 
-((-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1274 |vl| R) 
+(-1277 |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."))) 
-((-4404 . T) (-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T)) 
-((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4400))) 
-(-1275 R |VarSet| XPOLY) 
+((-4407 . T) (-4403 |has| |#2| (-6 -4403)) (-4405 . T) (-4404 . T)) 
+((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4403))) 
+(-1278 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.\\spad{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 
-(-1276 |vl| R) 
+(-1279 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) 
+((-4403 |has| |#2| (-6 -4403)) (-4405 . T) (-4404 . T) (-4407 . T)) 
 NIL 
-(-1277 S -2306) 
+(-1280 S -2234) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) 
-(-1278 -2306) 
+(-1281 -2234) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
-((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+((-4402 . T) (-4408 . T) (-4403 . T) ((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
-(-1279 |VarSet| R) 
+(-1282 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) 
-((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasAttribute| |#2| (QUOTE -4400))) 
-(-1280 |vl| R) 
+((-4403 |has| |#2| (-6 -4403)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -715) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasAttribute| |#2| (QUOTE -4403))) 
+(-1283 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) 
+((-4403 |has| |#2| (-6 -4403)) (-4405 . T) (-4404 . T) (-4407 . T)) 
 NIL 
-(-1281 R) 
+(-1284 R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) 
-((-4400 |has| |#1| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4400))) 
-(-1282 R E) 
+((-4403 |has| |#1| (-6 -4403)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4403))) 
+(-1285 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) 
-((-4404 . T) (-4405 |has| |#1| (-6 -4405)) (-4400 |has| |#1| (-6 -4400)) (-4402 . T) (-4401 . T)) 
-((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4400))) 
-(-1283 |VarSet| R) 
+((-4407 . T) (-4408 |has| |#1| (-6 -4408)) (-4403 |has| |#1| (-6 -4403)) (-4405 . T) (-4404 . T)) 
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4407)) (|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4403))) 
+(-1286 |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."))) 
-((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T)) 
-((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4400))) 
-(-1284 A) 
+((-4403 |has| |#2| (-6 -4403)) (-4405 . T) (-4404 . T) (-4407 . T)) 
+((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4403))) 
+(-1287 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 
-(-1285 R |ls| |ls2|) 
+(-1288 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}(\\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{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}(\\spad{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 
-(-1286 R) 
+(-1289 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}\\spad{'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}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-1287 |p|) 
+(-1290 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T)) 
+(((-4412 "*") . T) (-4404 . T) (-4405 . T) (-4407 . T)) 
 NIL 
 NIL 
 NIL 
@@ -5096,4 +5108,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2282736 2282741 2282746 2282751) (-2 NIL 2282716 2282721 2282726 2282731) (-1 NIL 2282696 2282701 2282706 2282711) (0 NIL 2282676 2282681 2282686 2282691) (-1287 "ZMOD.spad" 2282485 2282498 2282614 2282671) (-1286 "ZLINDEP.spad" 2281529 2281540 2282475 2282480) (-1285 "ZDSOLVE.spad" 2271378 2271400 2281519 2281524) (-1284 "YSTREAM.spad" 2270871 2270882 2271368 2271373) (-1283 "XRPOLY.spad" 2270091 2270111 2270727 2270796) (-1282 "XPR.spad" 2267882 2267895 2269809 2269908) (-1281 "XPOLY.spad" 2267437 2267448 2267738 2267807) (-1280 "XPOLYC.spad" 2266754 2266770 2267363 2267432) (-1279 "XPBWPOLY.spad" 2265191 2265211 2266534 2266603) (-1278 "XF.spad" 2263652 2263667 2265093 2265186) (-1277 "XF.spad" 2262093 2262110 2263536 2263541) (-1276 "XFALG.spad" 2259117 2259133 2262019 2262088) (-1275 "XEXPPKG.spad" 2258368 2258394 2259107 2259112) (-1274 "XDPOLY.spad" 2257982 2257998 2258224 2258293) (-1273 "XALG.spad" 2257642 2257653 2257938 2257977) (-1272 "WUTSET.spad" 2253481 2253498 2257288 2257315) (-1271 "WP.spad" 2252680 2252724 2253339 2253406) (-1270 "WHILEAST.spad" 2252478 2252487 2252670 2252675) (-1269 "WHEREAST.spad" 2252149 2252158 2252468 2252473) (-1268 "WFFINTBS.spad" 2249712 2249734 2252139 2252144) (-1267 "WEIER.spad" 2247926 2247937 2249702 2249707) (-1266 "VSPACE.spad" 2247599 2247610 2247894 2247921) (-1265 "VSPACE.spad" 2247292 2247305 2247589 2247594) (-1264 "VOID.spad" 2246969 2246978 2247282 2247287) (-1263 "VIEW.spad" 2244591 2244600 2246959 2246964) (-1262 "VIEWDEF.spad" 2239788 2239797 2244581 2244586) (-1261 "VIEW3D.spad" 2223623 2223632 2239778 2239783) (-1260 "VIEW2D.spad" 2211360 2211369 2223613 2223618) (-1259 "VECTOR.spad" 2210035 2210046 2210286 2210313) (-1258 "VECTOR2.spad" 2208662 2208675 2210025 2210030) (-1257 "VECTCAT.spad" 2206562 2206573 2208630 2208657) (-1256 "VECTCAT.spad" 2204270 2204283 2206340 2206345) (-1255 "VARIABLE.spad" 2204050 2204065 2204260 2204265) (-1254 "UTYPE.spad" 2203694 2203703 2204040 2204045) (-1253 "UTSODETL.spad" 2202987 2203011 2203650 2203655) (-1252 "UTSODE.spad" 2201175 2201195 2202977 2202982) (-1251 "UTS.spad" 2195964 2195992 2199642 2199739) (-1250 "UTSCAT.spad" 2193415 2193431 2195862 2195959) (-1249 "UTSCAT.spad" 2190510 2190528 2192959 2192964) (-1248 "UTS2.spad" 2190103 2190138 2190500 2190505) (-1247 "URAGG.spad" 2184735 2184746 2190093 2190098) (-1246 "URAGG.spad" 2179331 2179344 2184691 2184696) (-1245 "UPXSSING.spad" 2176974 2177000 2178412 2178545) (-1244 "UPXS.spad" 2174122 2174150 2175106 2175255) (-1243 "UPXSCONS.spad" 2171879 2171899 2172254 2172403) (-1242 "UPXSCCA.spad" 2170444 2170464 2171725 2171874) (-1241 "UPXSCCA.spad" 2169151 2169173 2170434 2170439) (-1240 "UPXSCAT.spad" 2167732 2167748 2168997 2169146) (-1239 "UPXS2.spad" 2167273 2167326 2167722 2167727) (-1238 "UPSQFREE.spad" 2165685 2165699 2167263 2167268) (-1237 "UPSCAT.spad" 2163278 2163302 2165583 2165680) (-1236 "UPSCAT.spad" 2160577 2160603 2162884 2162889) (-1235 "UPOLYC.spad" 2155555 2155566 2160419 2160572) (-1234 "UPOLYC.spad" 2150425 2150438 2155291 2155296) (-1233 "UPOLYC2.spad" 2149894 2149913 2150415 2150420) (-1232 "UP.spad" 2147087 2147102 2147480 2147633) (-1231 "UPMP.spad" 2145977 2145990 2147077 2147082) (-1230 "UPDIVP.spad" 2145540 2145554 2145967 2145972) (-1229 "UPDECOMP.spad" 2143777 2143791 2145530 2145535) (-1228 "UPCDEN.spad" 2142984 2143000 2143767 2143772) (-1227 "UP2.spad" 2142346 2142367 2142974 2142979) (-1226 "UNISEG.spad" 2141699 2141710 2142265 2142270) (-1225 "UNISEG2.spad" 2141192 2141205 2141655 2141660) (-1224 "UNIFACT.spad" 2140293 2140305 2141182 2141187) (-1223 "ULS.spad" 2130845 2130873 2131938 2132367) (-1222 "ULSCONS.spad" 2123239 2123259 2123611 2123760) (-1221 "ULSCCAT.spad" 2120968 2120988 2123085 2123234) (-1220 "ULSCCAT.spad" 2118805 2118827 2120924 2120929) (-1219 "ULSCAT.spad" 2117021 2117037 2118651 2118800) (-1218 "ULS2.spad" 2116533 2116586 2117011 2117016) (-1217 "UINT8.spad" 2116410 2116419 2116523 2116528) (-1216 "UINT64.spad" 2116286 2116295 2116400 2116405) (-1215 "UINT32.spad" 2116162 2116171 2116276 2116281) (-1214 "UINT16.spad" 2116038 2116047 2116152 2116157) (-1213 "UFD.spad" 2115103 2115112 2115964 2116033) (-1212 "UFD.spad" 2114230 2114241 2115093 2115098) (-1211 "UDVO.spad" 2113077 2113086 2114220 2114225) (-1210 "UDPO.spad" 2110504 2110515 2113033 2113038) (-1209 "TYPE.spad" 2110436 2110445 2110494 2110499) (-1208 "TYPEAST.spad" 2110355 2110364 2110426 2110431) (-1207 "TWOFACT.spad" 2109005 2109020 2110345 2110350) (-1206 "TUPLE.spad" 2108489 2108500 2108904 2108909) (-1205 "TUBETOOL.spad" 2105326 2105335 2108479 2108484) (-1204 "TUBE.spad" 2103967 2103984 2105316 2105321) (-1203 "TS.spad" 2102556 2102572 2103532 2103629) (-1202 "TSETCAT.spad" 2089683 2089700 2102524 2102551) (-1201 "TSETCAT.spad" 2076796 2076815 2089639 2089644) (-1200 "TRMANIP.spad" 2071162 2071179 2076502 2076507) (-1199 "TRIMAT.spad" 2070121 2070146 2071152 2071157) (-1198 "TRIGMNIP.spad" 2068638 2068655 2070111 2070116) (-1197 "TRIGCAT.spad" 2068150 2068159 2068628 2068633) (-1196 "TRIGCAT.spad" 2067660 2067671 2068140 2068145) (-1195 "TREE.spad" 2066231 2066242 2067267 2067294) (-1194 "TRANFUN.spad" 2066062 2066071 2066221 2066226) (-1193 "TRANFUN.spad" 2065891 2065902 2066052 2066057) (-1192 "TOPSP.spad" 2065565 2065574 2065881 2065886) (-1191 "TOOLSIGN.spad" 2065228 2065239 2065555 2065560) (-1190 "TEXTFILE.spad" 2063785 2063794 2065218 2065223) (-1189 "TEX.spad" 2060917 2060926 2063775 2063780) (-1188 "TEX1.spad" 2060473 2060484 2060907 2060912) (-1187 "TEMUTL.spad" 2060028 2060037 2060463 2060468) (-1186 "TBCMPPK.spad" 2058121 2058144 2060018 2060023) (-1185 "TBAGG.spad" 2057157 2057180 2058101 2058116) (-1184 "TBAGG.spad" 2056201 2056226 2057147 2057152) (-1183 "TANEXP.spad" 2055577 2055588 2056191 2056196) (-1182 "TABLE.spad" 2053988 2054011 2054258 2054285) (-1181 "TABLEAU.spad" 2053469 2053480 2053978 2053983) (-1180 "TABLBUMP.spad" 2050252 2050263 2053459 2053464) (-1179 "SYSTEM.spad" 2049480 2049489 2050242 2050247) (-1178 "SYSSOLP.spad" 2046953 2046964 2049470 2049475) (-1177 "SYSNNI.spad" 2046133 2046144 2046943 2046948) (-1176 "SYSINT.spad" 2045537 2045548 2046123 2046128) (-1175 "SYNTAX.spad" 2041731 2041740 2045527 2045532) (-1174 "SYMTAB.spad" 2039787 2039796 2041721 2041726) (-1173 "SYMS.spad" 2035772 2035781 2039777 2039782) (-1172 "SYMPOLY.spad" 2034779 2034790 2034861 2034988) (-1171 "SYMFUNC.spad" 2034254 2034265 2034769 2034774) (-1170 "SYMBOL.spad" 2031681 2031690 2034244 2034249) (-1169 "SWITCH.spad" 2028438 2028447 2031671 2031676) (-1168 "SUTS.spad" 2025337 2025365 2026905 2027002) (-1167 "SUPXS.spad" 2022472 2022500 2023469 2023618) (-1166 "SUP.spad" 2019277 2019288 2020058 2020211) (-1165 "SUPFRACF.spad" 2018382 2018400 2019267 2019272) (-1164 "SUP2.spad" 2017772 2017785 2018372 2018377) (-1163 "SUMRF.spad" 2016738 2016749 2017762 2017767) (-1162 "SUMFS.spad" 2016371 2016388 2016728 2016733) (-1161 "SULS.spad" 2006910 2006938 2008016 2008445) (-1160 "SUCHTAST.spad" 2006679 2006688 2006900 2006905) (-1159 "SUCH.spad" 2006359 2006374 2006669 2006674) (-1158 "SUBSPACE.spad" 1998366 1998381 2006349 2006354) (-1157 "SUBRESP.spad" 1997526 1997540 1998322 1998327) (-1156 "STTF.spad" 1993625 1993641 1997516 1997521) (-1155 "STTFNC.spad" 1990093 1990109 1993615 1993620) (-1154 "STTAYLOR.spad" 1982491 1982502 1989974 1989979) (-1153 "STRTBL.spad" 1980996 1981013 1981145 1981172) (-1152 "STRING.spad" 1980405 1980414 1980419 1980446) (-1151 "STRICAT.spad" 1980193 1980202 1980373 1980400) (-1150 "STREAM.spad" 1977051 1977062 1979718 1979733) (-1149 "STREAM3.spad" 1976596 1976611 1977041 1977046) (-1148 "STREAM2.spad" 1975664 1975677 1976586 1976591) (-1147 "STREAM1.spad" 1975368 1975379 1975654 1975659) (-1146 "STINPROD.spad" 1974274 1974290 1975358 1975363) (-1145 "STEP.spad" 1973475 1973484 1974264 1974269) (-1144 "STBL.spad" 1972001 1972029 1972168 1972183) (-1143 "STAGG.spad" 1971076 1971087 1971991 1971996) (-1142 "STAGG.spad" 1970149 1970162 1971066 1971071) (-1141 "STACK.spad" 1969500 1969511 1969756 1969783) (-1140 "SREGSET.spad" 1967204 1967221 1969146 1969173) (-1139 "SRDCMPK.spad" 1965749 1965769 1967194 1967199) (-1138 "SRAGG.spad" 1960846 1960855 1965717 1965744) (-1137 "SRAGG.spad" 1955963 1955974 1960836 1960841) (-1136 "SQMATRIX.spad" 1953579 1953597 1954495 1954582) (-1135 "SPLTREE.spad" 1948131 1948144 1953015 1953042) (-1134 "SPLNODE.spad" 1944719 1944732 1948121 1948126) (-1133 "SPFCAT.spad" 1943496 1943505 1944709 1944714) (-1132 "SPECOUT.spad" 1942046 1942055 1943486 1943491) (-1131 "SPADXPT.spad" 1934185 1934194 1942036 1942041) (-1130 "spad-parser.spad" 1933650 1933659 1934175 1934180) (-1129 "SPADAST.spad" 1933351 1933360 1933640 1933645) (-1128 "SPACEC.spad" 1917364 1917375 1933341 1933346) (-1127 "SPACE3.spad" 1917140 1917151 1917354 1917359) (-1126 "SORTPAK.spad" 1916685 1916698 1917096 1917101) (-1125 "SOLVETRA.spad" 1914442 1914453 1916675 1916680) (-1124 "SOLVESER.spad" 1912962 1912973 1914432 1914437) (-1123 "SOLVERAD.spad" 1908972 1908983 1912952 1912957) (-1122 "SOLVEFOR.spad" 1907392 1907410 1908962 1908967) (-1121 "SNTSCAT.spad" 1906992 1907009 1907360 1907387) (-1120 "SMTS.spad" 1905252 1905278 1906557 1906654) (-1119 "SMP.spad" 1902727 1902747 1903117 1903244) (-1118 "SMITH.spad" 1901570 1901595 1902717 1902722) (-1117 "SMATCAT.spad" 1899680 1899710 1901514 1901565) (-1116 "SMATCAT.spad" 1897722 1897754 1899558 1899563) (-1115 "SKAGG.spad" 1896683 1896694 1897690 1897717) (-1114 "SINT.spad" 1895509 1895518 1896549 1896678) (-1113 "SIMPAN.spad" 1895237 1895246 1895499 1895504) (-1112 "SIG.spad" 1894565 1894574 1895227 1895232) (-1111 "SIGNRF.spad" 1893673 1893684 1894555 1894560) (-1110 "SIGNEF.spad" 1892942 1892959 1893663 1893668) (-1109 "SIGAST.spad" 1892323 1892332 1892932 1892937) (-1108 "SHP.spad" 1890241 1890256 1892279 1892284) (-1107 "SHDP.spad" 1879952 1879979 1880461 1880592) (-1106 "SGROUP.spad" 1879560 1879569 1879942 1879947) (-1105 "SGROUP.spad" 1879166 1879177 1879550 1879555) (-1104 "SGCF.spad" 1872047 1872056 1879156 1879161) (-1103 "SFRTCAT.spad" 1870975 1870992 1872015 1872042) (-1102 "SFRGCD.spad" 1870038 1870058 1870965 1870970) (-1101 "SFQCMPK.spad" 1864675 1864695 1870028 1870033) (-1100 "SFORT.spad" 1864110 1864124 1864665 1864670) (-1099 "SEXOF.spad" 1863953 1863993 1864100 1864105) (-1098 "SEX.spad" 1863845 1863854 1863943 1863948) (-1097 "SEXCAT.spad" 1861396 1861436 1863835 1863840) (-1096 "SET.spad" 1859696 1859707 1860817 1860856) (-1095 "SETMN.spad" 1858130 1858147 1859686 1859691) (-1094 "SETCAT.spad" 1857452 1857461 1858120 1858125) (-1093 "SETCAT.spad" 1856772 1856783 1857442 1857447) (-1092 "SETAGG.spad" 1853293 1853304 1856752 1856767) (-1091 "SETAGG.spad" 1849822 1849835 1853283 1853288) (-1090 "SEQAST.spad" 1849525 1849534 1849812 1849817) (-1089 "SEGXCAT.spad" 1848647 1848660 1849515 1849520) (-1088 "SEG.spad" 1848460 1848471 1848566 1848571) (-1087 "SEGCAT.spad" 1847367 1847378 1848450 1848455) (-1086 "SEGBIND.spad" 1846439 1846450 1847322 1847327) (-1085 "SEGBIND2.spad" 1846135 1846148 1846429 1846434) (-1084 "SEGAST.spad" 1845849 1845858 1846125 1846130) (-1083 "SEG2.spad" 1845274 1845287 1845805 1845810) (-1082 "SDVAR.spad" 1844550 1844561 1845264 1845269) (-1081 "SDPOL.spad" 1841976 1841987 1842267 1842394) (-1080 "SCPKG.spad" 1840055 1840066 1841966 1841971) (-1079 "SCOPE.spad" 1839204 1839213 1840045 1840050) (-1078 "SCACHE.spad" 1837886 1837897 1839194 1839199) (-1077 "SASTCAT.spad" 1837795 1837804 1837876 1837881) (-1076 "SAOS.spad" 1837667 1837676 1837785 1837790) (-1075 "SAERFFC.spad" 1837380 1837400 1837657 1837662) (-1074 "SAE.spad" 1835555 1835571 1836166 1836301) (-1073 "SAEFACT.spad" 1835256 1835276 1835545 1835550) (-1072 "RURPK.spad" 1832897 1832913 1835246 1835251) (-1071 "RULESET.spad" 1832338 1832362 1832887 1832892) (-1070 "RULE.spad" 1830542 1830566 1832328 1832333) (-1069 "RULECOLD.spad" 1830394 1830407 1830532 1830537) (-1068 "RTVALUE.spad" 1830127 1830136 1830384 1830389) (-1067 "RSTRCAST.spad" 1829844 1829853 1830117 1830122) (-1066 "RSETGCD.spad" 1826222 1826242 1829834 1829839) (-1065 "RSETCAT.spad" 1816006 1816023 1826190 1826217) (-1064 "RSETCAT.spad" 1805810 1805829 1815996 1816001) (-1063 "RSDCMPK.spad" 1804262 1804282 1805800 1805805) (-1062 "RRCC.spad" 1802646 1802676 1804252 1804257) (-1061 "RRCC.spad" 1801028 1801060 1802636 1802641) (-1060 "RPTAST.spad" 1800730 1800739 1801018 1801023) (-1059 "RPOLCAT.spad" 1780090 1780105 1800598 1800725) (-1058 "RPOLCAT.spad" 1759164 1759181 1779674 1779679) (-1057 "ROUTINE.spad" 1755027 1755036 1757811 1757838) (-1056 "ROMAN.spad" 1754355 1754364 1754893 1755022) (-1055 "ROIRC.spad" 1753435 1753467 1754345 1754350) (-1054 "RNS.spad" 1752338 1752347 1753337 1753430) (-1053 "RNS.spad" 1751327 1751338 1752328 1752333) (-1052 "RNG.spad" 1751062 1751071 1751317 1751322) (-1051 "RMODULE.spad" 1750700 1750711 1751052 1751057) (-1050 "RMCAT2.spad" 1750108 1750165 1750690 1750695) (-1049 "RMATRIX.spad" 1748932 1748951 1749275 1749314) (-1048 "RMATCAT.spad" 1744465 1744496 1748888 1748927) (-1047 "RMATCAT.spad" 1739888 1739921 1744313 1744318) (-1046 "RINTERP.spad" 1739776 1739796 1739878 1739883) (-1045 "RING.spad" 1739246 1739255 1739756 1739771) (-1044 "RING.spad" 1738724 1738735 1739236 1739241) (-1043 "RIDIST.spad" 1738108 1738117 1738714 1738719) (-1042 "RGCHAIN.spad" 1736687 1736703 1737593 1737620) (-1041 "RGBCSPC.spad" 1736468 1736480 1736677 1736682) (-1040 "RGBCMDL.spad" 1735998 1736010 1736458 1736463) (-1039 "RF.spad" 1733612 1733623 1735988 1735993) (-1038 "RFFACTOR.spad" 1733074 1733085 1733602 1733607) (-1037 "RFFACT.spad" 1732809 1732821 1733064 1733069) (-1036 "RFDIST.spad" 1731797 1731806 1732799 1732804) (-1035 "RETSOL.spad" 1731214 1731227 1731787 1731792) (-1034 "RETRACT.spad" 1730642 1730653 1731204 1731209) (-1033 "RETRACT.spad" 1730068 1730081 1730632 1730637) (-1032 "RETAST.spad" 1729880 1729889 1730058 1730063) (-1031 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1694725) (-1012 "RDETRS.spad" 1693089 1693107 1694283 1694288) (-1011 "RDETR.spad" 1691196 1691214 1693079 1693084) (-1010 "RDEEFS.spad" 1690269 1690286 1691186 1691191) (-1009 "RDEEF.spad" 1689265 1689282 1690259 1690264) (-1008 "RCFIELD.spad" 1686451 1686460 1689167 1689260) (-1007 "RCFIELD.spad" 1683723 1683734 1686441 1686446) (-1006 "RCAGG.spad" 1681635 1681646 1683713 1683718) (-1005 "RCAGG.spad" 1679474 1679487 1681554 1681559) (-1004 "RATRET.spad" 1678834 1678845 1679464 1679469) (-1003 "RATFACT.spad" 1678526 1678538 1678824 1678829) (-1002 "RANDSRC.spad" 1677845 1677854 1678516 1678521) (-1001 "RADUTIL.spad" 1677599 1677608 1677835 1677840) (-1000 "RADIX.spad" 1674500 1674514 1676066 1676159) (-999 "RADFF.spad" 1672914 1672950 1673032 1673188) (-998 "RADCAT.spad" 1672508 1672516 1672904 1672909) (-997 "RADCAT.spad" 1672100 1672110 1672498 1672503) (-996 "QUEUE.spad" 1671443 1671453 1671707 1671734) (-995 "QUAT.spad" 1670025 1670035 1670367 1670432) (-994 "QUATCT2.spad" 1669644 1669662 1670015 1670020) (-993 "QUATCAT.spad" 1667809 1667819 1669574 1669639) (-992 "QUATCAT.spad" 1665725 1665737 1667492 1667497) (-991 "QUAGG.spad" 1664551 1664561 1665693 1665720) (-990 "QQUTAST.spad" 1664320 1664328 1664541 1664546) (-989 "QFORM.spad" 1663783 1663797 1664310 1664315) (-988 "QFCAT.spad" 1662486 1662496 1663685 1663778) (-987 "QFCAT.spad" 1660780 1660792 1661981 1661986) (-986 "QFCAT2.spad" 1660471 1660487 1660770 1660775) (-985 "QEQUAT.spad" 1660028 1660036 1660461 1660466) (-984 "QCMPACK.spad" 1654775 1654794 1660018 1660023) (-983 "QALGSET.spad" 1650850 1650882 1654689 1654694) (-982 "QALGSET2.spad" 1648846 1648864 1650840 1650845) (-981 "PWFFINTB.spad" 1646156 1646177 1648836 1648841) (-980 "PUSHVAR.spad" 1645485 1645504 1646146 1646151) (-979 "PTRANFN.spad" 1641611 1641621 1645475 1645480) (-978 "PTPACK.spad" 1638699 1638709 1641601 1641606) (-977 "PTFUNC2.spad" 1638520 1638534 1638689 1638694) (-976 "PTCAT.spad" 1637769 1637779 1638488 1638515) (-975 "PSQFR.spad" 1637076 1637100 1637759 1637764) (-974 "PSEUDLIN.spad" 1635934 1635944 1637066 1637071) (-973 "PSETPK.spad" 1621367 1621383 1635812 1635817) (-972 "PSETCAT.spad" 1615287 1615310 1621347 1621362) (-971 "PSETCAT.spad" 1609181 1609206 1615243 1615248) (-970 "PSCURVE.spad" 1608164 1608172 1609171 1609176) (-969 "PSCAT.spad" 1606931 1606960 1608062 1608159) (-968 "PSCAT.spad" 1605788 1605819 1606921 1606926) (-967 "PRTITION.spad" 1604733 1604741 1605778 1605783) (-966 "PRTDAST.spad" 1604452 1604460 1604723 1604728) (-965 "PRS.spad" 1594014 1594031 1604408 1604413) (-964 "PRQAGG.spad" 1593445 1593455 1593982 1594009) (-963 "PROPLOG.spad" 1592740 1592748 1593435 1593440) (-962 "PROPFRML.spad" 1591548 1591559 1592730 1592735) (-961 "PROPERTY.spad" 1591034 1591042 1591538 1591543) (-960 "PRODUCT.spad" 1588714 1588726 1589000 1589055) (-959 "PR.spad" 1587100 1587112 1587805 1587932) (-958 "PRINT.spad" 1586852 1586860 1587090 1587095) (-957 "PRIMES.spad" 1585103 1585113 1586842 1586847) (-956 "PRIMELT.spad" 1583084 1583098 1585093 1585098) (-955 "PRIMCAT.spad" 1582707 1582715 1583074 1583079) (-954 "PRIMARR.spad" 1581712 1581722 1581890 1581917) (-953 "PRIMARR2.spad" 1580435 1580447 1581702 1581707) (-952 "PREASSOC.spad" 1579807 1579819 1580425 1580430) (-951 "PPCURVE.spad" 1578944 1578952 1579797 1579802) (-950 "PORTNUM.spad" 1578719 1578727 1578934 1578939) (-949 "POLYROOT.spad" 1577548 1577570 1578675 1578680) (-948 "POLY.spad" 1574881 1574891 1575398 1575525) (-947 "POLYLIFT.spad" 1574142 1574165 1574871 1574876) (-946 "POLYCATQ.spad" 1572244 1572266 1574132 1574137) (-945 "POLYCAT.spad" 1565650 1565671 1572112 1572239) (-944 "POLYCAT.spad" 1558394 1558417 1564858 1564863) (-943 "POLY2UP.spad" 1557842 1557856 1558384 1558389) (-942 "POLY2.spad" 1557437 1557449 1557832 1557837) (-941 "POLUTIL.spad" 1556378 1556407 1557393 1557398) (-940 "POLTOPOL.spad" 1555126 1555141 1556368 1556373) (-939 "POINT.spad" 1553965 1553975 1554052 1554079) (-938 "PNTHEORY.spad" 1550631 1550639 1553955 1553960) (-937 "PMTOOLS.spad" 1549388 1549402 1550621 1550626) (-936 "PMSYM.spad" 1548933 1548943 1549378 1549383) (-935 "PMQFCAT.spad" 1548520 1548534 1548923 1548928) (-934 "PMPRED.spad" 1547989 1548003 1548510 1548515) (-933 "PMPREDFS.spad" 1547433 1547455 1547979 1547984) (-932 "PMPLCAT.spad" 1546503 1546521 1547365 1547370) (-931 "PMLSAGG.spad" 1546084 1546098 1546493 1546498) (-930 "PMKERNEL.spad" 1545651 1545663 1546074 1546079) (-929 "PMINS.spad" 1545227 1545237 1545641 1545646) (-928 "PMFS.spad" 1544800 1544818 1545217 1545222) (-927 "PMDOWN.spad" 1544086 1544100 1544790 1544795) (-926 "PMASS.spad" 1543094 1543102 1544076 1544081) (-925 "PMASSFS.spad" 1542059 1542075 1543084 1543089) (-924 "PLOTTOOL.spad" 1541839 1541847 1542049 1542054) (-923 "PLOT.spad" 1536670 1536678 1541829 1541834) (-922 "PLOT3D.spad" 1533090 1533098 1536660 1536665) (-921 "PLOT1.spad" 1532231 1532241 1533080 1533085) (-920 "PLEQN.spad" 1519447 1519474 1532221 1532226) (-919 "PINTERP.spad" 1519063 1519082 1519437 1519442) (-918 "PINTERPA.spad" 1518845 1518861 1519053 1519058) (-917 "PI.spad" 1518452 1518460 1518819 1518840) (-916 "PID.spad" 1517408 1517416 1518378 1518447) (-915 "PICOERCE.spad" 1517065 1517075 1517398 1517403) (-914 "PGROEB.spad" 1515662 1515676 1517055 1517060) (-913 "PGE.spad" 1506915 1506923 1515652 1515657) (-912 "PGCD.spad" 1505797 1505814 1506905 1506910) (-911 "PFRPAC.spad" 1504940 1504950 1505787 1505792) (-910 "PFR.spad" 1501597 1501607 1504842 1504935) (-909 "PFOTOOLS.spad" 1500855 1500871 1501587 1501592) (-908 "PFOQ.spad" 1500225 1500243 1500845 1500850) (-907 "PFO.spad" 1499644 1499671 1500215 1500220) (-906 "PF.spad" 1499218 1499230 1499449 1499542) (-905 "PFECAT.spad" 1496884 1496892 1499144 1499213) (-904 "PFECAT.spad" 1494578 1494588 1496840 1496845) (-903 "PFBRU.spad" 1492448 1492460 1494568 1494573) (-902 "PFBR.spad" 1489986 1490009 1492438 1492443) (-901 "PERM.spad" 1485667 1485677 1489816 1489831) (-900 "PERMGRP.spad" 1480403 1480413 1485657 1485662) (-899 "PERMCAT.spad" 1478955 1478965 1480383 1480398) (-898 "PERMAN.spad" 1477487 1477501 1478945 1478950) (-897 "PENDTREE.spad" 1476826 1476836 1477116 1477121) (-896 "PDRING.spad" 1475317 1475327 1476806 1476821) (-895 "PDRING.spad" 1473816 1473828 1475307 1475312) (-894 "PDEPROB.spad" 1472831 1472839 1473806 1473811) (-893 "PDEPACK.spad" 1466833 1466841 1472821 1472826) (-892 "PDECOMP.spad" 1466295 1466312 1466823 1466828) (-891 "PDECAT.spad" 1464649 1464657 1466285 1466290) (-890 "PCOMP.spad" 1464500 1464513 1464639 1464644) (-889 "PBWLB.spad" 1463082 1463099 1464490 1464495) (-888 "PATTERN.spad" 1457513 1457523 1463072 1463077) (-887 "PATTERN2.spad" 1457249 1457261 1457503 1457508) (-886 "PATTERN1.spad" 1455551 1455567 1457239 1457244) (-885 "PATRES.spad" 1453098 1453110 1455541 1455546) (-884 "PATRES2.spad" 1452760 1452774 1453088 1453093) (-883 "PATMATCH.spad" 1450917 1450948 1452468 1452473) (-882 "PATMAB.spad" 1450342 1450352 1450907 1450912) (-881 "PATLRES.spad" 1449426 1449440 1450332 1450337) (-880 "PATAB.spad" 1449190 1449200 1449416 1449421) (-879 "PARTPERM.spad" 1446552 1446560 1449180 1449185) (-878 "PARSURF.spad" 1445980 1446008 1446542 1446547) (-877 "PARSU2.spad" 1445775 1445791 1445970 1445975) (-876 "script-parser.spad" 1445295 1445303 1445765 1445770) (-875 "PARSCURV.spad" 1444723 1444751 1445285 1445290) (-874 "PARSC2.spad" 1444512 1444528 1444713 1444718) (-873 "PARPCURV.spad" 1443970 1443998 1444502 1444507) (-872 "PARPC2.spad" 1443759 1443775 1443960 1443965) (-871 "PAN2EXPR.spad" 1443171 1443179 1443749 1443754) (-870 "PALETTE.spad" 1442141 1442149 1443161 1443166) (-869 "PAIR.spad" 1441124 1441137 1441729 1441734) (-868 "PADICRC.spad" 1438454 1438472 1439629 1439722) (-867 "PADICRAT.spad" 1436469 1436481 1436690 1436783) (-866 "PADIC.spad" 1436164 1436176 1436395 1436464) (-865 "PADICCT.spad" 1434705 1434717 1436090 1436159) (-864 "PADEPAC.spad" 1433384 1433403 1434695 1434700) (-863 "PADE.spad" 1432124 1432140 1433374 1433379) (-862 "OWP.spad" 1431364 1431394 1431982 1432049) (-861 "OVERSET.spad" 1430937 1430945 1431354 1431359) (-860 "OVAR.spad" 1430718 1430741 1430927 1430932) (-859 "OUT.spad" 1429802 1429810 1430708 1430713) (-858 "OUTFORM.spad" 1419098 1419106 1429792 1429797) (-857 "OUTBFILE.spad" 1418516 1418524 1419088 1419093) (-856 "OUTBCON.spad" 1417514 1417522 1418506 1418511) (-855 "OUTBCON.spad" 1416510 1416520 1417504 1417509) (-854 "OSI.spad" 1415985 1415993 1416500 1416505) (-853 "OSGROUP.spad" 1415903 1415911 1415975 1415980) (-852 "ORTHPOL.spad" 1414364 1414374 1415820 1415825) (-851 "OREUP.spad" 1413817 1413845 1414044 1414083) (-850 "ORESUP.spad" 1413116 1413140 1413497 1413536) (-849 "OREPCTO.spad" 1410935 1410947 1413036 1413041) (-848 "OREPCAT.spad" 1404992 1405002 1410891 1410930) (-847 "OREPCAT.spad" 1398939 1398951 1404840 1404845) (-846 "ORDSET.spad" 1398105 1398113 1398929 1398934) (-845 "ORDSET.spad" 1397269 1397279 1398095 1398100) (-844 "ORDRING.spad" 1396659 1396667 1397249 1397264) (-843 "ORDRING.spad" 1396057 1396067 1396649 1396654) (-842 "ORDMON.spad" 1395912 1395920 1396047 1396052) (-841 "ORDFUNS.spad" 1395038 1395054 1395902 1395907) (-840 "ORDFIN.spad" 1394858 1394866 1395028 1395033) (-839 "ORDCOMP.spad" 1393323 1393333 1394405 1394434) (-838 "ORDCOMP2.spad" 1392608 1392620 1393313 1393318) (-837 "OPTPROB.spad" 1391246 1391254 1392598 1392603) (-836 "OPTPACK.spad" 1383631 1383639 1391236 1391241) (-835 "OPTCAT.spad" 1381306 1381314 1383621 1383626) (-834 "OPSIG.spad" 1380958 1380966 1381296 1381301) (-833 "OPQUERY.spad" 1380507 1380515 1380948 1380953) (-832 "OP.spad" 1380249 1380259 1380329 1380396) (-831 "OPERCAT.spad" 1379837 1379847 1380239 1380244) (-830 "OPERCAT.spad" 1379423 1379435 1379827 1379832) (-829 "ONECOMP.spad" 1378168 1378178 1378970 1378999) (-828 "ONECOMP2.spad" 1377586 1377598 1378158 1378163) (-827 "OMSERVER.spad" 1376588 1376596 1377576 1377581) (-826 "OMSAGG.spad" 1376376 1376386 1376544 1376583) (-825 "OMPKG.spad" 1374988 1374996 1376366 1376371) (-824 "OM.spad" 1373953 1373961 1374978 1374983) (-823 "OMLO.spad" 1373378 1373390 1373839 1373878) (-822 "OMEXPR.spad" 1373212 1373222 1373368 1373373) (-821 "OMERR.spad" 1372755 1372763 1373202 1373207) (-820 "OMERRK.spad" 1371789 1371797 1372745 1372750) (-819 "OMENC.spad" 1371133 1371141 1371779 1371784) (-818 "OMDEV.spad" 1365422 1365430 1371123 1371128) (-817 "OMCONN.spad" 1364831 1364839 1365412 1365417) (-816 "OINTDOM.spad" 1364594 1364602 1364757 1364826) (-815 "OFMONOID.spad" 1360781 1360791 1364584 1364589) (-814 "ODVAR.spad" 1360042 1360052 1360771 1360776) (-813 "ODR.spad" 1359686 1359712 1359854 1360003) (-812 "ODPOL.spad" 1357068 1357078 1357408 1357535) (-811 "ODP.spad" 1346915 1346935 1347288 1347419) (-810 "ODETOOLS.spad" 1345498 1345517 1346905 1346910) (-809 "ODESYS.spad" 1343148 1343165 1345488 1345493) (-808 "ODERTRIC.spad" 1339089 1339106 1343105 1343110) (-807 "ODERED.spad" 1338476 1338500 1339079 1339084) (-806 "ODERAT.spad" 1336027 1336044 1338466 1338471) (-805 "ODEPRRIC.spad" 1332918 1332940 1336017 1336022) (-804 "ODEPROB.spad" 1332175 1332183 1332908 1332913) (-803 "ODEPRIM.spad" 1329449 1329471 1332165 1332170) (-802 "ODEPAL.spad" 1328825 1328849 1329439 1329444) (-801 "ODEPACK.spad" 1315427 1315435 1328815 1328820) (-800 "ODEINT.spad" 1314858 1314874 1315417 1315422) (-799 "ODEIFTBL.spad" 1312253 1312261 1314848 1314853) (-798 "ODEEF.spad" 1307620 1307636 1312243 1312248) (-797 "ODECONST.spad" 1307139 1307157 1307610 1307615) (-796 "ODECAT.spad" 1305735 1305743 1307129 1307134) (-795 "OCT.spad" 1303873 1303883 1304589 1304628) (-794 "OCTCT2.spad" 1303517 1303538 1303863 1303868) (-793 "OC.spad" 1301291 1301301 1303473 1303512) (-792 "OC.spad" 1298790 1298802 1300974 1300979) (-791 "OCAMON.spad" 1298638 1298646 1298780 1298785) (-790 "OASGP.spad" 1298453 1298461 1298628 1298633) (-789 "OAMONS.spad" 1297973 1297981 1298443 1298448) (-788 "OAMON.spad" 1297834 1297842 1297963 1297968) (-787 "OAGROUP.spad" 1297696 1297704 1297824 1297829) (-786 "NUMTUBE.spad" 1297283 1297299 1297686 1297691) (-785 "NUMQUAD.spad" 1285145 1285153 1297273 1297278) (-784 "NUMODE.spad" 1276281 1276289 1285135 1285140) (-783 "NUMINT.spad" 1273839 1273847 1276271 1276276) (-782 "NUMFMT.spad" 1272679 1272687 1273829 1273834) (-781 "NUMERIC.spad" 1264751 1264761 1272484 1272489) (-780 "NTSCAT.spad" 1263253 1263269 1264719 1264746) (-779 "NTPOLFN.spad" 1262798 1262808 1263170 1263175) (-778 "NSUP.spad" 1255844 1255854 1260384 1260537) (-777 "NSUP2.spad" 1255236 1255248 1255834 1255839) (-776 "NSMP.spad" 1251467 1251486 1251775 1251902) (-775 "NREP.spad" 1249839 1249853 1251457 1251462) (-774 "NPCOEF.spad" 1249085 1249105 1249829 1249834) (-773 "NORMRETR.spad" 1248683 1248722 1249075 1249080) (-772 "NORMPK.spad" 1246585 1246604 1248673 1248678) (-771 "NORMMA.spad" 1246273 1246299 1246575 1246580) (-770 "NONE.spad" 1246014 1246022 1246263 1246268) (-769 "NONE1.spad" 1245690 1245700 1246004 1246009) (-768 "NODE1.spad" 1245159 1245175 1245680 1245685) (-767 "NNI.spad" 1244046 1244054 1245133 1245154) (-766 "NLINSOL.spad" 1242668 1242678 1244036 1244041) (-765 "NIPROB.spad" 1241209 1241217 1242658 1242663) (-764 "NFINTBAS.spad" 1238669 1238686 1241199 1241204) (-763 "NETCLT.spad" 1238643 1238654 1238659 1238664) (-762 "NCODIV.spad" 1236841 1236857 1238633 1238638) (-761 "NCNTFRAC.spad" 1236483 1236497 1236831 1236836) (-760 "NCEP.spad" 1234643 1234657 1236473 1236478) (-759 "NASRING.spad" 1234239 1234247 1234633 1234638) (-758 "NASRING.spad" 1233833 1233843 1234229 1234234) (-757 "NARNG.spad" 1233177 1233185 1233823 1233828) (-756 "NARNG.spad" 1232519 1232529 1233167 1233172) (-755 "NAGSP.spad" 1231592 1231600 1232509 1232514) (-754 "NAGS.spad" 1221117 1221125 1231582 1231587) (-753 "NAGF07.spad" 1219510 1219518 1221107 1221112) (-752 "NAGF04.spad" 1213742 1213750 1219500 1219505) (-751 "NAGF02.spad" 1207551 1207559 1213732 1213737) (-750 "NAGF01.spad" 1203154 1203162 1207541 1207546) (-749 "NAGE04.spad" 1196614 1196622 1203144 1203149) (-748 "NAGE02.spad" 1186956 1186964 1196604 1196609) (-747 "NAGE01.spad" 1182840 1182848 1186946 1186951) (-746 "NAGD03.spad" 1180760 1180768 1182830 1182835) (-745 "NAGD02.spad" 1173291 1173299 1180750 1180755) (-744 "NAGD01.spad" 1167404 1167412 1173281 1173286) (-743 "NAGC06.spad" 1163191 1163199 1167394 1167399) (-742 "NAGC05.spad" 1161660 1161668 1163181 1163186) (-741 "NAGC02.spad" 1160915 1160923 1161650 1161655) (-740 "NAALG.spad" 1160450 1160460 1160883 1160910) (-739 "NAALG.spad" 1160005 1160017 1160440 1160445) (-738 "MULTSQFR.spad" 1156963 1156980 1159995 1160000) (-737 "MULTFACT.spad" 1156346 1156363 1156953 1156958) (-736 "MTSCAT.spad" 1154380 1154401 1156244 1156341) (-735 "MTHING.spad" 1154037 1154047 1154370 1154375) (-734 "MSYSCMD.spad" 1153471 1153479 1154027 1154032) (-733 "MSET.spad" 1151413 1151423 1153177 1153216) (-732 "MSETAGG.spad" 1151258 1151268 1151381 1151408) (-731 "MRING.spad" 1148229 1148241 1150966 1151033) (-730 "MRF2.spad" 1147797 1147811 1148219 1148224) (-729 "MRATFAC.spad" 1147343 1147360 1147787 1147792) (-728 "MPRFF.spad" 1145373 1145392 1147333 1147338) (-727 "MPOLY.spad" 1142844 1142859 1143203 1143330) (-726 "MPCPF.spad" 1142108 1142127 1142834 1142839) (-725 "MPC3.spad" 1141923 1141963 1142098 1142103) (-724 "MPC2.spad" 1141565 1141598 1141913 1141918) (-723 "MONOTOOL.spad" 1139900 1139917 1141555 1141560) (-722 "MONOID.spad" 1139219 1139227 1139890 1139895) (-721 "MONOID.spad" 1138536 1138546 1139209 1139214) (-720 "MONOGEN.spad" 1137282 1137295 1138396 1138531) (-719 "MONOGEN.spad" 1136050 1136065 1137166 1137171) (-718 "MONADWU.spad" 1134064 1134072 1136040 1136045) (-717 "MONADWU.spad" 1132076 1132086 1134054 1134059) (-716 "MONAD.spad" 1131220 1131228 1132066 1132071) (-715 "MONAD.spad" 1130362 1130372 1131210 1131215) (-714 "MOEBIUS.spad" 1129048 1129062 1130342 1130357) (-713 "MODULE.spad" 1128918 1128928 1129016 1129043) (-712 "MODULE.spad" 1128808 1128820 1128908 1128913) (-711 "MODRING.spad" 1128139 1128178 1128788 1128803) (-710 "MODOP.spad" 1126798 1126810 1127961 1128028) (-709 "MODMONOM.spad" 1126527 1126545 1126788 1126793) (-708 "MODMON.spad" 1123322 1123338 1124041 1124194) (-707 "MODFIELD.spad" 1122680 1122719 1123224 1123317) (-706 "MMLFORM.spad" 1121540 1121548 1122670 1122675) (-705 "MMAP.spad" 1121280 1121314 1121530 1121535) (-704 "MLO.spad" 1119707 1119717 1121236 1121275) (-703 "MLIFT.spad" 1118279 1118296 1119697 1119702) (-702 "MKUCFUNC.spad" 1117812 1117830 1118269 1118274) (-701 "MKRECORD.spad" 1117414 1117427 1117802 1117807) (-700 "MKFUNC.spad" 1116795 1116805 1117404 1117409) (-699 "MKFLCFN.spad" 1115751 1115761 1116785 1116790) (-698 "MKBCFUNC.spad" 1115236 1115254 1115741 1115746) (-697 "MINT.spad" 1114675 1114683 1115138 1115231) (-696 "MHROWRED.spad" 1113176 1113186 1114665 1114670) (-695 "MFLOAT.spad" 1111692 1111700 1113066 1113171) (-694 "MFINFACT.spad" 1111092 1111114 1111682 1111687) (-693 "MESH.spad" 1108824 1108832 1111082 1111087) (-692 "MDDFACT.spad" 1107017 1107027 1108814 1108819) (-691 "MDAGG.spad" 1106304 1106314 1106997 1107012) (-690 "MCMPLX.spad" 1102316 1102324 1102930 1103131) (-689 "MCDEN.spad" 1101524 1101536 1102306 1102311) (-688 "MCALCFN.spad" 1098626 1098652 1101514 1101519) (-687 "MAYBE.spad" 1097910 1097921 1098616 1098621) (-686 "MATSTOR.spad" 1095186 1095196 1097900 1097905) (-685 "MATRIX.spad" 1093890 1093900 1094374 1094401) (-684 "MATLIN.spad" 1091216 1091240 1093774 1093779) (-683 "MATCAT.spad" 1082801 1082823 1091184 1091211) (-682 "MATCAT.spad" 1074258 1074282 1082643 1082648) (-681 "MATCAT2.spad" 1073526 1073574 1074248 1074253) (-680 "MAPPKG3.spad" 1072425 1072439 1073516 1073521) (-679 "MAPPKG2.spad" 1071759 1071771 1072415 1072420) (-678 "MAPPKG1.spad" 1070577 1070587 1071749 1071754) (-677 "MAPPAST.spad" 1069890 1069898 1070567 1070572) (-676 "MAPHACK3.spad" 1069698 1069712 1069880 1069885) (-675 "MAPHACK2.spad" 1069463 1069475 1069688 1069693) (-674 "MAPHACK1.spad" 1069093 1069103 1069453 1069458) (-673 "MAGMA.spad" 1066883 1066900 1069083 1069088) (-672 "MACROAST.spad" 1066462 1066470 1066873 1066878) (-671 "M3D.spad" 1064158 1064168 1065840 1065845) (-670 "LZSTAGG.spad" 1061386 1061396 1064148 1064153) (-669 "LZSTAGG.spad" 1058612 1058624 1061376 1061381) (-668 "LWORD.spad" 1055317 1055334 1058602 1058607) (-667 "LSTAST.spad" 1055101 1055109 1055307 1055312) (-666 "LSQM.spad" 1053327 1053341 1053725 1053776) (-665 "LSPP.spad" 1052860 1052877 1053317 1053322) (-664 "LSMP.spad" 1051700 1051728 1052850 1052855) (-663 "LSMP1.spad" 1049504 1049518 1051690 1051695) (-662 "LSAGG.spad" 1049173 1049183 1049472 1049499) (-661 "LSAGG.spad" 1048862 1048874 1049163 1049168) (-660 "LPOLY.spad" 1047816 1047835 1048718 1048787) (-659 "LPEFRAC.spad" 1047073 1047083 1047806 1047811) (-658 "LO.spad" 1046474 1046488 1047007 1047034) (-657 "LOGIC.spad" 1046076 1046084 1046464 1046469) (-656 "LOGIC.spad" 1045676 1045686 1046066 1046071) (-655 "LODOOPS.spad" 1044594 1044606 1045666 1045671) (-654 "LODO.spad" 1043978 1043994 1044274 1044313) (-653 "LODOF.spad" 1043022 1043039 1043935 1043940) (-652 "LODOCAT.spad" 1041680 1041690 1042978 1043017) (-651 "LODOCAT.spad" 1040336 1040348 1041636 1041641) (-650 "LODO2.spad" 1039609 1039621 1040016 1040055) (-649 "LODO1.spad" 1039009 1039019 1039289 1039328) (-648 "LODEEF.spad" 1037781 1037799 1038999 1039004) (-647 "LNAGG.spad" 1033583 1033593 1037771 1037776) (-646 "LNAGG.spad" 1029349 1029361 1033539 1033544) (-645 "LMOPS.spad" 1026085 1026102 1029339 1029344) (-644 "LMODULE.spad" 1025727 1025737 1026075 1026080) (-643 "LMDICT.spad" 1025010 1025020 1025278 1025305) (-642 "LITERAL.spad" 1024916 1024927 1025000 1025005) (-641 "LIST.spad" 1022634 1022644 1024063 1024090) (-640 "LIST3.spad" 1021925 1021939 1022624 1022629) (-639 "LIST2.spad" 1020565 1020577 1021915 1021920) (-638 "LIST2MAP.spad" 1017442 1017454 1020555 1020560) (-637 "LINEXP.spad" 1016874 1016884 1017422 1017437) (-636 "LINDEP.spad" 1015651 1015663 1016786 1016791) (-635 "LIMITRF.spad" 1013565 1013575 1015641 1015646) (-634 "LIMITPS.spad" 1012448 1012461 1013555 1013560) (-633 "LIE.spad" 1010462 1010474 1011738 1011883) (-632 "LIECAT.spad" 1009938 1009948 1010388 1010457) (-631 "LIECAT.spad" 1009442 1009454 1009894 1009899) (-630 "LIB.spad" 1007490 1007498 1008101 1008116) (-629 "LGROBP.spad" 1004843 1004862 1007480 1007485) (-628 "LF.spad" 1003762 1003778 1004833 1004838) (-627 "LFCAT.spad" 1002781 1002789 1003752 1003757) (-626 "LEXTRIPK.spad" 998284 998299 1002771 1002776) (-625 "LEXP.spad" 996287 996314 998264 998279) (-624 "LETAST.spad" 995986 995994 996277 996282) (-623 "LEADCDET.spad" 994370 994387 995976 995981) (-622 "LAZM3PK.spad" 993074 993096 994360 994365) (-621 "LAUPOL.spad" 991763 991776 992667 992736) (-620 "LAPLACE.spad" 991336 991352 991753 991758) (-619 "LA.spad" 990776 990790 991258 991297) (-618 "LALG.spad" 990552 990562 990756 990771) (-617 "LALG.spad" 990336 990348 990542 990547) (-616 "KVTFROM.spad" 990071 990081 990326 990331) (-615 "KTVLOGIC.spad" 989583 989591 990061 990066) (-614 "KRCFROM.spad" 989321 989331 989573 989578) (-613 "KOVACIC.spad" 988034 988051 989311 989316) (-612 "KONVERT.spad" 987756 987766 988024 988029) (-611 "KOERCE.spad" 987493 987503 987746 987751) (-610 "KERNEL.spad" 986028 986038 987277 987282) (-609 "KERNEL2.spad" 985731 985743 986018 986023) (-608 "KDAGG.spad" 984834 984856 985711 985726) (-607 "KDAGG.spad" 983945 983969 984824 984829) (-606 "KAFILE.spad" 982908 982924 983143 983170) (-605 "JORDAN.spad" 980735 980747 982198 982343) (-604 "JOINAST.spad" 980429 980437 980725 980730) (-603 "JAVACODE.spad" 980295 980303 980419 980424) (-602 "IXAGG.spad" 978418 978442 980285 980290) (-601 "IXAGG.spad" 976396 976422 978265 978270) (-600 "IVECTOR.spad" 975167 975182 975322 975349) (-599 "ITUPLE.spad" 974312 974322 975157 975162) (-598 "ITRIGMNP.spad" 973123 973142 974302 974307) (-597 "ITFUN3.spad" 972617 972631 973113 973118) (-596 "ITFUN2.spad" 972347 972359 972607 972612) (-595 "ITAYLOR.spad" 970139 970154 972183 972308) (-594 "ISUPS.spad" 962550 962565 969113 969210) (-593 "ISUMP.spad" 962047 962063 962540 962545) (-592 "ISTRING.spad" 961050 961063 961216 961243) (-591 "ISAST.spad" 960769 960777 961040 961045) (-590 "IRURPK.spad" 959482 959501 960759 960764) (-589 "IRSN.spad" 957442 957450 959472 959477) (-588 "IRRF2F.spad" 955917 955927 957398 957403) (-587 "IRREDFFX.spad" 955518 955529 955907 955912) (-586 "IROOT.spad" 953849 953859 955508 955513) (-585 "IR.spad" 951638 951652 953704 953731) (-584 "IR2.spad" 950658 950674 951628 951633) (-583 "IR2F.spad" 949858 949874 950648 950653) (-582 "IPRNTPK.spad" 949618 949626 949848 949853) (-581 "IPF.spad" 949183 949195 949423 949516) (-580 "IPADIC.spad" 948944 948970 949109 949178) (-579 "IP4ADDR.spad" 948501 948509 948934 948939) (-578 "IOMODE.spad" 948122 948130 948491 948496) (-577 "IOBFILE.spad" 947483 947491 948112 948117) (-576 "IOBCON.spad" 947348 947356 947473 947478) (-575 "INVLAPLA.spad" 946993 947009 947338 947343) (-574 "INTTR.spad" 940239 940256 946983 946988) (-573 "INTTOOLS.spad" 937950 937966 939813 939818) (-572 "INTSLPE.spad" 937256 937264 937940 937945) (-571 "INTRVL.spad" 936822 936832 937170 937251) (-570 "INTRF.spad" 935186 935200 936812 936817) (-569 "INTRET.spad" 934618 934628 935176 935181) (-568 "INTRAT.spad" 933293 933310 934608 934613) (-567 "INTPM.spad" 931656 931672 932936 932941) (-566 "INTPAF.spad" 929424 929442 931588 931593) (-565 "INTPACK.spad" 919734 919742 929414 929419) (-564 "INT.spad" 919095 919103 919588 919729) (-563 "INTHERTR.spad" 918361 918378 919085 919090) (-562 "INTHERAL.spad" 918027 918051 918351 918356) (-561 "INTHEORY.spad" 914440 914448 918017 918022) (-560 "INTG0.spad" 907903 907921 914372 914377) (-559 "INTFTBL.spad" 901932 901940 907893 907898) (-558 "INTFACT.spad" 900991 901001 901922 901927) (-557 "INTEF.spad" 899306 899322 900981 900986) (-556 "INTDOM.spad" 897921 897929 899232 899301) (-555 "INTDOM.spad" 896598 896608 897911 897916) (-554 "INTCAT.spad" 894851 894861 896512 896593) (-553 "INTBIT.spad" 894354 894362 894841 894846) (-552 "INTALG.spad" 893536 893563 894344 894349) (-551 "INTAF.spad" 893028 893044 893526 893531) (-550 "INTABL.spad" 891546 891577 891709 891736) (-549 "INT8.spad" 891426 891434 891536 891541) (-548 "INT64.spad" 891305 891313 891416 891421) (-547 "INT32.spad" 891184 891192 891295 891300) (-546 "INT16.spad" 891063 891071 891174 891179) (-545 "INS.spad" 888530 888538 890965 891058) (-544 "INS.spad" 886083 886093 888520 888525) (-543 "INPSIGN.spad" 885517 885530 886073 886078) (-542 "INPRODPF.spad" 884583 884602 885507 885512) (-541 "INPRODFF.spad" 883641 883665 884573 884578) (-540 "INNMFACT.spad" 882612 882629 883631 883636) (-539 "INMODGCD.spad" 882096 882126 882602 882607) (-538 "INFSP.spad" 880381 880403 882086 882091) (-537 "INFPROD0.spad" 879431 879450 880371 880376) (-536 "INFORM.spad" 876592 876600 879421 879426) (-535 "INFORM1.spad" 876217 876227 876582 876587) (-534 "INFINITY.spad" 875769 875777 876207 876212) (-533 "INETCLTS.spad" 875746 875754 875759 875764) (-532 "INEP.spad" 874278 874300 875736 875741) (-531 "INDE.spad" 874007 874024 874268 874273) (-530 "INCRMAPS.spad" 873428 873438 873997 874002) (-529 "INBFILE.spad" 872500 872508 873418 873423) (-528 "INBFF.spad" 868270 868281 872490 872495) (-527 "INBCON.spad" 866558 866566 868260 868265) (-526 "INBCON.spad" 864844 864854 866548 866553) (-525 "INAST.spad" 864505 864513 864834 864839) (-524 "IMPTAST.spad" 864213 864221 864495 864500) (-523 "IMATRIX.spad" 863158 863184 863670 863697) (-522 "IMATQF.spad" 862252 862296 863114 863119) (-521 "IMATLIN.spad" 860857 860881 862208 862213) (-520 "ILIST.spad" 859513 859528 860040 860067) (-519 "IIARRAY2.spad" 858901 858939 859120 859147) (-518 "IFF.spad" 858311 858327 858582 858675) (-517 "IFAST.spad" 857925 857933 858301 858306) (-516 "IFARRAY.spad" 855412 855427 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"IAN.spad" 831300 831308 832903 832996) (-494 "IALGFACT.spad" 830901 830934 831290 831295) (-493 "HYPCAT.spad" 830325 830333 830891 830896) (-492 "HYPCAT.spad" 829747 829757 830315 830320) (-491 "HOSTNAME.spad" 829555 829563 829737 829742) (-490 "HOMOTOP.spad" 829298 829308 829545 829550) (-489 "HOAGG.spad" 826566 826576 829288 829293) (-488 "HOAGG.spad" 823609 823621 826333 826338) (-487 "HEXADEC.spad" 821711 821719 822076 822169) (-486 "HEUGCD.spad" 820726 820737 821701 821706) (-485 "HELLFDIV.spad" 820316 820340 820716 820721) (-484 "HEAP.spad" 819708 819718 819923 819950) (-483 "HEADAST.spad" 819239 819247 819698 819703) (-482 "HDP.spad" 809082 809098 809459 809590) (-481 "HDMP.spad" 806294 806309 806912 807039) (-480 "HB.spad" 804531 804539 806284 806289) (-479 "HASHTBL.spad" 803001 803032 803212 803239) (-478 "HASAST.spad" 802717 802725 802991 802996) (-477 "HACKPI.spad" 802200 802208 802619 802712) (-476 "GTSET.spad" 801139 801155 801846 801873) (-475 "GSTBL.spad" 799658 799693 799832 799847) (-474 "GSERIES.spad" 796825 796852 797790 797939) (-473 "GROUP.spad" 796094 796102 796805 796820) (-472 "GROUP.spad" 795371 795381 796084 796089) (-471 "GROEBSOL.spad" 793859 793880 795361 795366) (-470 "GRMOD.spad" 792430 792442 793849 793854) (-469 "GRMOD.spad" 790999 791013 792420 792425) (-468 "GRIMAGE.spad" 783604 783612 790989 790994) (-467 "GRDEF.spad" 781983 781991 783594 783599) (-466 "GRAY.spad" 780442 780450 781973 781978) (-465 "GRALG.spad" 779489 779501 780432 780437) (-464 "GRALG.spad" 778534 778548 779479 779484) (-463 "GPOLSET.spad" 777988 778011 778216 778243) (-462 "GOSPER.spad" 777253 777271 777978 777983) (-461 "GMODPOL.spad" 776391 776418 777221 777248) (-460 "GHENSEL.spad" 775460 775474 776381 776386) (-459 "GENUPS.spad" 771561 771574 775450 775455) (-458 "GENUFACT.spad" 771138 771148 771551 771556) (-457 "GENPGCD.spad" 770722 770739 771128 771133) (-456 "GENMFACT.spad" 770174 770193 770712 770717) (-455 "GENEEZ.spad" 768113 768126 770164 770169) (-454 "GDMP.spad" 765167 765184 765943 766070) (-453 "GCNAALG.spad" 759062 759089 764961 765028) (-452 "GCDDOM.spad" 758234 758242 758988 759057) (-451 "GCDDOM.spad" 757468 757478 758224 758229) (-450 "GB.spad" 754986 755024 757424 757429) (-449 "GBINTERN.spad" 751006 751044 754976 754981) (-448 "GBF.spad" 746763 746801 750996 751001) (-447 "GBEUCLID.spad" 744637 744675 746753 746758) (-446 "GAUSSFAC.spad" 743934 743942 744627 744632) (-445 "GALUTIL.spad" 742256 742266 743890 743895) (-444 "GALPOLYU.spad" 740702 740715 742246 742251) (-443 "GALFACTU.spad" 738867 738886 740692 740697) (-442 "GALFACT.spad" 729000 729011 738857 738862) (-441 "FVFUN.spad" 726023 726031 728990 728995) (-440 "FVC.spad" 725075 725083 726013 726018) (-439 "FUNDESC.spad" 724753 724761 725065 725070) (-438 "FUNCTION.spad" 724602 724614 724743 724748) (-437 "FT.spad" 722895 722903 724592 724597) (-436 "FTEM.spad" 722058 722066 722885 722890) (-435 "FSUPFACT.spad" 720958 720977 721994 721999) (-434 "FST.spad" 719044 719052 720948 720953) (-433 "FSRED.spad" 718522 718538 719034 719039) (-432 "FSPRMELT.spad" 717346 717362 718479 718484) (-431 "FSPECF.spad" 715423 715439 717336 717341) (-430 "FS.spad" 709485 709495 715198 715418) (-429 "FS.spad" 703325 703337 709040 709045) (-428 "FSINT.spad" 702983 702999 703315 703320) (-427 "FSERIES.spad" 702170 702182 702803 702902) (-426 "FSCINT.spad" 701483 701499 702160 702165) (-425 "FSAGG.spad" 700600 700610 701439 701478) (-424 "FSAGG.spad" 699679 699691 700520 700525) (-423 "FSAGG2.spad" 698378 698394 699669 699674) (-422 "FS2UPS.spad" 692861 692895 698368 698373) (-421 "FS2.spad" 692506 692522 692851 692856) (-420 "FS2EXPXP.spad" 691629 691652 692496 692501) (-419 "FRUTIL.spad" 690571 690581 691619 691624) (-418 "FR.spad" 684265 684275 689595 689664) (-417 "FRNAALG.spad" 679352 679362 684207 684260) (-416 "FRNAALG.spad" 674451 674463 679308 679313) (-415 "FRNAAF2.spad" 673905 673923 674441 674446) (-414 "FRMOD.spad" 673299 673329 673836 673841) (-413 "FRIDEAL.spad" 672494 672515 673279 673294) (-412 "FRIDEAL2.spad" 672096 672128 672484 672489) (-411 "FRETRCT.spad" 671607 671617 672086 672091) (-410 "FRETRCT.spad" 670984 670996 671465 671470) (-409 "FRAMALG.spad" 669312 669325 670940 670979) (-408 "FRAMALG.spad" 667672 667687 669302 669307) (-407 "FRAC.spad" 664771 664781 665174 665347) (-406 "FRAC2.spad" 664374 664386 664761 664766) (-405 "FR2.spad" 663708 663720 664364 664369) (-404 "FPS.spad" 660517 660525 663598 663703) (-403 "FPS.spad" 657354 657364 660437 660442) (-402 "FPC.spad" 656396 656404 657256 657349) (-401 "FPC.spad" 655524 655534 656386 656391) (-400 "FPATMAB.spad" 655286 655296 655514 655519) (-399 "FPARFRAC.spad" 653759 653776 655276 655281) (-398 "FORTRAN.spad" 652265 652308 653749 653754) (-397 "FORT.spad" 651194 651202 652255 652260) (-396 "FORTFN.spad" 648364 648372 651184 651189) (-395 "FORTCAT.spad" 648048 648056 648354 648359) (-394 "FORMULA.spad" 645512 645520 648038 648043) (-393 "FORMULA1.spad" 644991 645001 645502 645507) (-392 "FORDER.spad" 644682 644706 644981 644986) (-391 "FOP.spad" 643883 643891 644672 644677) (-390 "FNLA.spad" 643307 643329 643851 643878) (-389 "FNCAT.spad" 641894 641902 643297 643302) (-388 "FNAME.spad" 641786 641794 641884 641889) (-387 "FMTC.spad" 641584 641592 641712 641781) (-386 "FMONOID.spad" 638639 638649 641540 641545) (-385 "FM.spad" 638334 638346 638573 638600) (-384 "FMFUN.spad" 635364 635372 638324 638329) (-383 "FMC.spad" 634416 634424 635354 635359) (-382 "FMCAT.spad" 632070 632088 634384 634411) (-381 "FM1.spad" 631427 631439 632004 632031) (-380 "FLOATRP.spad" 629148 629162 631417 631422) (-379 "FLOAT.spad" 622436 622444 629014 629143) (-378 "FLOATCP.spad" 619853 619867 622426 622431) (-377 "FLINEXP.spad" 619565 619575 619833 619848) (-376 "FLINEXP.spad" 619231 619243 619501 619506) (-375 "FLASORT.spad" 618551 618563 619221 619226) (-374 "FLALG.spad" 616197 616216 618477 618546) (-373 "FLAGG.spad" 613215 613225 616177 616192) (-372 "FLAGG.spad" 610134 610146 613098 613103) (-371 "FLAGG2.spad" 608815 608831 610124 610129) (-370 "FINRALG.spad" 606844 606857 608771 608810) (-369 "FINRALG.spad" 604799 604814 606728 606733) (-368 "FINITE.spad" 603951 603959 604789 604794) (-367 "FINAALG.spad" 592932 592942 603893 603946) (-366 "FINAALG.spad" 581925 581937 592888 592893) (-365 "FILE.spad" 581508 581518 581915 581920) (-364 "FILECAT.spad" 580026 580043 581498 581503) (-363 "FIELD.spad" 579432 579440 579928 580021) (-362 "FIELD.spad" 578924 578934 579422 579427) (-361 "FGROUP.spad" 577533 577543 578904 578919) (-360 "FGLMICPK.spad" 576320 576335 577523 577528) (-359 "FFX.spad" 575695 575710 576036 576129) (-358 "FFSLPE.spad" 575184 575205 575685 575690) (-357 "FFPOLY.spad" 566436 566447 575174 575179) (-356 "FFPOLY2.spad" 565496 565513 566426 566431) (-355 "FFP.spad" 564893 564913 565212 565305) (-354 "FF.spad" 564341 564357 564574 564667) (-353 "FFNBX.spad" 562853 562873 564057 564150) (-352 "FFNBP.spad" 561366 561383 562569 562662) (-351 "FFNB.spad" 559831 559852 561047 561140) (-350 "FFINTBAS.spad" 557245 557264 559821 559826) (-349 "FFIELDC.spad" 554820 554828 557147 557240) (-348 "FFIELDC.spad" 552481 552491 554810 554815) (-347 "FFHOM.spad" 551229 551246 552471 552476) (-346 "FFF.spad" 548664 548675 551219 551224) (-345 "FFCGX.spad" 547511 547531 548380 548473) (-344 "FFCGP.spad" 546400 546420 547227 547320) (-343 "FFCG.spad" 545192 545213 546081 546174) (-342 "FFCAT.spad" 538219 538241 545031 545187) (-341 "FFCAT.spad" 531325 531349 538139 538144) (-340 "FFCAT2.spad" 531070 531110 531315 531320) (-339 "FEXPR.spad" 522779 522825 530826 530865) (-338 "FEVALAB.spad" 522485 522495 522769 522774) (-337 "FEVALAB.spad" 521976 521988 522262 522267) (-336 "FDIV.spad" 521418 521442 521966 521971) (-335 "FDIVCAT.spad" 519460 519484 521408 521413) (-334 "FDIVCAT.spad" 517500 517526 519450 519455) (-333 "FDIV2.spad" 517154 517194 517490 517495) (-332 "FCPAK1.spad" 515707 515715 517144 517149) (-331 "FCOMP.spad" 515086 515096 515697 515702) (-330 "FC.spad" 505001 505009 515076 515081) (-329 "FAXF.spad" 497936 497950 504903 504996) (-328 "FAXF.spad" 490923 490939 497892 497897) (-327 "FARRAY.spad" 489069 489079 490106 490133) (-326 "FAMR.spad" 487189 487201 488967 489064) (-325 "FAMR.spad" 485293 485307 487073 487078) (-324 "FAMONOID.spad" 484943 484953 485247 485252) (-323 "FAMONC.spad" 483165 483177 484933 484938) (-322 "FAGROUP.spad" 482771 482781 483061 483088) (-321 "FACUTIL.spad" 480967 480984 482761 482766) (-320 "FACTFUNC.spad" 480143 480153 480957 480962) (-319 "EXPUPXS.spad" 476976 476999 478275 478424) (-318 "EXPRTUBE.spad" 474204 474212 476966 476971) (-317 "EXPRODE.spad" 471076 471092 474194 474199) (-316 "EXPR.spad" 466351 466361 467065 467472) (-315 "EXPR2UPS.spad" 462443 462456 466341 466346) (-314 "EXPR2.spad" 462146 462158 462433 462438) (-313 "EXPEXPAN.spad" 459084 459109 459718 459811) (-312 "EXIT.spad" 458755 458763 459074 459079) (-311 "EXITAST.spad" 458491 458499 458745 458750) (-310 "EVALCYC.spad" 457949 457963 458481 458486) (-309 "EVALAB.spad" 457513 457523 457939 457944) (-308 "EVALAB.spad" 457075 457087 457503 457508) (-307 "EUCDOM.spad" 454617 454625 457001 457070) (-306 "EUCDOM.spad" 452221 452231 454607 454612) (-305 "ESTOOLS.spad" 444061 444069 452211 452216) (-304 "ESTOOLS2.spad" 443662 443676 444051 444056) (-303 "ESTOOLS1.spad" 443347 443358 443652 443657) (-302 "ES.spad" 435894 435902 443337 443342) (-301 "ES.spad" 428347 428357 435792 435797) (-300 "ESCONT.spad" 425120 425128 428337 428342) (-299 "ESCONT1.spad" 424869 424881 425110 425115) (-298 "ES2.spad" 424364 424380 424859 424864) (-297 "ES1.spad" 423930 423946 424354 424359) (-296 "ERROR.spad" 421251 421259 423920 423925) (-295 "EQTBL.spad" 419723 419745 419932 419959) (-294 "EQ.spad" 414597 414607 417396 417508) (-293 "EQ2.spad" 414313 414325 414587 414592) (-292 "EP.spad" 410627 410637 414303 414308) (-291 "ENV.spad" 409279 409287 410617 410622) (-290 "ENTIRER.spad" 408947 408955 409223 409274) (-289 "EMR.spad" 408148 408189 408873 408942) (-288 "ELTAGG.spad" 406388 406407 408138 408143) (-287 "ELTAGG.spad" 404592 404613 406344 406349) (-286 "ELTAB.spad" 404039 404057 404582 404587) (-285 "ELFUTS.spad" 403418 403437 404029 404034) (-284 "ELEMFUN.spad" 403107 403115 403408 403413) (-283 "ELEMFUN.spad" 402794 402804 403097 403102) (-282 "ELAGG.spad" 400737 400747 402774 402789) (-281 "ELAGG.spad" 398617 398629 400656 400661) (-280 "ELABEXPR.spad" 397540 397548 398607 398612) (-279 "EFUPXS.spad" 394316 394346 397496 397501) (-278 "EFULS.spad" 391152 391175 394272 394277) (-277 "EFSTRUC.spad" 389107 389123 391142 391147) (-276 "EF.spad" 383873 383889 389097 389102) (-275 "EAB.spad" 382149 382157 383863 383868) (-274 "E04UCFA.spad" 381685 381693 382139 382144) (-273 "E04NAFA.spad" 381262 381270 381675 381680) (-272 "E04MBFA.spad" 380842 380850 381252 381257) (-271 "E04JAFA.spad" 380378 380386 380832 380837) (-270 "E04GCFA.spad" 379914 379922 380368 380373) (-269 "E04FDFA.spad" 379450 379458 379904 379909) (-268 "E04DGFA.spad" 378986 378994 379440 379445) (-267 "E04AGNT.spad" 374828 374836 378976 378981) (-266 "DVARCAT.spad" 371513 371523 374818 374823) (-265 "DVARCAT.spad" 368196 368208 371503 371508) (-264 "DSMP.spad" 365663 365677 365968 366095) (-263 "DROPT.spad" 359608 359616 365653 365658) (-262 "DROPT1.spad" 359271 359281 359598 359603) (-261 "DROPT0.spad" 354098 354106 359261 359266) (-260 "DRAWPT.spad" 352253 352261 354088 354093) (-259 "DRAW.spad" 344853 344866 352243 352248) (-258 "DRAWHACK.spad" 344161 344171 344843 344848) (-257 "DRAWCX.spad" 341603 341611 344151 344156) (-256 "DRAWCURV.spad" 341140 341155 341593 341598) (-255 "DRAWCFUN.spad" 330312 330320 341130 341135) (-254 "DQAGG.spad" 328480 328490 330280 330307) (-253 "DPOLCAT.spad" 323821 323837 328348 328475) (-252 "DPOLCAT.spad" 319248 319266 323777 323782) (-251 "DPMO.spad" 311474 311490 311612 311913) (-250 "DPMM.spad" 303713 303731 303838 304139) (-249 "DOMCTOR.spad" 303605 303613 303703 303708) (-248 "DOMAIN.spad" 302736 302744 303595 303600) (-247 "DMP.spad" 299994 300009 300566 300693) (-246 "DLP.spad" 299342 299352 299984 299989) (-245 "DLIST.spad" 297921 297931 298525 298552) (-244 "DLAGG.spad" 296332 296342 297911 297916) (-243 "DIVRING.spad" 295874 295882 296276 296327) (-242 "DIVRING.spad" 295460 295470 295864 295869) (-241 "DISPLAY.spad" 293640 293648 295450 295455) (-240 "DIRPROD.spad" 283220 283236 283860 283991) (-239 "DIRPROD2.spad" 282028 282046 283210 283215) (-238 "DIRPCAT.spad" 280970 280986 281892 282023) (-237 "DIRPCAT.spad" 279641 279659 280565 280570) (-236 "DIOSP.spad" 278466 278474 279631 279636) (-235 "DIOPS.spad" 277450 277460 278446 278461) (-234 "DIOPS.spad" 276408 276420 277406 277411) (-233 "DIFRING.spad" 275700 275708 276388 276403) (-232 "DIFRING.spad" 275000 275010 275690 275695) (-231 "DIFEXT.spad" 274159 274169 274980 274995) (-230 "DIFEXT.spad" 273235 273247 274058 274063) (-229 "DIAGG.spad" 272865 272875 273215 273230) (-228 "DIAGG.spad" 272503 272515 272855 272860) (-227 "DHMATRIX.spad" 270807 270817 271960 271987) (-226 "DFSFUN.spad" 264215 264223 270797 270802) (-225 "DFLOAT.spad" 260936 260944 264105 264210) (-224 "DFINTTLS.spad" 259145 259161 260926 260931) (-223 "DERHAM.spad" 257055 257087 259125 259140) (-222 "DEQUEUE.spad" 256373 256383 256662 256689) (-221 "DEGRED.spad" 255988 256002 256363 256368) (-220 "DEFINTRF.spad" 253513 253523 255978 255983) (-219 "DEFINTEF.spad" 252009 252025 253503 253508) (-218 "DEFAST.spad" 251377 251385 251999 252004) (-217 "DECIMAL.spad" 249483 249491 249844 249937) (-216 "DDFACT.spad" 247282 247299 249473 249478) (-215 "DBLRESP.spad" 246880 246904 247272 247277) (-214 "DBASE.spad" 245534 245544 246870 246875) (-213 "DATAARY.spad" 244996 245009 245524 245529) (-212 "D03FAFA.spad" 244824 244832 244986 244991) (-211 "D03EEFA.spad" 244644 244652 244814 244819) (-210 "D03AGNT.spad" 243724 243732 244634 244639) (-209 "D02EJFA.spad" 243186 243194 243714 243719) (-208 "D02CJFA.spad" 242664 242672 243176 243181) (-207 "D02BHFA.spad" 242154 242162 242654 242659) (-206 "D02BBFA.spad" 241644 241652 242144 242149) (-205 "D02AGNT.spad" 236448 236456 241634 241639) (-204 "D01WGTS.spad" 234767 234775 236438 236443) (-203 "D01TRNS.spad" 234744 234752 234757 234762) (-202 "D01GBFA.spad" 234266 234274 234734 234739) (-201 "D01FCFA.spad" 233788 233796 234256 234261) (-200 "D01ASFA.spad" 233256 233264 233778 233783) (-199 "D01AQFA.spad" 232702 232710 233246 233251) (-198 "D01APFA.spad" 232126 232134 232692 232697) (-197 "D01ANFA.spad" 231620 231628 232116 232121) (-196 "D01AMFA.spad" 231130 231138 231610 231615) (-195 "D01ALFA.spad" 230670 230678 231120 231125) (-194 "D01AKFA.spad" 230196 230204 230660 230665) (-193 "D01AJFA.spad" 229719 229727 230186 230191) (-192 "D01AGNT.spad" 225778 225786 229709 229714) (-191 "CYCLOTOM.spad" 225284 225292 225768 225773) (-190 "CYCLES.spad" 222116 222124 225274 225279) (-189 "CVMP.spad" 221533 221543 222106 222111) (-188 "CTRIGMNP.spad" 220023 220039 221523 221528) (-187 "CTOR.spad" 219714 219722 220013 220018) (-186 "CTORKIND.spad" 219317 219325 219704 219709) (-185 "CTORCAT.spad" 218566 218574 219307 219312) (-184 "CTORCAT.spad" 217813 217823 218556 218561) (-183 "CTORCALL.spad" 217393 217401 217803 217808) (-182 "CSTTOOLS.spad" 216636 216649 217383 217388) (-181 "CRFP.spad" 210340 210353 216626 216631) (-180 "CRCEAST.spad" 210060 210068 210330 210335) (-179 "CRAPACK.spad" 209103 209113 210050 210055) (-178 "CPMATCH.spad" 208603 208618 209028 209033) (-177 "CPIMA.spad" 208308 208327 208593 208598) (-176 "COORDSYS.spad" 203201 203211 208298 208303) (-175 "CONTOUR.spad" 202608 202616 203191 203196) (-174 "CONTFRAC.spad" 198220 198230 202510 202603) (-173 "CONDUIT.spad" 197978 197986 198210 198215) (-172 "COMRING.spad" 197652 197660 197916 197973) (-171 "COMPPROP.spad" 197166 197174 197642 197647) (-170 "COMPLPAT.spad" 196933 196948 197156 197161) (-169 "COMPLEX.spad" 191071 191081 191315 191576) (-168 "COMPLEX2.spad" 190784 190796 191061 191066) (-167 "COMPFACT.spad" 190386 190400 190774 190779) (-166 "COMPCAT.spad" 188454 188464 190120 190381) (-165 "COMPCAT.spad" 186251 186263 187919 187924) (-164 "COMMUPC.spad" 185997 186015 186241 186246) (-163 "COMMONOP.spad" 185530 185538 185987 185992) (-162 "COMM.spad" 185339 185347 185520 185525) (-161 "COMMAAST.spad" 185102 185110 185329 185334) (-160 "COMBOPC.spad" 184007 184015 185092 185097) (-159 "COMBINAT.spad" 182752 182762 183997 184002) (-158 "COMBF.spad" 180120 180136 182742 182747) (-157 "COLOR.spad" 178957 178965 180110 180115) (-156 "COLONAST.spad" 178623 178631 178947 178952) (-155 "CMPLXRT.spad" 178332 178349 178613 178618) (-154 "CLLCTAST.spad" 177994 178002 178322 178327) (-153 "CLIP.spad" 174086 174094 177984 177989) (-152 "CLIF.spad" 172725 172741 174042 174081) (-151 "CLAGG.spad" 169210 169220 172715 172720) (-150 "CLAGG.spad" 165566 165578 169073 169078) (-149 "CINTSLPE.spad" 164891 164904 165556 165561) (-148 "CHVAR.spad" 162969 162991 164881 164886) (-147 "CHARZ.spad" 162884 162892 162949 162964) (-146 "CHARPOL.spad" 162392 162402 162874 162879) (-145 "CHARNZ.spad" 162145 162153 162372 162387) (-144 "CHAR.spad" 160013 160021 162135 162140) (-143 "CFCAT.spad" 159329 159337 160003 160008) (-142 "CDEN.spad" 158487 158501 159319 159324) (-141 "CCLASS.spad" 156636 156644 157898 157937) (-140 "CATEGORY.spad" 155726 155734 156626 156631) (-139 "CATCTOR.spad" 155617 155625 155716 155721) (-138 "CATAST.spad" 155235 155243 155607 155612) (-137 "CASEAST.spad" 154949 154957 155225 155230) (-136 "CARTEN.spad" 150052 150076 154939 154944) (-135 "CARTEN2.spad" 149438 149465 150042 150047) (-134 "CARD.spad" 146727 146735 149412 149433) (-133 "CAPSLAST.spad" 146501 146509 146717 146722) (-132 "CACHSET.spad" 146123 146131 146491 146496) (-131 "CABMON.spad" 145676 145684 146113 146118) (-130 "BYTEORD.spad" 145351 145359 145666 145671) (-129 "BYTE.spad" 144776 144784 145341 145346) (-128 "BYTEBUF.spad" 142633 142641 143945 143972) (-127 "BTREE.spad" 141702 141712 142240 142267) (-126 "BTOURN.spad" 140705 140715 141309 141336) (-125 "BTCAT.spad" 140093 140103 140673 140700) (-124 "BTCAT.spad" 139501 139513 140083 140088) (-123 "BTAGG.spad" 138623 138631 139469 139496) (-122 "BTAGG.spad" 137765 137775 138613 138618) (-121 "BSTREE.spad" 136500 136510 137372 137399) (-120 "BRILL.spad" 134695 134706 136490 136495) (-119 "BRAGG.spad" 133619 133629 134685 134690) (-118 "BRAGG.spad" 132507 132519 133575 133580) (-117 "BPADICRT.spad" 130488 130500 130743 130836) (-116 "BPADIC.spad" 130152 130164 130414 130483) (-115 "BOUNDZRO.spad" 129808 129825 130142 130147) (-114 "BOP.spad" 124826 124834 129798 129803) (-113 "BOP1.spad" 122246 122256 124816 124821) (-112 "BOOLEAN.spad" 121678 121686 122236 122241) (-111 "BMODULE.spad" 121390 121402 121646 121673) (-110 "BITS.spad" 120809 120817 121026 121053) (-109 "BINDING.spad" 120220 120228 120799 120804) (-108 "BINARY.spad" 118331 118339 118687 118780) (-107 "BGAGG.spad" 117528 117538 118311 118326) (-106 "BGAGG.spad" 116733 116745 117518 117523) (-105 "BFUNCT.spad" 116297 116305 116713 116728) (-104 "BEZOUT.spad" 115431 115458 116247 116252) (-103 "BBTREE.spad" 112250 112260 115038 115065) (-102 "BASTYPE.spad" 111922 111930 112240 112245) (-101 "BASTYPE.spad" 111592 111602 111912 111917) (-100 "BALFACT.spad" 111031 111044 111582 111587) (-99 "AUTOMOR.spad" 110478 110487 111011 111026) (-98 "ATTREG.spad" 107197 107204 110230 110473) (-97 "ATTRBUT.spad" 103220 103227 107177 107192) (-96 "ATTRAST.spad" 102937 102944 103210 103215) (-95 "ATRIG.spad" 102407 102414 102927 102932) (-94 "ATRIG.spad" 101875 101884 102397 102402) (-93 "ASTCAT.spad" 101779 101786 101865 101870) (-92 "ASTCAT.spad" 101681 101690 101769 101774) (-91 "ASTACK.spad" 101014 101023 101288 101315) (-90 "ASSOCEQ.spad" 99814 99825 100970 100975) (-89 "ASP9.spad" 98895 98908 99804 99809) (-88 "ASP8.spad" 97938 97951 98885 98890) (-87 "ASP80.spad" 97260 97273 97928 97933) (-86 "ASP7.spad" 96420 96433 97250 97255) (-85 "ASP78.spad" 95871 95884 96410 96415) (-84 "ASP77.spad" 95240 95253 95861 95866) (-83 "ASP74.spad" 94332 94345 95230 95235) (-82 "ASP73.spad" 93603 93616 94322 94327) (-81 "ASP6.spad" 92470 92483 93593 93598) (-80 "ASP55.spad" 90979 90992 92460 92465) (-79 "ASP50.spad" 88796 88809 90969 90974) (-78 "ASP4.spad" 88091 88104 88786 88791) (-77 "ASP49.spad" 87090 87103 88081 88086) (-76 "ASP42.spad" 85497 85536 87080 87085) (-75 "ASP41.spad" 84076 84115 85487 85492) (-74 "ASP35.spad" 83064 83077 84066 84071) (-73 "ASP34.spad" 82365 82378 83054 83059) (-72 "ASP33.spad" 81925 81938 82355 82360) (-71 "ASP31.spad" 81065 81078 81915 81920) (-70 "ASP30.spad" 79957 79970 81055 81060) (-69 "ASP29.spad" 79423 79436 79947 79952) (-68 "ASP28.spad" 70696 70709 79413 79418) (-67 "ASP27.spad" 69593 69606 70686 70691) (-66 "ASP24.spad" 68680 68693 69583 69588) (-65 "ASP20.spad" 68144 68157 68670 68675) (-64 "ASP1.spad" 67525 67538 68134 68139) (-63 "ASP19.spad" 62211 62224 67515 67520) (-62 "ASP12.spad" 61625 61638 62201 62206) (-61 "ASP10.spad" 60896 60909 61615 61620) (-60 "ARRAY2.spad" 60256 60265 60503 60530) (-59 "ARRAY1.spad" 59091 59100 59439 59466) (-58 "ARRAY12.spad" 57760 57771 59081 59086) (-57 "ARR2CAT.spad" 53422 53443 57728 57755) (-56 "ARR2CAT.spad" 49104 49127 53412 53417) (-55 "ARITY.spad" 48476 48483 49094 49099) (-54 "APPRULE.spad" 47720 47742 48466 48471) (-53 "APPLYORE.spad" 47335 47348 47710 47715) (-52 "ANY.spad" 45677 45684 47325 47330) (-51 "ANY1.spad" 44748 44757 45667 45672) (-50 "ANTISYM.spad" 43187 43203 44728 44743) (-49 "ANON.spad" 42880 42887 43177 43182) (-48 "AN.spad" 41181 41188 42696 42789) (-47 "AMR.spad" 39360 39371 41079 41176) (-46 "AMR.spad" 37376 37389 39097 39102) (-45 "ALIST.spad" 34788 34809 35138 35165) (-44 "ALGSC.spad" 33911 33937 34660 34713) (-43 "ALGPKG.spad" 29620 29631 33867 33872) (-42 "ALGMFACT.spad" 28809 28823 29610 29615) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
-\ No newline at end of file
+((-3 NIL 2284116 2284121 2284126 2284131) (-2 NIL 2284096 2284101 2284106 2284111) (-1 NIL 2284076 2284081 2284086 2284091) (0 NIL 2284056 2284061 2284066 2284071) (-1290 "ZMOD.spad" 2283865 2283878 2283994 2284051) (-1289 "ZLINDEP.spad" 2282909 2282920 2283855 2283860) (-1288 "ZDSOLVE.spad" 2272758 2272780 2282899 2282904) (-1287 "YSTREAM.spad" 2272251 2272262 2272748 2272753) (-1286 "XRPOLY.spad" 2271471 2271491 2272107 2272176) (-1285 "XPR.spad" 2269262 2269275 2271189 2271288) (-1284 "XPOLY.spad" 2268817 2268828 2269118 2269187) (-1283 "XPOLYC.spad" 2268134 2268150 2268743 2268812) (-1282 "XPBWPOLY.spad" 2266571 2266591 2267914 2267983) (-1281 "XF.spad" 2265032 2265047 2266473 2266566) (-1280 "XF.spad" 2263473 2263490 2264916 2264921) (-1279 "XFALG.spad" 2260497 2260513 2263399 2263468) (-1278 "XEXPPKG.spad" 2259748 2259774 2260487 2260492) (-1277 "XDPOLY.spad" 2259362 2259378 2259604 2259673) (-1276 "XALG.spad" 2259022 2259033 2259318 2259357) (-1275 "WUTSET.spad" 2254861 2254878 2258668 2258695) (-1274 "WP.spad" 2254060 2254104 2254719 2254786) (-1273 "WHILEAST.spad" 2253858 2253867 2254050 2254055) (-1272 "WHEREAST.spad" 2253529 2253538 2253848 2253853) (-1271 "WFFINTBS.spad" 2251092 2251114 2253519 2253524) (-1270 "WEIER.spad" 2249306 2249317 2251082 2251087) (-1269 "VSPACE.spad" 2248979 2248990 2249274 2249301) (-1268 "VSPACE.spad" 2248672 2248685 2248969 2248974) (-1267 "VOID.spad" 2248349 2248358 2248662 2248667) (-1266 "VIEW.spad" 2245971 2245980 2248339 2248344) (-1265 "VIEWDEF.spad" 2241168 2241177 2245961 2245966) (-1264 "VIEW3D.spad" 2225003 2225012 2241158 2241163) (-1263 "VIEW2D.spad" 2212740 2212749 2224993 2224998) (-1262 "VECTOR.spad" 2211414 2211425 2211665 2211692) (-1261 "VECTOR2.spad" 2210041 2210054 2211404 2211409) (-1260 "VECTCAT.spad" 2207941 2207952 2210009 2210036) (-1259 "VECTCAT.spad" 2205648 2205661 2207718 2207723) (-1258 "VARIABLE.spad" 2205428 2205443 2205638 2205643) (-1257 "UTYPE.spad" 2205072 2205081 2205418 2205423) (-1256 "UTSODETL.spad" 2204365 2204389 2205028 2205033) (-1255 "UTSODE.spad" 2202553 2202573 2204355 2204360) (-1254 "UTS.spad" 2197342 2197370 2201020 2201117) (-1253 "UTSCAT.spad" 2194793 2194809 2197240 2197337) (-1252 "UTSCAT.spad" 2191888 2191906 2194337 2194342) (-1251 "UTS2.spad" 2191481 2191516 2191878 2191883) (-1250 "URAGG.spad" 2186113 2186124 2191471 2191476) (-1249 "URAGG.spad" 2180709 2180722 2186069 2186074) (-1248 "UPXSSING.spad" 2178352 2178378 2179790 2179923) (-1247 "UPXS.spad" 2175500 2175528 2176484 2176633) (-1246 "UPXSCONS.spad" 2173257 2173277 2173632 2173781) (-1245 "UPXSCCA.spad" 2171822 2171842 2173103 2173252) (-1244 "UPXSCCA.spad" 2170529 2170551 2171812 2171817) (-1243 "UPXSCAT.spad" 2169110 2169126 2170375 2170524) (-1242 "UPXS2.spad" 2168651 2168704 2169100 2169105) (-1241 "UPSQFREE.spad" 2167063 2167077 2168641 2168646) (-1240 "UPSCAT.spad" 2164656 2164680 2166961 2167058) (-1239 "UPSCAT.spad" 2161955 2161981 2164262 2164267) (-1238 "UPOLYC.spad" 2156933 2156944 2161797 2161950) (-1237 "UPOLYC.spad" 2151803 2151816 2156669 2156674) (-1236 "UPOLYC2.spad" 2151272 2151291 2151793 2151798) (-1235 "UP.spad" 2148465 2148480 2148858 2149011) (-1234 "UPMP.spad" 2147355 2147368 2148455 2148460) (-1233 "UPDIVP.spad" 2146918 2146932 2147345 2147350) (-1232 "UPDECOMP.spad" 2145155 2145169 2146908 2146913) (-1231 "UPCDEN.spad" 2144362 2144378 2145145 2145150) (-1230 "UP2.spad" 2143724 2143745 2144352 2144357) (-1229 "UNISEG.spad" 2143077 2143088 2143643 2143648) (-1228 "UNISEG2.spad" 2142570 2142583 2143033 2143038) (-1227 "UNIFACT.spad" 2141671 2141683 2142560 2142565) (-1226 "ULS.spad" 2132223 2132251 2133316 2133745) (-1225 "ULSCONS.spad" 2124617 2124637 2124989 2125138) (-1224 "ULSCCAT.spad" 2122346 2122366 2124463 2124612) (-1223 "ULSCCAT.spad" 2120183 2120205 2122302 2122307) (-1222 "ULSCAT.spad" 2118399 2118415 2120029 2120178) (-1221 "ULS2.spad" 2117911 2117964 2118389 2118394) (-1220 "UINT8.spad" 2117788 2117797 2117901 2117906) (-1219 "UINT64.spad" 2117664 2117673 2117778 2117783) (-1218 "UINT32.spad" 2117540 2117549 2117654 2117659) (-1217 "UINT16.spad" 2117416 2117425 2117530 2117535) (-1216 "UFD.spad" 2116481 2116490 2117342 2117411) (-1215 "UFD.spad" 2115608 2115619 2116471 2116476) (-1214 "UDVO.spad" 2114455 2114464 2115598 2115603) (-1213 "UDPO.spad" 2111882 2111893 2114411 2114416) (-1212 "TYPE.spad" 2111814 2111823 2111872 2111877) (-1211 "TYPEAST.spad" 2111733 2111742 2111804 2111809) (-1210 "TWOFACT.spad" 2110383 2110398 2111723 2111728) (-1209 "TUPLE.spad" 2109867 2109878 2110282 2110287) (-1208 "TUBETOOL.spad" 2106704 2106713 2109857 2109862) (-1207 "TUBE.spad" 2105345 2105362 2106694 2106699) (-1206 "TS.spad" 2103934 2103950 2104910 2105007) (-1205 "TSETCAT.spad" 2091061 2091078 2103902 2103929) (-1204 "TSETCAT.spad" 2078174 2078193 2091017 2091022) (-1203 "TRMANIP.spad" 2072540 2072557 2077880 2077885) (-1202 "TRIMAT.spad" 2071499 2071524 2072530 2072535) (-1201 "TRIGMNIP.spad" 2070016 2070033 2071489 2071494) (-1200 "TRIGCAT.spad" 2069528 2069537 2070006 2070011) (-1199 "TRIGCAT.spad" 2069038 2069049 2069518 2069523) (-1198 "TREE.spad" 2067609 2067620 2068645 2068672) (-1197 "TRANFUN.spad" 2067440 2067449 2067599 2067604) (-1196 "TRANFUN.spad" 2067269 2067280 2067430 2067435) (-1195 "TOPSP.spad" 2066943 2066952 2067259 2067264) (-1194 "TOOLSIGN.spad" 2066606 2066617 2066933 2066938) (-1193 "TEXTFILE.spad" 2065163 2065172 2066596 2066601) (-1192 "TEX.spad" 2062295 2062304 2065153 2065158) (-1191 "TEX1.spad" 2061851 2061862 2062285 2062290) (-1190 "TEMUTL.spad" 2061406 2061415 2061841 2061846) (-1189 "TBCMPPK.spad" 2059499 2059522 2061396 2061401) (-1188 "TBAGG.spad" 2058535 2058558 2059479 2059494) (-1187 "TBAGG.spad" 2057579 2057604 2058525 2058530) (-1186 "TANEXP.spad" 2056955 2056966 2057569 2057574) (-1185 "TABLE.spad" 2055366 2055389 2055636 2055663) (-1184 "TABLEAU.spad" 2054847 2054858 2055356 2055361) (-1183 "TABLBUMP.spad" 2051630 2051641 2054837 2054842) (-1182 "SYSTEM.spad" 2050858 2050867 2051620 2051625) (-1181 "SYSSOLP.spad" 2048331 2048342 2050848 2050853) (-1180 "SYSNNI.spad" 2047511 2047522 2048321 2048326) (-1179 "SYSINT.spad" 2046915 2046926 2047501 2047506) (-1178 "SYNTAX.spad" 2043109 2043118 2046905 2046910) (-1177 "SYMTAB.spad" 2041165 2041174 2043099 2043104) (-1176 "SYMS.spad" 2037150 2037159 2041155 2041160) (-1175 "SYMPOLY.spad" 2036157 2036168 2036239 2036366) (-1174 "SYMFUNC.spad" 2035632 2035643 2036147 2036152) (-1173 "SYMBOL.spad" 2033059 2033068 2035622 2035627) (-1172 "SWITCH.spad" 2029816 2029825 2033049 2033054) (-1171 "SUTS.spad" 2026715 2026743 2028283 2028380) (-1170 "SUPXS.spad" 2023850 2023878 2024847 2024996) (-1169 "SUP.spad" 2020655 2020666 2021436 2021589) (-1168 "SUPFRACF.spad" 2019760 2019778 2020645 2020650) (-1167 "SUP2.spad" 2019150 2019163 2019750 2019755) (-1166 "SUMRF.spad" 2018116 2018127 2019140 2019145) (-1165 "SUMFS.spad" 2017749 2017766 2018106 2018111) (-1164 "SULS.spad" 2008288 2008316 2009394 2009823) (-1163 "SUCHTAST.spad" 2008057 2008066 2008278 2008283) (-1162 "SUCH.spad" 2007737 2007752 2008047 2008052) (-1161 "SUBSPACE.spad" 1999744 1999759 2007727 2007732) (-1160 "SUBRESP.spad" 1998904 1998918 1999700 1999705) (-1159 "STTF.spad" 1995003 1995019 1998894 1998899) (-1158 "STTFNC.spad" 1991471 1991487 1994993 1994998) (-1157 "STTAYLOR.spad" 1983869 1983880 1991352 1991357) (-1156 "STRTBL.spad" 1982374 1982391 1982523 1982550) (-1155 "STRING.spad" 1981783 1981792 1981797 1981824) (-1154 "STRICAT.spad" 1981571 1981580 1981751 1981778) (-1153 "STREAM.spad" 1978429 1978440 1981096 1981111) (-1152 "STREAM3.spad" 1977974 1977989 1978419 1978424) (-1151 "STREAM2.spad" 1977042 1977055 1977964 1977969) (-1150 "STREAM1.spad" 1976746 1976757 1977032 1977037) (-1149 "STINPROD.spad" 1975652 1975668 1976736 1976741) (-1148 "STEP.spad" 1974853 1974862 1975642 1975647) (-1147 "STBL.spad" 1973379 1973407 1973546 1973561) (-1146 "STAGG.spad" 1972454 1972465 1973369 1973374) (-1145 "STAGG.spad" 1971527 1971540 1972444 1972449) (-1144 "STACK.spad" 1970878 1970889 1971134 1971161) (-1143 "SREGSET.spad" 1968582 1968599 1970524 1970551) (-1142 "SRDCMPK.spad" 1967127 1967147 1968572 1968577) (-1141 "SRAGG.spad" 1962224 1962233 1967095 1967122) (-1140 "SRAGG.spad" 1957341 1957352 1962214 1962219) (-1139 "SQMATRIX.spad" 1954957 1954975 1955873 1955960) (-1138 "SPLTREE.spad" 1949509 1949522 1954393 1954420) (-1137 "SPLNODE.spad" 1946097 1946110 1949499 1949504) (-1136 "SPFCAT.spad" 1944874 1944883 1946087 1946092) (-1135 "SPECOUT.spad" 1943424 1943433 1944864 1944869) (-1134 "SPADXPT.spad" 1935563 1935572 1943414 1943419) (-1133 "spad-parser.spad" 1935028 1935037 1935553 1935558) (-1132 "SPADAST.spad" 1934729 1934738 1935018 1935023) (-1131 "SPACEC.spad" 1918742 1918753 1934719 1934724) (-1130 "SPACE3.spad" 1918518 1918529 1918732 1918737) (-1129 "SORTPAK.spad" 1918063 1918076 1918474 1918479) (-1128 "SOLVETRA.spad" 1915820 1915831 1918053 1918058) (-1127 "SOLVESER.spad" 1914340 1914351 1915810 1915815) (-1126 "SOLVERAD.spad" 1910350 1910361 1914330 1914335) (-1125 "SOLVEFOR.spad" 1908770 1908788 1910340 1910345) (-1124 "SNTSCAT.spad" 1908370 1908387 1908738 1908765) (-1123 "SMTS.spad" 1906630 1906656 1907935 1908032) (-1122 "SMP.spad" 1904105 1904125 1904495 1904622) (-1121 "SMITH.spad" 1902948 1902973 1904095 1904100) (-1120 "SMATCAT.spad" 1901058 1901088 1902892 1902943) (-1119 "SMATCAT.spad" 1899100 1899132 1900936 1900941) (-1118 "SKAGG.spad" 1898061 1898072 1899068 1899095) (-1117 "SINT.spad" 1896887 1896896 1897927 1898056) (-1116 "SIMPAN.spad" 1896615 1896624 1896877 1896882) (-1115 "SIG.spad" 1895943 1895952 1896605 1896610) (-1114 "SIGNRF.spad" 1895051 1895062 1895933 1895938) (-1113 "SIGNEF.spad" 1894320 1894337 1895041 1895046) (-1112 "SIGAST.spad" 1893701 1893710 1894310 1894315) (-1111 "SHP.spad" 1891619 1891634 1893657 1893662) (-1110 "SHDP.spad" 1881330 1881357 1881839 1881970) (-1109 "SGROUP.spad" 1880938 1880947 1881320 1881325) (-1108 "SGROUP.spad" 1880544 1880555 1880928 1880933) (-1107 "SGCF.spad" 1873425 1873434 1880534 1880539) (-1106 "SFRTCAT.spad" 1872353 1872370 1873393 1873420) (-1105 "SFRGCD.spad" 1871416 1871436 1872343 1872348) (-1104 "SFQCMPK.spad" 1866053 1866073 1871406 1871411) (-1103 "SFORT.spad" 1865488 1865502 1866043 1866048) (-1102 "SEXOF.spad" 1865331 1865371 1865478 1865483) (-1101 "SEX.spad" 1865223 1865232 1865321 1865326) (-1100 "SEXCAT.spad" 1862774 1862814 1865213 1865218) (-1099 "SET.spad" 1861074 1861085 1862195 1862234) (-1098 "SETMN.spad" 1859508 1859525 1861064 1861069) (-1097 "SETCAT.spad" 1858830 1858839 1859498 1859503) (-1096 "SETCAT.spad" 1858150 1858161 1858820 1858825) (-1095 "SETAGG.spad" 1854671 1854682 1858130 1858145) (-1094 "SETAGG.spad" 1851200 1851213 1854661 1854666) (-1093 "SEQAST.spad" 1850903 1850912 1851190 1851195) (-1092 "SEGXCAT.spad" 1850025 1850038 1850893 1850898) (-1091 "SEG.spad" 1849838 1849849 1849944 1849949) (-1090 "SEGCAT.spad" 1848745 1848756 1849828 1849833) (-1089 "SEGBIND.spad" 1847817 1847828 1848700 1848705) (-1088 "SEGBIND2.spad" 1847513 1847526 1847807 1847812) (-1087 "SEGAST.spad" 1847227 1847236 1847503 1847508) (-1086 "SEG2.spad" 1846652 1846665 1847183 1847188) (-1085 "SDVAR.spad" 1845928 1845939 1846642 1846647) (-1084 "SDPOL.spad" 1843354 1843365 1843645 1843772) (-1083 "SCPKG.spad" 1841433 1841444 1843344 1843349) (-1082 "SCOPE.spad" 1840582 1840591 1841423 1841428) (-1081 "SCACHE.spad" 1839264 1839275 1840572 1840577) (-1080 "SASTCAT.spad" 1839173 1839182 1839254 1839259) (-1079 "SAOS.spad" 1839045 1839054 1839163 1839168) (-1078 "SAERFFC.spad" 1838758 1838778 1839035 1839040) (-1077 "SAE.spad" 1836933 1836949 1837544 1837679) (-1076 "SAEFACT.spad" 1836634 1836654 1836923 1836928) (-1075 "RURPK.spad" 1834275 1834291 1836624 1836629) (-1074 "RULESET.spad" 1833716 1833740 1834265 1834270) (-1073 "RULE.spad" 1831920 1831944 1833706 1833711) (-1072 "RULECOLD.spad" 1831772 1831785 1831910 1831915) (-1071 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1151906 1151916 1152029 1152056) (-733 "MRING.spad" 1148877 1148889 1151614 1151681) (-732 "MRF2.spad" 1148445 1148459 1148867 1148872) (-731 "MRATFAC.spad" 1147991 1148008 1148435 1148440) (-730 "MPRFF.spad" 1146021 1146040 1147981 1147986) (-729 "MPOLY.spad" 1143492 1143507 1143851 1143978) (-728 "MPCPF.spad" 1142756 1142775 1143482 1143487) (-727 "MPC3.spad" 1142571 1142611 1142746 1142751) (-726 "MPC2.spad" 1142213 1142246 1142561 1142566) (-725 "MONOTOOL.spad" 1140548 1140565 1142203 1142208) (-724 "MONOID.spad" 1139867 1139875 1140538 1140543) (-723 "MONOID.spad" 1139184 1139194 1139857 1139862) (-722 "MONOGEN.spad" 1137930 1137943 1139044 1139179) (-721 "MONOGEN.spad" 1136698 1136713 1137814 1137819) (-720 "MONADWU.spad" 1134712 1134720 1136688 1136693) (-719 "MONADWU.spad" 1132724 1132734 1134702 1134707) (-718 "MONAD.spad" 1131868 1131876 1132714 1132719) (-717 "MONAD.spad" 1131010 1131020 1131858 1131863) (-716 "MOEBIUS.spad" 1129696 1129710 1130990 1131005) (-715 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1113819) (-696 "MFINFACT.spad" 1111740 1111762 1112330 1112335) (-695 "MESH.spad" 1109472 1109480 1111730 1111735) (-694 "MDDFACT.spad" 1107665 1107675 1109462 1109467) (-693 "MDAGG.spad" 1106952 1106962 1107645 1107660) (-692 "MCMPLX.spad" 1102963 1102971 1103577 1103778) (-691 "MCDEN.spad" 1102171 1102183 1102953 1102958) (-690 "MCALCFN.spad" 1099273 1099299 1102161 1102166) (-689 "MAYBE.spad" 1098557 1098568 1099263 1099268) (-688 "MATSTOR.spad" 1095833 1095843 1098547 1098552) (-687 "MATRIX.spad" 1094537 1094547 1095021 1095048) (-686 "MATLIN.spad" 1091863 1091887 1094421 1094426) (-685 "MATCAT.spad" 1083448 1083470 1091831 1091858) (-684 "MATCAT.spad" 1074905 1074929 1083290 1083295) (-683 "MATCAT2.spad" 1074173 1074221 1074895 1074900) (-682 "MAPPKG3.spad" 1073072 1073086 1074163 1074168) (-681 "MAPPKG2.spad" 1072406 1072418 1073062 1073067) (-680 "MAPPKG1.spad" 1071224 1071234 1072396 1072401) (-679 "MAPPAST.spad" 1070537 1070545 1071214 1071219) (-678 "MAPHACK3.spad" 1070345 1070359 1070527 1070532) (-677 "MAPHACK2.spad" 1070110 1070122 1070335 1070340) (-676 "MAPHACK1.spad" 1069740 1069750 1070100 1070105) (-675 "MAGMA.spad" 1067530 1067547 1069730 1069735) (-674 "MACROAST.spad" 1067109 1067117 1067520 1067525) (-673 "M3D.spad" 1064805 1064815 1066487 1066492) (-672 "LZSTAGG.spad" 1062033 1062043 1064795 1064800) (-671 "LZSTAGG.spad" 1059259 1059271 1062023 1062028) (-670 "LWORD.spad" 1055964 1055981 1059249 1059254) (-669 "LSTAST.spad" 1055748 1055756 1055954 1055959) (-668 "LSQM.spad" 1053974 1053988 1054372 1054423) (-667 "LSPP.spad" 1053507 1053524 1053964 1053969) (-666 "LSMP.spad" 1052347 1052375 1053497 1053502) (-665 "LSMP1.spad" 1050151 1050165 1052337 1052342) (-664 "LSAGG.spad" 1049820 1049830 1050119 1050146) (-663 "LSAGG.spad" 1049509 1049521 1049810 1049815) (-662 "LPOLY.spad" 1048463 1048482 1049365 1049434) (-661 "LPEFRAC.spad" 1047720 1047730 1048453 1048458) (-660 "LO.spad" 1047121 1047135 1047654 1047681) (-659 "LOGIC.spad" 1046723 1046731 1047111 1047116) (-658 "LOGIC.spad" 1046323 1046333 1046713 1046718) (-657 "LODOOPS.spad" 1045241 1045253 1046313 1046318) (-656 "LODO.spad" 1044625 1044641 1044921 1044960) (-655 "LODOF.spad" 1043669 1043686 1044582 1044587) (-654 "LODOCAT.spad" 1042327 1042337 1043625 1043664) (-653 "LODOCAT.spad" 1040983 1040995 1042283 1042288) (-652 "LODO2.spad" 1040256 1040268 1040663 1040702) (-651 "LODO1.spad" 1039656 1039666 1039936 1039975) (-650 "LODEEF.spad" 1038428 1038446 1039646 1039651) (-649 "LNAGG.spad" 1034230 1034240 1038418 1038423) (-648 "LNAGG.spad" 1029996 1030008 1034186 1034191) (-647 "LMOPS.spad" 1026732 1026749 1029986 1029991) (-646 "LMODULE.spad" 1026500 1026510 1026722 1026727) (-645 "LMDICT.spad" 1025783 1025793 1026051 1026078) (-644 "LLINSET.spad" 1025180 1025190 1025773 1025778) (-643 "LITERAL.spad" 1025086 1025097 1025170 1025175) (-642 "LIST.spad" 1022804 1022814 1024233 1024260) (-641 "LIST3.spad" 1022095 1022109 1022794 1022799) (-640 "LIST2.spad" 1020735 1020747 1022085 1022090) (-639 "LIST2MAP.spad" 1017612 1017624 1020725 1020730) (-638 "LINSET.spad" 1017234 1017244 1017602 1017607) (-637 "LINEXP.spad" 1016666 1016676 1017214 1017229) (-636 "LINDEP.spad" 1015443 1015455 1016578 1016583) (-635 "LIMITRF.spad" 1013357 1013367 1015433 1015438) (-634 "LIMITPS.spad" 1012240 1012253 1013347 1013352) (-633 "LIE.spad" 1010254 1010266 1011530 1011675) (-632 "LIECAT.spad" 1009730 1009740 1010180 1010249) (-631 "LIECAT.spad" 1009234 1009246 1009686 1009691) (-630 "LIB.spad" 1007282 1007290 1007893 1007908) (-629 "LGROBP.spad" 1004635 1004654 1007272 1007277) (-628 "LF.spad" 1003554 1003570 1004625 1004630) (-627 "LFCAT.spad" 1002573 1002581 1003544 1003549) (-626 "LEXTRIPK.spad" 998076 998091 1002563 1002568) (-625 "LEXP.spad" 996079 996106 998056 998071) (-624 "LETAST.spad" 995778 995786 996069 996074) (-623 "LEADCDET.spad" 994162 994179 995768 995773) (-622 "LAZM3PK.spad" 992866 992888 994152 994157) (-621 "LAUPOL.spad" 991555 991568 992459 992528) (-620 "LAPLACE.spad" 991128 991144 991545 991550) (-619 "LA.spad" 990568 990582 991050 991089) (-618 "LALG.spad" 990344 990354 990548 990563) (-617 "LALG.spad" 990128 990140 990334 990339) (-616 "KVTFROM.spad" 989863 989873 990118 990123) (-615 "KTVLOGIC.spad" 989375 989383 989853 989858) (-614 "KRCFROM.spad" 989113 989123 989365 989370) (-613 "KOVACIC.spad" 987826 987843 989103 989108) (-612 "KONVERT.spad" 987548 987558 987816 987821) (-611 "KOERCE.spad" 987285 987295 987538 987543) (-610 "KERNEL.spad" 985820 985830 987069 987074) (-609 "KERNEL2.spad" 985523 985535 985810 985815) (-608 "KDAGG.spad" 984626 984648 985503 985518) (-607 "KDAGG.spad" 983737 983761 984616 984621) (-606 "KAFILE.spad" 982700 982716 982935 982962) (-605 "JORDAN.spad" 980527 980539 981990 982135) (-604 "JOINAST.spad" 980221 980229 980517 980522) (-603 "JAVACODE.spad" 980087 980095 980211 980216) (-602 "IXAGG.spad" 978210 978234 980077 980082) (-601 "IXAGG.spad" 976188 976214 978057 978062) (-600 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914168) (-559 "INTFTBL.spad" 901723 901731 907684 907689) (-558 "INTFACT.spad" 900782 900792 901713 901718) (-557 "INTEF.spad" 899097 899113 900772 900777) (-556 "INTDOM.spad" 897712 897720 899023 899092) (-555 "INTDOM.spad" 896389 896399 897702 897707) (-554 "INTCAT.spad" 894642 894652 896303 896384) (-553 "INTBIT.spad" 894145 894153 894632 894637) (-552 "INTALG.spad" 893327 893354 894135 894140) (-551 "INTAF.spad" 892819 892835 893317 893322) (-550 "INTABL.spad" 891337 891368 891500 891527) (-549 "INT8.spad" 891217 891225 891327 891332) (-548 "INT64.spad" 891096 891104 891207 891212) (-547 "INT32.spad" 890975 890983 891086 891091) (-546 "INT16.spad" 890854 890862 890965 890970) (-545 "INS.spad" 888321 888329 890756 890849) (-544 "INS.spad" 885874 885884 888311 888316) (-543 "INPSIGN.spad" 885308 885321 885864 885869) (-542 "INPRODPF.spad" 884374 884393 885298 885303) (-541 "INPRODFF.spad" 883432 883456 884364 884369) (-540 "INNMFACT.spad" 882403 882420 883422 883427) (-539 "INMODGCD.spad" 881887 881917 882393 882398) (-538 "INFSP.spad" 880172 880194 881877 881882) (-537 "INFPROD0.spad" 879222 879241 880162 880167) (-536 "INFORM.spad" 876383 876391 879212 879217) (-535 "INFORM1.spad" 876008 876018 876373 876378) (-534 "INFINITY.spad" 875560 875568 875998 876003) (-533 "INETCLTS.spad" 875537 875545 875550 875555) (-532 "INEP.spad" 874069 874091 875527 875532) (-531 "INDE.spad" 873798 873815 874059 874064) (-530 "INCRMAPS.spad" 873219 873229 873788 873793) (-529 "INBFILE.spad" 872291 872299 873209 873214) (-528 "INBFF.spad" 868061 868072 872281 872286) (-527 "INBCON.spad" 866349 866357 868051 868056) (-526 "INBCON.spad" 864635 864645 866339 866344) (-525 "INAST.spad" 864296 864304 864625 864630) (-524 "IMPTAST.spad" 864004 864012 864286 864291) (-523 "IMATRIX.spad" 862949 862975 863461 863488) (-522 "IMATQF.spad" 862043 862087 862905 862910) (-521 "IMATLIN.spad" 860648 860672 861999 862004) (-520 "ILIST.spad" 859304 859319 859831 859858) (-519 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836377 839473 839478) (-498 "IBACHIN.spad" 834845 834860 836348 836353) (-497 "IARRAY2.spad" 833833 833859 834452 834479) (-496 "IARRAY1.spad" 832878 832893 833016 833043) (-495 "IAN.spad" 831091 831099 832694 832787) (-494 "IALGFACT.spad" 830692 830725 831081 831086) (-493 "HYPCAT.spad" 830116 830124 830682 830687) (-492 "HYPCAT.spad" 829538 829548 830106 830111) (-491 "HOSTNAME.spad" 829346 829354 829528 829533) (-490 "HOMOTOP.spad" 829089 829099 829336 829341) (-489 "HOAGG.spad" 826357 826367 829079 829084) (-488 "HOAGG.spad" 823400 823412 826124 826129) (-487 "HEXADEC.spad" 821502 821510 821867 821960) (-486 "HEUGCD.spad" 820517 820528 821492 821497) (-485 "HELLFDIV.spad" 820107 820131 820507 820512) (-484 "HEAP.spad" 819499 819509 819714 819741) (-483 "HEADAST.spad" 819030 819038 819489 819494) (-482 "HDP.spad" 808873 808889 809250 809381) (-481 "HDMP.spad" 806085 806100 806703 806830) (-480 "HB.spad" 804322 804330 806075 806080) (-479 "HASHTBL.spad" 802792 802823 803003 803030) 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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 28532714..392259cf 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,599 +1,669 @@
 
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T) ((-897 . -309) 149563) ((-710 . -614) 149517) ((-343 . -1052) T) ((-642 . -490) 149498) ((-141 . -102) T) ((-44 . -131) T) ((-289 . -1106) T) ((-677 . -93) T) ((-672 . -93) T) ((-660 . -611) 149480) ((-642 . -611) 149433) ((-478 . -93) T) ((-355 . -611) 149415) ((-352 . -611) 149397) ((-344 . -611) 149379) ((-264 . -612) 149127) ((-264 . -611) 149109) ((-247 . -611) 149091) ((-247 . -612) 148952) ((-133 . -93) T) ((-138 . -93) T) ((-137 . -93) T) ((-1223 . -1034) 148918) ((-1203 . -514) 148885) ((-1135 . -611) 148867) ((-815 . -853) T) ((-815 . -722) T) ((-600 . -288) 148844) ((-581 . -713) 148809) ((-479 . -612) NIL) ((-479 . -611) 148791) ((-518 . -713) 148736) ((-316 . -102) T) ((-313 . -102) T) ((-289 . -23) T) ((-152 . -131) T) ((-906 . -611) 148718) ((-386 . -722) T) ((-868 . -1051) 148670) ((-906 . -612) 148652) ((-868 . -111) 148590) ((-710 . -1045) T) ((-708 . -1235) 148574) ((-139 . -102) T) ((-136 . -102) T) ((-114 . -102) T) ((-690 . -349) NIL) ((-519 . -611) 148506) 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146754) ((-481 . -722) T) ((-1244 . -896) 146660) ((-1243 . -1051) 146495) ((-1223 . -896) 146328) ((-1222 . -1051) 146136) ((-1203 . -290) 146115) ((-1179 . -1209) T) ((-1177 . -368) T) ((-1176 . -368) T) ((-1140 . -151) 146099) ((-1114 . -102) T) ((-1112 . -1094) T) ((-1074 . -23) T) ((-1069 . -102) T) ((-923 . -951) T) ((-733 . -309) 146037) ((-75 . -1209) T) ((-30 . -951) T) ((-169 . -905) 145990) ((-660 . -382) 145962) ((-112 . -840) T) ((-1 . -611) 145944) ((-1074 . -1106) T) ((-128 . -647) 145926) ((-50 . -618) 145910) ((-999 . -409) 145882) ((-594 . -896) 145795) ((-438 . -102) T) ((-141 . -309) NIL) ((-128 . -373) 145777) ((-868 . -1045) T) ((-829 . -846) 145756) ((-81 . -1209) T) ((-707 . -290) T) ((-40 . -1052) T) ((-581 . -172) T) ((-518 . -172) T) ((-511 . -611) 145738) ((-169 . -644) 145648) ((-507 . -611) 145630) ((-351 . -147) 145612) ((-351 . -145) T) ((-359 . -1106) T) ((-353 . -1106) T) ((-345 . -1106) T) ((-1000 . -307) T) ((-910 . -307) T) ((-868 . -243) T) ((-108 . -1106) T) ((-868 . -233) 145591) ((-1243 . -111) 145412) ((-1222 . -111) 145201) ((-245 . -1247) 145185) ((-564 . -844) T) ((-359 . -23) T) ((-354 . -349) T) ((-316 . -309) 145172) ((-313 . -309) 145113) ((-353 . -23) T) ((-319 . -131) T) ((-345 . -23) T) ((-1000 . -1018) T) ((-31 . -614) 145094) ((-108 . -23) T) ((-245 . -602) 145071) ((-1245 . -38) 144963) ((-1232 . -905) 144942) ((-112 . -1094) T) ((-1031 . -102) T) ((-1232 . -644) 144867) ((-867 . -790) NIL) ((-851 . -644) 144841) ((-867 . -787) NIL) ((-812 . -882) NIL) ((-867 . -722) T) ((-1081 . -514) 144714) ((-778 . -514) 144661) ((-776 . -514) 144613) ((-571 . -644) 144600) ((-812 . -1034) 144428) ((-454 . -514) 144371) ((-388 . -389) T) ((-1243 . -614) 144184) ((-1222 . -614) 143932) ((-60 . -1209) T) ((-619 . -846) 143911) ((-500 . -657) T) ((-1140 . -972) 143880) ((-999 . -452) T) ((-695 . -844) T) ((-510 . -788) T) ((-474 . -1051) 143715) ((-343 . -1094) T) ((-313 . -1145) NIL) ((-289 . -131) T) ((-394 . -1094) T) ((-690 . -370) 143682) ((-866 . -1052) T) ((-223 . -618) 143659) ((-327 . -286) 143636) ((-474 . -111) 143457) ((-1243 . -1045) T) ((-1222 . -1045) T) ((-812 . -377) 143441) ((-169 . -722) T) ((-650 . -102) T) ((-1243 . -243) 143420) ((-1243 . -233) 143372) ((-1222 . -233) 143277) ((-1222 . -243) 143256) ((-999 . -402) NIL) ((-666 . -637) 143204) ((-316 . -38) 143114) ((-313 . -38) 143043) ((-69 . -611) 143025) ((-319 . -493) 142991) ((-1182 . -288) 142970) ((-1217 . -846) T) ((-1107 . -1106) 142880) ((-83 . -1209) T) ((-61 . -611) 142862) ((-479 . -288) 142841) ((-1274 . -1034) 142818) ((-1158 . -1094) T) ((-1107 . -23) 142688) ((-812 . -896) 142624) ((-1232 . -722) T) ((-1096 . -1209) T) ((-474 . -614) 142450) ((-1081 . -290) 142381) ((-962 . -1094) T) ((-889 . -102) T) ((-778 . -290) 142292) ((-327 . -19) 142276) ((-59 . -288) 142253) ((-776 . -290) 142184) ((-851 . -722) T) ((-117 . -844) NIL) ((-516 . -288) 142161) ((-327 . -602) 142138) ((-496 . -288) 142115) ((-454 . -290) 142046) 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139292) ((-343 . -172) T) ((-152 . -25) T) ((-88 . -611) 139274) ((-152 . -21) T) ((-906 . -111) 139230) ((-40 . -713) 139175) ((-866 . -1094) T) ((-660 . -614) 139152) ((-642 . -614) 139133) ((-355 . -614) 139070) ((-352 . -614) 139007) ((-547 . -1094) T) ((-344 . -614) 138944) ((-327 . -612) 138905) ((-327 . -611) 138817) ((-264 . -614) 138570) ((-247 . -614) 138355) ((-1222 . -788) 138308) ((-1222 . -791) 138261) ((-251 . -377) 138230) ((-250 . -377) 138199) ((-650 . -38) 138169) ((-606 . -34) T) ((-482 . -1106) 138079) ((-475 . -34) T) ((-1107 . -131) 137949) ((-960 . -25) 137760) ((-906 . -614) 137710) ((-870 . -611) 137692) ((-960 . -21) 137647) ((-811 . -21) 137557) ((-811 . -25) 137408) ((-1215 . -368) T) ((-621 . -1052) T) ((-1172 . -556) 137387) ((-1166 . -47) 137364) ((-355 . -1045) T) ((-352 . -1045) T) ((-482 . -23) 137234) ((-344 . -1045) T) ((-247 . -1045) T) ((-264 . -1045) T) ((-1119 . -47) 137206) ((-117 . -1052) T) ((-1030 . -644) 137180) ((-954 . -34) T) ((-355 . 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136310) ((-129 . -846) T) ((-1166 . -1034) 136190) ((-1119 . -1034) 136073) ((-183 . -611) 136055) ((-850 . -1034) 135951) ((-778 . -286) 135878) ((-813 . -1106) T) ((-1030 . -722) T) ((-600 . -647) 135862) ((-1042 . -972) 135791) ((-995 . -102) T) ((-813 . -23) T) ((-708 . -1145) 135769) ((-690 . -1052) T) ((-600 . -373) 135753) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -722) T) ((-706 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 135735) ((-1166 . -377) 135719) ((-1119 . -377) 135703) ((-1020 . -411) 135665) ((-141 . -229) 135647) ((-379 . -790) T) ((-379 . -787) T) ((-866 . -172) T) ((-379 . -722) T) ((-707 . -611) 135629) ((-708 . -38) 135458) ((-1259 . -1257) 135442) ((-351 . -402) T) ((-1259 . -1094) 135392) ((-580 . -713) 135379) ((-564 . -713) 135366) ((-495 . -713) 135331) ((-316 . -627) 135310) ((-832 . -722) T) ((-823 . -722) T) ((-641 . -1209) T) ((-1074 . -637) 135258) ((-1166 . -896) 135201) ((-1119 . -896) 135185) ((-658 . -1051) 135169) ((-108 . -637) 135151) ((-482 . -131) 135021) ((-1172 . -1106) T) ((-948 . -47) 134990) ((-621 . -1094) T) ((-658 . -111) 134969) ((-491 . -611) 134935) ((-327 . -288) 134912) ((-481 . -47) 134869) ((-1172 . -23) T) ((-117 . -1094) T) ((-103 . -102) 134847) ((-1271 . -1106) T) ((-548 . -846) T) ((-1049 . -131) T) ((-1020 . -1052) T) ((-815 . -1034) 134831) ((-999 . -720) 134803) ((-1271 . -23) T) ((-695 . -713) 134768) ((-585 . -611) 134750) ((-386 . -1034) 134734) ((-354 . -1052) T) ((-385 . -131) T) ((-324 . -1034) 134718) ((-225 . -882) 134700) ((-1000 . -916) T) ((-91 . -34) T) ((-1000 . -816) T) ((-910 . -916) T) ((-1189 . -611) 134682) ((-1114 . -824) T) ((-487 . -1213) T) ((-1099 . -1094) T) ((-1074 . -21) T) ((-1074 . -25) T) ((-217 . -1213) T) ((-995 . -309) 134647) ((-225 . -1034) 134607) ((-40 . -290) T) ((-710 . -644) 134567) ((-677 . -614) 134548) ((-672 . -614) 134529) ((-487 . -556) T) ((-478 . -614) 134510) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -556) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -614) 134487) ((-138 . -614) 134468) ((-137 . -614) 134449) ((-133 . -614) 134430) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1052) T) ((-580 . -172) T) ((-564 . -172) T) ((-495 . -172) T) ((-654 . -611) 134412) ((-733 . -732) 134396) ((-336 . -611) 134378) ((-68 . -383) T) ((-68 . -395) T) ((-1096 . -107) 134362) ((-1056 . -882) 134344) ((-948 . -882) 134269) ((-649 . -1106) T) ((-621 . -713) 134256) ((-481 . -882) NIL) ((-1140 . -102) T) ((-1088 . -616) 134240) ((-1056 . -1034) 134222) ((-97 . -611) 134204) ((-477 . -147) T) ((-948 . -1034) 134084) ((-117 . -713) 134029) ((-649 . -23) T) ((-481 . -1034) 133905) ((-1081 . -612) NIL) ((-1081 . -611) 133887) ((-778 . -612) NIL) ((-778 . -611) 133848) ((-776 . -612) 133482) ((-776 . -611) 133396) ((-1107 . -637) 133302) ((-461 . -611) 133284) ((-454 . -611) 133266) ((-454 . -612) 133127) ((-1031 . -229) 133073) ((-868 . -905) 133052) ((-126 . -34) T) ((-813 . -131) T) ((-645 . -611) 133034) ((-578 . -102) T) ((-355 . -1278) 133018) ((-352 . -1278) 133002) ((-344 . -1278) 132986) ((-127 . -514) 132919) ((-121 . -514) 132852) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 132790) ((-222 . -102) 132768) ((-690 . -1094) T) ((-695 . -172) T) ((-868 . -644) 132720) ((-65 . -384) T) ((-275 . -611) 132702) ((-65 . -395) T) ((-948 . -377) 132686) ((-866 . -290) T) ((-50 . -611) 132668) ((-995 . -38) 132616) ((-581 . -611) 132598) ((-481 . -377) 132582) ((-581 . -612) 132564) ((-518 . -611) 132546) ((-906 . -1278) 132533) ((-867 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132499) ((-487 . -363) T) ((-355 . -368) 132478) ((-352 . -368) 132457) ((-344 . -368) 132436) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132420) ((-867 . -880) 132397) ((-867 . -882) NIL) ((-960 . -846) 132296) ((-811 . -846) 132247) ((-1216 . -102) T) ((-650 . -652) 132231) ((-1195 . -34) T) ((-171 . -611) 132213) ((-1107 . -21) 132123) ((-1107 . -25) 131974) ((-867 . -1034) 131951) ((-948 . -896) 131932) ((-1232 . -47) 131909) ((-906 . -368) T) ((-59 . -647) 131893) ((-516 . -647) 131877) ((-481 . -896) 131854) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 131838) ((-59 . -373) 131822) ((-621 . -172) T) ((-516 . -373) 131806) ((-496 . -373) 131790) ((-823 . -704) 131774) ((-1166 . -307) 131753) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 131691) ((-169 . -1209) T) ((-633 . -740) 131675) ((-605 . -740) 131659) ((-1271 . -131) T) ((-1244 . -916) 131638) ((-1223 . -916) 131617) ((-1223 . -816) NIL) ((-690 . -713) 131567) ((-1222 . -905) 131520) ((-1020 . -1094) T) ((-867 . -377) 131497) ((-867 . -338) 131474) ((-901 . -1106) T) ((-169 . -880) 131458) ((-169 . -882) 131383) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1034) 131279) ((-319 . -846) T) ((-1259 . -514) 131212) ((-1243 . 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. -1034) 114683) ((-117 . -111) 114612) ((-59 . -1209) T) ((-519 . -1209) T) ((-516 . -1209) T) ((-497 . -1209) T) ((-496 . -1209) T) ((-437 . -611) 114594) ((-434 . -611) 114576) ((-3 . -102) T) ((-1023 . -1202) 114545) ((-829 . -102) T) ((-685 . -57) 114503) ((-695 . -1045) T) ((-50 . -644) 114477) ((-289 . -452) T) ((-476 . -1202) 114446) ((0 . -102) T) ((-581 . -644) 114411) ((-518 . -644) 114356) ((-49 . -102) T) ((-906 . -1034) 114343) ((-695 . -243) T) ((-1074 . -409) 114322) ((-727 . -637) 114270) ((-995 . -1094) T) ((-708 . -172) 114161) ((-621 . -614) 114056) ((-487 . -988) 114038) ((-264 . -377) 114022) ((-247 . -377) 114006) ((-399 . -1094) T) ((-1022 . -102) 113984) ((-339 . -38) 113968) ((-217 . -988) 113950) ((-117 . -614) 113880) ((-174 . -38) 113812) ((-1243 . -307) 113791) ((-1222 . -307) 113770) ((-654 . -722) T) ((-99 . -611) 113752) ((-1161 . -637) 113704) ((-485 . -25) T) ((-485 . -21) T) ((-1222 . -1018) 113656) ((-621 . -1045) T) ((-379 . -404) T) ((-390 . -102) T) ((-1099 . -616) 113571) ((-264 . -896) 113517) ((-247 . -896) 113494) ((-117 . -1045) T) ((-812 . -1106) T) ((-1081 . -722) T) ((-621 . -233) 113473) ((-619 . -102) T) ((-778 . -722) T) ((-776 . -722) T) ((-413 . -1106) T) ((-117 . -243) T) ((-40 . -368) NIL) ((-117 . -233) NIL) ((-1214 . -846) T) ((-454 . -722) T) ((-812 . -23) T) ((-727 . -25) T) ((-727 . -21) T) ((-1071 . -286) 113452) ((-78 . -396) T) ((-78 . -395) T) ((-533 . -763) 113434) ((-690 . -1051) 113384) ((-1251 . -131) T) ((-1244 . -131) T) ((-1223 . -131) T) ((-1168 . -25) T) ((-1136 . -411) 113368) ((-633 . -367) 113300) ((-605 . -367) 113232) ((-1150 . -1143) 113216) ((-103 . -1094) 113194) ((-1168 . -21) T) ((-1167 . -21) T) ((-861 . -611) 113176) ((-995 . -713) 113124) ((-223 . -644) 113091) ((-690 . -111) 113025) ((-50 . -722) T) ((-1167 . -25) T) ((-351 . -349) T) ((-1161 . -21) T) ((-1074 . -452) 112976) ((-1161 . -25) T) ((-708 . -514) 112923) ((-581 . -722) T) ((-518 . -722) T) ((-1120 . -21) T) ((-1120 . 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-791) T) ((-695 . -788) T) ((-999 . -411) 111893) ((-354 . -111) 111822) ((-379 . -916) T) ((-407 . -844) 111801) ((-708 . -290) 111712) ((-223 . -722) T) ((-1251 . -493) 111678) ((-1244 . -493) 111644) ((-1223 . -493) 111610) ((-578 . -1094) T) ((-316 . -998) 111589) ((-222 . -1094) 111567) ((-1216 . -840) T) ((-319 . -969) 111529) ((-105 . -102) T) ((-48 . -1051) 111494) ((-1283 . -102) T) ((-381 . -102) T) ((-48 . -111) 111450) ((-1000 . -637) 111432) ((-1245 . -611) 111414) ((-531 . -102) T) ((-500 . -102) T) ((-1127 . -1128) 111398) ((-152 . -1266) 111382) ((-245 . -1209) T) ((-1208 . -102) T) ((-1020 . -614) 111319) ((-1166 . -1213) 111298) ((-354 . -614) 111228) ((-1119 . -1213) 111207) ((-240 . -21) 111117) ((-240 . -25) 110968) ((-127 . -119) 110952) ((-121 . -119) 110936) ((-44 . -740) 110920) ((-1166 . -556) 110831) ((-1119 . -556) 110762) ((-1216 . -1094) T) ((-1031 . -286) 110737) ((-1160 . -1077) T) ((-990 . -1077) T) ((-812 . -131) T) ((-117 . -791) NIL) ((-117 . -788) NIL) ((-355 . -307) T) ((-352 . -307) T) ((-344 . -307) T) ((-251 . -1106) 110647) ((-250 . -1106) 110557) ((-1020 . -1045) T) ((-999 . -1052) T) ((-48 . -614) 110490) ((-343 . -644) 110435) ((-619 . -38) 110419) ((-1272 . -611) 110381) ((-1272 . -612) 110342) ((-1071 . -611) 110324) ((-1020 . -243) T) ((-354 . -1045) T) ((-811 . -1266) 110294) ((-251 . -23) T) ((-250 . -23) T) ((-983 . -611) 110276) ((-733 . -612) 110237) ((-733 . -611) 110219) ((-795 . -846) 110198) ((-1153 . -151) 110145) ((-995 . -514) 110057) ((-354 . -233) T) ((-354 . -243) T) ((-388 . -614) 110038) ((-1000 . -25) T) ((-141 . -611) 110020) ((-141 . -612) 109979) ((-906 . -307) T) ((-1000 . -21) T) ((-967 . -25) T) ((-910 . -21) T) ((-910 . -25) T) ((-427 . -21) T) ((-427 . -25) T) ((-839 . -411) 109963) ((-48 . -1045) T) ((-1281 . -1273) 109947) ((-1279 . -1273) 109931) ((-1031 . -602) 109906) ((-316 . -612) 109767) ((-316 . -611) 109749) ((-313 . -612) NIL) ((-313 . -611) 109731) ((-48 . -243) T) ((-48 . -233) 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. -1106) T) ((-324 . -23) T) ((-1161 . -988) 107331) ((-839 . -1094) T) ((-1245 . -1051) 107236) ((-1120 . -736) 107215) ((-1243 . -916) 107194) ((-1222 . -916) 107173) ((-866 . -722) T) ((-169 . -556) 107084) ((-580 . -644) 107071) ((-564 . -644) 107058) ((-407 . -1094) T) ((-263 . -1094) T) ((-213 . -611) 107040) ((-495 . -644) 107005) ((-225 . -23) T) ((-1222 . -816) 106958) ((-1281 . -102) T) ((-354 . -1278) 106935) ((-1279 . -102) T) ((-1245 . -111) 106827) ((-144 . -611) 106809) ((-989 . -131) T) ((-44 . -102) T) ((-240 . -846) 106760) ((-1232 . -1213) 106739) ((-103 . -489) 106723) ((-1282 . -713) 106693) ((-1081 . -47) 106654) ((-1056 . -1106) T) ((-948 . -1106) T) ((-127 . -34) T) ((-121 . -34) T) ((-778 . -47) 106631) ((-776 . -47) 106603) ((-1232 . -556) 106514) ((-354 . -368) T) ((-481 . -1106) T) ((-1166 . -131) T) ((-1119 . -131) T) ((-454 . -47) 106493) ((-867 . -363) T) ((-850 . -131) T) ((-152 . -102) T) ((-1056 . -23) T) ((-948 . -23) T) ((-571 . -556) T) ((-812 . -25) T) ((-812 . -21) T) ((-1136 . -514) 106426) ((-591 . -1077) T) ((-585 . -1034) 106410) ((-1245 . -614) 106284) ((-481 . -23) T) ((-351 . -1052) T) ((-1203 . -896) 106265) ((-666 . -309) 106203) ((-1107 . -1266) 106173) ((-695 . -644) 106138) ((-999 . -172) T) ((-959 . -145) 106117) ((-633 . -1094) T) ((-605 . -1094) T) ((-959 . -147) 106096) ((-1000 . -846) T) ((-731 . -147) 106075) ((-731 . -145) 106054) ((-967 . -846) T) ((-474 . -916) 106033) ((-316 . -1051) 105943) ((-313 . -1051) 105872) ((-995 . -286) 105830) ((-407 . -713) 105782) ((-697 . -844) T) ((-1245 . -1045) T) ((-316 . -111) 105678) ((-313 . -111) 105591) ((-960 . -102) T) ((-811 . -102) 105381) ((-708 . -612) NIL) ((-708 . -611) 105363) ((-654 . -1034) 105259) ((-1245 . -326) 105203) ((-1031 . -288) 105178) ((-580 . -722) T) ((-564 . -790) T) ((-169 . -363) 105129) ((-564 . -787) T) ((-564 . -722) T) ((-495 . -722) T) ((-1140 . -489) 105113) ((-1081 . -882) NIL) ((-867 . -1106) T) ((-117 . -905) NIL) ((-1281 . -1280) 105089) ((-1279 . -1280) 105068) ((-778 . -882) NIL) ((-776 . -882) 104927) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 104905) ((-1100 . -395) T) ((-621 . -644) 104892) ((-454 . -882) NIL) ((-671 . -102) 104870) ((-1081 . -1034) 104697) ((-867 . -23) T) ((-778 . -1034) 104556) ((-776 . -1034) 104413) ((-117 . -644) 104358) ((-454 . -1034) 104234) ((-316 . -614) 103798) ((-313 . -614) 103681) ((-645 . -1034) 103665) ((-625 . -102) T) ((-222 . -489) 103649) ((-1259 . -34) T) ((-136 . -614) 103633) ((-633 . -713) 103617) ((-605 . -713) 103601) ((-666 . -38) 103561) ((-319 . -102) T) ((-85 . -611) 103543) ((-50 . -1034) 103527) ((-1114 . -1051) 103514) ((-1081 . -377) 103498) ((-778 . -377) 103482) ((-60 . -57) 103444) ((-695 . -790) T) ((-695 . -787) T) ((-581 . -1034) 103431) ((-518 . -1034) 103408) ((-695 . -722) T) ((-324 . -131) T) ((-316 . -1045) 103298) ((-313 . -1045) T) ((-169 . -1106) T) ((-776 . -377) 103282) ((-45 . -151) 103232) ((-1000 . -988) 103214) ((-454 . -377) 103198) ((-407 . -172) T) ((-316 . -243) 103177) ((-313 . -243) T) ((-313 . -233) NIL) ((-294 . -1094) 102959) ((-225 . -131) T) ((-1114 . -111) 102944) ((-169 . -23) T) ((-795 . -147) 102923) ((-795 . -145) 102902) ((-251 . -637) 102808) ((-250 . -637) 102714) ((-319 . -284) 102680) ((-1150 . -514) 102613) ((-1127 . -1094) T) ((-225 . -1054) T) ((-811 . -309) 102551) ((-1081 . -896) 102486) ((-778 . -896) 102429) ((-776 . -896) 102413) ((-1281 . -38) 102383) ((-1279 . -38) 102353) ((-1232 . -1106) T) ((-851 . -1106) T) ((-454 . -896) 102330) ((-854 . -1094) T) ((-1232 . -23) T) ((-1114 . -614) 102302) ((-571 . -1106) T) ((-851 . -23) T) ((-621 . -722) T) ((-355 . -916) T) ((-352 . -916) T) ((-289 . -102) T) ((-344 . -916) T) ((-1056 . -131) T) ((-966 . -1077) T) ((-948 . -131) T) ((-117 . -790) NIL) ((-117 . -787) NIL) ((-117 . -722) T) ((-690 . -905) NIL) ((-1042 . -514) 102203) ((-481 . -131) T) ((-571 . -23) T) ((-671 . -309) 102141) ((-633 . -757) T) ((-605 . -757) T) ((-1223 . -846) NIL) ((-999 . -290) T) ((-251 . -21) T) ((-690 . -644) 102091) ((-351 . -1094) T) ((-251 . -25) T) ((-250 . -21) T) ((-250 . -25) T) ((-152 . -38) 102075) ((-2 . -102) T) ((-906 . -916) T) ((-482 . -1266) 102045) ((-223 . -1034) 102022) ((-1114 . -1045) T) ((-707 . -307) T) ((-294 . -713) 101964) ((-697 . -1052) T) ((-487 . -452) T) ((-407 . -514) 101876) ((-217 . -452) T) ((-1114 . -233) T) ((-295 . -151) 101826) ((-995 . -612) 101787) ((-995 . -611) 101769) ((-985 . -611) 101751) ((-116 . -1052) T) ((-650 . -1051) 101735) ((-225 . -493) T) ((-399 . -611) 101717) ((-399 . -612) 101694) ((-1049 . -1266) 101664) ((-650 . -111) 101643) ((-1136 . -489) 101627) ((-811 . -38) 101597) ((-63 . -441) T) ((-63 . -395) T) ((-1153 . -102) T) ((-867 . -131) T) ((-484 . -102) 101575) ((-1287 . -368) T) ((-1074 . -102) T) ((-1055 . -102) T) ((-351 . -713) 101520) ((-727 . -147) 101499) ((-727 . -145) 101478) ((-650 . -614) 101396) ((-1020 . -644) 101333) ((-523 . -1094) 101311) 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-21) T) ((-778 . -307) 100396) ((-643 . -102) 100374) ((-630 . -102) T) ((-1153 . -309) 100169) ((-571 . -131) T) ((-619 . -844) 100148) ((-1150 . -489) 100132) ((-1144 . -151) 100082) ((-1140 . -611) 100044) ((-1140 . -612) 100005) ((-1020 . -787) T) ((-1020 . -790) T) ((-1020 . -722) T) ((-708 . -1051) 99828) ((-484 . -309) 99766) ((-453 . -417) 99736) ((-351 . -172) T) ((-289 . -38) 99723) ((-274 . -102) T) ((-273 . -102) T) ((-272 . -102) T) ((-271 . -102) T) ((-270 . -102) T) ((-269 . -102) T) ((-343 . -1034) 99700) ((-268 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-207 . -102) T) ((-206 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-194 . -102) T) ((-193 . -102) T) ((-354 . -722) T) ((-708 . -111) 99509) ((-666 . -231) 99493) ((-581 . -307) T) ((-518 . -307) T) ((-294 . -514) 99442) ((-108 . -309) NIL) ((-72 . -395) T) ((-1107 . -102) 99232) ((-829 . -411) 99216) ((-1114 . -791) T) ((-1114 . -788) T) ((-697 . -1094) T) ((-578 . -611) 99198) ((-379 . -363) T) ((-169 . -493) 99176) ((-222 . -611) 99108) ((-134 . -1094) T) ((-116 . -1094) T) ((-48 . -722) T) ((-1042 . -489) 99073) ((-141 . -425) 99055) ((-141 . -368) T) ((-1023 . -102) T) ((-512 . -509) 99034) ((-708 . -614) 98790) ((-476 . -102) T) ((-463 . -102) T) ((-1030 . -1106) T) ((-1216 . -611) 98772) ((-1175 . -1034) 98708) ((-1168 . -35) 98674) ((-1168 . -95) 98640) ((-1168 . -1197) 98606) ((-1168 . -1194) 98572) ((-1152 . -309) NIL) ((-89 . -396) T) ((-89 . -395) T) ((-1074 . -1145) 98551) ((-1167 . -1194) 98517) ((-1167 . -1197) 98483) ((-1030 . -23) T) ((-1167 . -95) 98449) ((-571 . -493) T) ((-1167 . -35) 98415) ((-1161 . -1194) 98381) ((-1161 . -1197) 98347) ((-1161 . -95) 98313) ((-361 . -1106) T) ((-359 . -1145) 98292) ((-353 . -1145) 98271) ((-345 . -1145) 98250) ((-1161 . -35) 98216) ((-1120 . -35) 98182) ((-1120 . -95) 98148) ((-108 . -1145) T) ((-1120 . -1197) 98114) ((-829 . -1052) 98093) ((-643 . -309) 98031) ((-630 . -309) 97882) ((-1120 . -1194) 97848) ((-708 . -1045) T) ((-1056 . -637) 97830) ((-1074 . -38) 97698) ((-948 . -637) 97646) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1106) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97625) ((-708 . -326) 97602) ((-481 . -637) 97550) ((-40 . -1034) 97438) ((-708 . -233) T) ((-697 . -713) 97425) ((-339 . -1094) T) ((-174 . -1094) T) ((-331 . -846) T) ((-418 . -452) 97375) ((-379 . -23) T) ((-359 . -38) 97340) ((-353 . -38) 97305) ((-345 . -38) 97270) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1106) T) ((-108 . -38) 97220) ((-823 . -1106) T) ((-770 . -1094) T) ((-116 . -713) 97207) ((-668 . -1034) 97191) ((-610 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1150 . -286) 97168) ((-1107 . -309) 97106) ((-1096 . -235) 97090) ((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97067) ((-96 . -102) T) ((-649 . -848) 97051) ((-1129 . -1077) T) ((-1056 . -21) T) ((-1056 . -25) T) ((-811 . -231) 97020) ((-948 . -25) T) ((-948 . -21) T) ((-619 . -1052) T) ((-1114 . -368) T) ((-481 . -25) T) ((-481 . -21) T) ((-1023 . -309) 96958) ((-885 . -611) 96940) ((-881 . -611) 96922) ((-251 . -846) 96873) ((-250 . -846) 96824) ((-523 . -514) 96757) ((-867 . -637) 96734) ((-476 . -309) 96672) ((-463 . -309) 96610) ((-351 . -290) T) ((-1150 . -1247) 96594) ((-1136 . -611) 96556) ((-1136 . -612) 96517) ((-1134 . -102) T) ((-995 . -1051) 96413) ((-40 . -896) 96365) ((-1150 . -602) 96342) ((-1287 . -644) 96329) ((-862 . -490) 96306) ((-1057 . -151) 96252) ((-868 . -1213) T) ((-995 . -111) 96134) ((-339 . -713) 96118) ((-862 . -611) 96080) ((-174 . -713) 96012) ((-407 . -286) 95970) ((-868 . -556) T) ((-108 . -400) 95952) ((-84 . -384) T) ((-84 . -395) T) ((-697 . -172) T) ((-615 . -611) 95934) ((-99 . -722) T) ((-482 . -102) 95724) ((-99 . -473) T) ((-116 . -172) T) ((-1107 . -38) 95694) 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-1034) 94786) ((-594 . -147) 94765) ((-594 . -145) 94744) ((-495 . -1034) 94687) ((-1129 . -1131) T) ((-87 . -384) T) ((-87 . -395) T) ((-868 . -363) T) ((-832 . -131) T) ((-823 . -131) T) ((-710 . -23) T) ((-506 . -611) 94653) ((-502 . -611) 94635) ((-1283 . -1052) T) ((-379 . -1054) T) ((-1022 . -1094) 94613) ((-55 . -1034) 94595) ((-897 . -34) T) ((-482 . -309) 94533) ((-591 . -102) T) ((-1150 . -612) 94494) ((-1150 . -611) 94426) ((-45 . -102) T) ((-813 . -102) T) ((-1232 . -25) T) ((-1232 . -21) T) ((-851 . -25) T) ((-44 . -367) 94410) ((-851 . -21) T) ((-727 . -452) 94361) ((-1282 . -611) 94343) ((-1049 . -309) 94281) ((-667 . -1077) T) ((-604 . -1077) T) ((-390 . -1094) T) ((-571 . -25) T) ((-571 . -21) T) ((-180 . -1077) T) ((-161 . -1077) T) ((-156 . -1077) T) ((-154 . -1077) T) ((-619 . -1094) T) ((-695 . -882) 94263) ((-1259 . -1209) T) ((-227 . -309) 94201) ((-144 . -368) T) ((-1042 . -612) 94143) ((-1042 . -611) 94086) ((-313 . -905) NIL) ((-1217 . -840) T) ((-695 . -1034) 94031) ((-707 . -916) T) ((-474 . -1213) 94010) ((-1167 . -452) 93989) ((-1161 . -452) 93968) ((-330 . -102) T) ((-868 . -1106) T) ((-316 . -644) 93789) ((-313 . -644) 93718) ((-474 . -556) 93669) ((-339 . -514) 93635) ((-550 . -151) 93585) ((-40 . -307) T) ((-839 . -611) 93567) ((-697 . -290) T) ((-868 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93537) ((-512 . -102) T) ((-407 . -612) 93344) ((-407 . -611) 93326) ((-263 . -611) 93308) ((-116 . -290) T) ((-1245 . -722) T) ((-1243 . -363) 93287) ((-1222 . -363) 93266) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93248) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93232) ((-733 . -34) T) ((-482 . -38) 93202) ((-141 . -34) T) ((-117 . -880) 93179) ((-117 . -882) NIL) ((-621 . -1034) 93062) ((-641 . -846) 93041) ((-1271 . -102) T) ((-295 . -102) T) ((-708 . -368) 93020) ((-117 . -1034) 92997) ((-390 . -713) 92981) ((-619 . -713) 92965) ((-45 . -309) 92769) ((-812 . -145) 92748) ((-812 . -147) 92727) 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-611) 91705) ((-966 . -102) T) ((-860 . -102) T) ((-621 . -896) 91664) ((-1283 . -1094) T) ((-381 . -1094) T) ((-82 . -1209) T) ((-1208 . -1094) T) ((-1056 . -846) T) ((-117 . -896) NIL) ((-778 . -916) 91643) ((-709 . -846) T) ((-531 . -1094) T) ((-500 . -1094) T) ((-355 . -1213) T) ((-352 . -1213) T) ((-344 . -1213) T) ((-264 . -1213) 91622) ((-247 . -1213) 91601) ((-533 . -856) T) ((-1107 . -231) 91570) ((-1152 . -824) T) ((-1136 . -1051) 91554) ((-390 . -757) T) ((-690 . -1209) T) ((-687 . -1034) 91538) ((-355 . -556) T) ((-352 . -556) T) ((-344 . -556) T) ((-264 . -556) 91469) ((-247 . -556) 91400) ((-525 . -1077) T) ((-1136 . -111) 91379) ((-453 . -740) 91349) ((-862 . -1051) 91319) ((-813 . -38) 91261) ((-690 . -880) 91243) ((-690 . -882) 91225) ((-295 . -309) 91029) ((-906 . -1213) T) ((-666 . -411) 91013) ((-862 . -111) 90978) ((-690 . -1034) 90923) ((-1000 . -452) T) ((-906 . -556) T) ((-533 . -611) 90905) ((-581 . -916) T) ((-474 . -1106) T) ((-518 . -916) T) ((-1150 . -288) 90882) ((-910 . -452) T) ((-65 . -611) 90864) ((-630 . -229) 90810) ((-474 . -23) T) ((-1114 . -790) T) ((-868 . -131) T) ((-1114 . -787) T) ((-1274 . -1276) 90789) ((-1114 . -722) T) ((-650 . -644) 90763) ((-294 . -611) 90504) ((-1136 . -614) 90422) ((-1031 . -34) T) ((-811 . -844) 90401) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -713) 90371) ((-690 . -377) 90353) ((-690 . -338) 90335) ((-477 . -172) T) ((-381 . -713) 90305) ((-862 . -614) 90240) ((-867 . -846) NIL) ((-564 . -1018) T) ((-495 . -1018) T) ((-1127 . -611) 90222) ((-1107 . -238) 90201) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90183) ((-1136 . -1045) T) ((-1172 . -38) 90080) ((-854 . -611) 90062) ((-564 . -545) T) ((-666 . -1052) T) ((-727 . -945) 90015) ((-1136 . -233) 89994) ((-1076 . -1094) T) ((-1030 . -25) T) ((-1030 . -21) T) ((-999 . -1051) 89939) ((-901 . -102) T) ((-862 . -1045) T) ((-690 . -896) NIL) ((-355 . -329) 89923) ((-355 . -363) T) ((-352 . -329) 89907) ((-352 . -363) T) 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-988) 89016) ((-819 . -102) T) ((-1282 . -111) 88995) ((-649 . -38) 88965) ((-571 . -846) T) ((-355 . -1106) T) ((-352 . -1106) T) ((-344 . -1106) T) ((-264 . -1106) T) ((-247 . -1106) T) ((-621 . -307) 88944) ((-1144 . -309) 88748) ((-524 . -1077) T) ((-311 . -1094) T) ((-660 . -23) T) ((-482 . -231) 88717) ((-152 . -1052) T) ((-355 . -23) T) ((-352 . -23) T) ((-344 . -23) T) ((-117 . -307) T) ((-264 . -23) T) ((-247 . -23) T) ((-999 . -1045) T) ((-708 . -905) 88696) ((-1150 . -614) 88673) ((-999 . -233) 88645) ((-999 . -243) T) ((-117 . -1018) NIL) ((-906 . -1106) T) ((-1244 . -452) 88624) ((-1223 . -452) 88603) ((-523 . -611) 88535) ((-708 . -644) 88460) ((-407 . -1051) 88412) ((-504 . -611) 88394) ((-906 . -23) T) ((-487 . -309) NIL) ((-1282 . -614) 88350) ((-474 . -131) T) ((-217 . -309) NIL) ((-407 . -111) 88288) ((-811 . -1052) 88218) ((-733 . -1092) 88202) ((-1243 . -493) 88168) ((-1222 . -493) 88134) ((-548 . -840) T) ((-141 . -1092) 88116) ((-477 . -290) T) ((-1282 . -1045) T) ((-1214 . -102) T) ((-1057 . -102) T) ((-839 . -614) 87984) ((-500 . -514) NIL) ((-482 . -238) 87963) ((-407 . -614) 87861) ((-1166 . -145) 87840) ((-1166 . -147) 87819) ((-1119 . -147) 87798) ((-1119 . -145) 87777) ((-633 . -1051) 87761) ((-605 . -1051) 87745) ((-1168 . -1250) 87729) ((-666 . -1094) T) ((-666 . -1048) 87669) ((-1168 . -1237) 87646) ((-548 . -1094) T) ((-487 . -1145) T) ((-1167 . -1242) 87607) ((-1167 . -1237) 87577) ((-1167 . -1240) 87561) ((-217 . -1145) T) ((-343 . -916) T) ((-814 . -266) 87545) ((-633 . -111) 87524) ((-605 . -111) 87503) ((-1161 . -1221) 87464) ((-839 . -1045) 87443) ((-1161 . -1237) 87420) ((-515 . -25) T) ((-495 . -302) T) ((-511 . -23) T) ((-510 . -25) T) ((-508 . -25) T) ((-507 . -23) T) ((-1161 . -1219) 87404) ((-407 . -1045) T) ((-319 . -1052) T) ((-690 . -307) T) ((-108 . -844) T) ((-708 . -722) T) ((-407 . -243) T) ((-407 . -233) 87383) ((-487 . -38) 87333) ((-217 . -38) 87283) ((-474 . -493) 87249) ((-1216 . -368) T) ((-1152 . -1138) T) 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86374) ((-1107 . -844) 86353) ((-770 . -611) 86335) ((-128 . -846) T) ((-606 . -235) 86282) ((-475 . -235) 86232) ((-1281 . -713) 86202) ((-48 . -307) T) ((-1279 . -713) 86172) ((-65 . -614) 86101) ((-960 . -1094) T) ((-811 . -1094) 85891) ((-312 . -102) T) ((-897 . -1209) T) ((-48 . -1018) T) ((-1222 . -637) 85799) ((-685 . -102) 85777) ((-44 . -713) 85761) ((-550 . -102) T) ((-294 . -614) 85692) ((-67 . -383) T) ((-67 . -395) T) ((-658 . -23) T) ((-666 . -757) T) ((-1206 . -1094) 85670) ((-351 . -1051) 85615) ((-671 . -1094) 85593) ((-1056 . -147) T) ((-948 . -147) 85572) ((-948 . -145) 85551) ((-795 . -102) T) ((-152 . -713) 85535) ((-481 . -147) 85514) ((-481 . -145) 85493) ((-351 . -111) 85422) ((-1074 . -1052) T) ((-322 . -846) 85401) ((-1251 . -969) 85370) ((-625 . -1094) T) ((-1244 . -969) 85332) ((-511 . -131) T) ((-507 . -131) T) ((-295 . -229) 85282) ((-359 . -1052) T) ((-353 . -1052) T) ((-345 . -1052) T) ((-294 . -1045) 85224) ((-1223 . -969) 85193) ((-379 . -846) T) ((-108 . -1052) T) ((-995 . -722) T) ((-866 . -916) T) ((-839 . -791) 85172) ((-839 . -788) 85151) ((-418 . -309) 85090) ((-468 . -102) T) ((-594 . -969) 85059) ((-319 . -1094) T) ((-407 . -791) 85038) ((-407 . -788) 85017) ((-500 . -489) 84999) ((-1245 . -1034) 84965) ((-1243 . -21) T) ((-1243 . -25) T) ((-1222 . -21) T) ((-1222 . -25) T) ((-811 . -713) 84907) ((-351 . -614) 84837) ((-695 . -404) T) ((-1272 . -1209) T) ((-604 . -102) T) ((-1107 . -411) 84806) ((-999 . -368) NIL) ((-667 . -102) T) ((-180 . -102) T) ((-161 . -102) T) ((-156 . -102) T) ((-154 . -102) T) ((-103 . -34) T) ((-733 . -1209) T) ((-44 . -757) T) ((-592 . -102) T) ((-77 . -396) T) ((-77 . -395) T) ((-649 . -652) 84790) ((-141 . -1209) T) ((-867 . -147) T) ((-867 . -145) NIL) ((-1208 . -93) T) ((-351 . -1045) T) ((-70 . -383) T) ((-70 . -395) T) ((-1159 . -102) T) ((-666 . -514) 84723) ((-685 . -309) 84661) ((-959 . -38) 84558) ((-731 . -38) 84528) ((-550 . -309) 84332) ((-316 . -1209) T) ((-351 . -233) T) ((-351 . -243) T) ((-313 . -1209) T) ((-289 . -1094) T) ((-1174 . -611) 84314) ((-707 . -1213) T) ((-1150 . -647) 84298) ((-1203 . -556) 84277) ((-707 . -556) T) ((-316 . -880) 84261) ((-316 . -882) 84186) ((-313 . -880) 84147) ((-313 . -882) NIL) ((-795 . -309) 84112) ((-319 . -713) 83953) ((-324 . -323) 83930) ((-485 . -102) T) ((-474 . -25) T) ((-474 . -21) T) ((-418 . -38) 83904) ((-316 . -1034) 83567) ((-225 . -1194) T) ((-225 . -1197) T) ((-3 . -611) 83549) ((-313 . -1034) 83479) ((-2 . -1094) T) ((-2 . |RecordCategory|) T) ((-829 . -611) 83461) ((-1107 . -1052) 83391) ((-580 . -916) T) ((-564 . -816) T) ((-564 . -916) T) ((-495 . -916) T) ((-136 . -1034) 83375) ((-225 . -95) T) ((-75 . -441) T) ((-75 . -395) T) ((0 . -611) 83357) ((-169 . -147) 83336) ((-169 . -145) 83287) ((-225 . -35) T) ((-49 . -611) 83269) ((-477 . -1052) T) ((-487 . -231) 83251) ((-484 . -964) 83235) ((-482 . -844) 83214) ((-217 . -231) 83196) ((-81 . -441) T) ((-81 . -395) T) ((-1140 . -34) T) ((-811 . -172) 83175) ((-727 . -102) T) ((-1022 . -611) 83142) ((-500 . -286) 83117) ((-316 . -377) 83086) ((-313 . -377) 83047) ((-313 . -338) 83008) ((-1079 . -611) 82990) ((-812 . -945) 82937) ((-658 . -131) T) ((-1232 . -145) 82916) ((-1232 . -147) 82895) ((-1168 . -102) T) ((-1167 . -102) T) ((-1161 . -102) T) ((-1153 . -1094) T) ((-1120 . -102) T) ((-222 . -34) T) ((-289 . -713) 82882) ((-1153 . -608) 82858) ((-592 . -309) NIL) ((-484 . -1094) 82836) ((-390 . -611) 82818) ((-510 . -846) T) ((-1144 . -229) 82768) ((-1251 . -1250) 82752) ((-1251 . -1237) 82729) ((-1244 . -1242) 82690) ((-1244 . -1237) 82660) ((-1244 . -1240) 82644) ((-1223 . -1221) 82605) ((-1223 . -1237) 82582) ((-619 . -611) 82564) ((-1223 . -1219) 82548) ((-695 . -916) T) ((-1168 . -284) 82514) ((-1167 . -284) 82480) ((-1161 . -284) 82446) ((-1074 . -1094) T) ((-1055 . -1094) T) ((-48 . -302) T) ((-316 . -896) 82412) ((-313 . -896) NIL) ((-1055 . -1062) 82391) ((-1114 . -882) 82373) ((-795 . -38) 82357) ((-264 . -637) 82305) 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81119) ((-398 . -611) 81101) ((-671 . -514) 81034) ((-660 . -25) T) ((-660 . -21) T) ((-454 . -556) 80965) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -916) T) ((-117 . -816) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -614) 80947) ((-116 . -614) 80919) ((-1261 . -611) 80901) ((-1215 . -846) T) ((-1203 . -1106) T) ((-1203 . -23) T) ((-1161 . -309) 80786) ((-1120 . -309) 80773) ((-1074 . -713) 80641) ((-862 . -644) 80601) ((-939 . -976) 80585) ((-906 . -21) T) ((-289 . -172) T) ((-906 . -25) T) ((-311 . -93) T) ((-868 . -846) 80536) ((-707 . -1106) T) ((-707 . -23) T) ((-697 . -1045) T) ((-643 . -1094) 80514) ((-630 . -1094) T) ((-581 . -1213) T) ((-518 . -1213) T) ((-697 . -233) T) ((-630 . -608) 80489) ((-581 . -556) T) ((-518 . -556) T) ((-359 . -713) 80441) ((-339 . -1051) 80425) ((-353 . -713) 80377) ((-345 . -713) 80329) ((-174 . -1051) 80261) 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. -309) 78968) ((-500 . -611) 78950) ((-500 . -612) 78932) ((-1208 . -611) 78898) ((-1161 . -1145) NIL) ((-1023 . -1065) 78867) ((-1023 . -1094) T) ((-1000 . -102) T) ((-967 . -102) T) ((-910 . -102) T) ((-889 . -1034) 78844) ((-1136 . -722) T) ((-999 . -644) 78789) ((-476 . -1094) T) ((-463 . -1094) T) ((-585 . -23) T) ((-571 . -35) T) ((-571 . -95) T) ((-427 . -102) T) ((-1057 . -229) 78735) ((-1168 . -38) 78632) ((-862 . -722) T) ((-690 . -916) T) ((-511 . -25) T) ((-507 . -21) T) ((-507 . -25) T) ((-1167 . -38) 78473) ((-339 . -1045) T) ((-1161 . -38) 78269) ((-1074 . -172) T) ((-174 . -1045) T) ((-1120 . -38) 78166) ((-708 . -47) 78143) ((-359 . -172) T) ((-353 . -172) T) ((-519 . -57) 78117) ((-497 . -57) 78067) ((-351 . -1278) 78044) ((-225 . -452) T) ((-319 . -290) 77995) ((-345 . -172) T) ((-174 . -243) T) ((-1222 . -846) 77894) ((-108 . -172) T) ((-868 . -988) 77878) ((-654 . -1106) T) ((-581 . -363) T) ((-581 . -329) 77865) ((-518 . -329) 77842) ((-518 . -363) T) ((-316 . -307) 77821) ((-313 . -307) T) ((-600 . -846) 77800) ((-1107 . -713) 77742) ((-520 . -282) 77726) ((-654 . -23) T) ((-418 . -231) 77710) ((-313 . -1018) NIL) ((-336 . -23) T) ((-103 . -1006) 77694) ((-45 . -36) 77673) ((-610 . -1094) T) ((-351 . -368) T) ((-524 . -102) T) ((-495 . -27) T) ((-240 . -309) 77611) ((-1081 . -1106) T) ((-1282 . -644) 77585) ((-778 . -1106) T) ((-776 . -1106) T) ((-454 . -1106) T) ((-1056 . -452) T) ((-948 . -452) 77536) ((-1109 . -1077) T) ((-110 . -1094) T) ((-1081 . -23) T) ((-813 . -1052) T) ((-778 . -23) T) ((-776 . -23) T) ((-481 . -452) 77487) ((-1153 . -514) 77270) ((-381 . -382) 77249) ((-1172 . -411) 77233) ((-461 . -23) T) ((-454 . -23) T) ((-96 . -1094) T) ((-484 . -514) 77166) ((-289 . -290) T) ((-1076 . -611) 77148) ((-1076 . -612) 77129) ((-407 . -905) 77108) ((-50 . -1106) T) ((-1020 . -916) T) ((-999 . -722) T) ((-708 . -882) NIL) ((-581 . -1106) T) ((-518 . -1106) T) ((-839 . -644) 77081) ((-1203 . -131) T) ((-1161 . -400) 77033) ((-1000 . -309) NIL) ((-811 . -489) 77017) ((-354 . -916) T) ((-1150 . -34) T) ((-407 . -644) 76969) ((-50 . -23) T) ((-707 . -131) T) ((-708 . -1034) 76849) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 76820) ((-1134 . -1094) T) ((-1274 . -1273) 76804) ((-697 . -791) T) ((-697 . -788) T) ((-1114 . -307) T) ((-379 . -147) T) ((-280 . -611) 76786) ((-1222 . -988) 76756) ((-48 . -916) T) ((-671 . -489) 76740) ((-251 . -1266) 76710) ((-250 . -1266) 76680) ((-1170 . -846) T) ((-1107 . -172) 76659) ((-1114 . -1018) T) ((-1042 . -34) T) ((-832 . -147) 76638) ((-832 . -145) 76617) ((-733 . -107) 76601) ((-610 . -132) T) ((-482 . -1094) 76391) ((-1172 . -1052) T) ((-867 . -452) T) ((-85 . -1209) T) ((-240 . -38) 76361) ((-141 . -107) 76343) ((-708 . -377) 76327) ((-829 . -614) 76195) ((-1114 . -545) T) ((-579 . -102) T) ((-129 . -490) 76177) ((-390 . -1051) 76161) ((-1282 . -722) T) ((-1166 . -945) 76130) ((-129 . -611) 76097) ((-52 . -611) 76079) ((-1119 . -945) 76046) ((-649 . -411) 76030) ((-1271 . -1052) T) ((-619 . -1051) 76014) ((-658 . -25) T) ((-658 . -21) T) ((-1152 . -514) NIL) ((-1251 . -102) T) ((-1244 . -102) T) ((-390 . -111) 75993) ((-222 . -254) 75977) ((-1223 . -102) T) ((-1049 . -1094) T) ((-1000 . -1145) T) ((-1049 . -1048) 75917) ((-814 . -1094) T) ((-343 . -1213) T) ((-633 . -644) 75901) ((-619 . -111) 75880) ((-605 . -644) 75864) ((-595 . -102) T) ((-311 . -490) 75845) ((-585 . -131) T) ((-594 . -102) T) ((-414 . -1094) T) ((-385 . -1094) T) ((-311 . -611) 75811) ((-227 . -1094) 75789) ((-643 . -514) 75722) ((-630 . -514) 75566) ((-829 . -1045) 75545) ((-641 . -151) 75529) ((-343 . -556) T) ((-708 . -896) 75472) ((-550 . -229) 75422) ((-1251 . -284) 75388) ((-1074 . -290) 75339) ((-487 . -844) T) ((-223 . -1106) T) ((-1244 . -284) 75305) ((-1223 . -284) 75271) ((-1000 . -38) 75221) ((-217 . -844) T) ((-1203 . -493) 75187) ((-910 . -38) 75139) ((-839 . -790) 75118) ((-839 . -787) 75097) ((-839 . -722) 75076) ((-359 . -290) T) ((-353 . -290) T) ((-345 . -290) T) ((-169 . -452) 75007) ((-427 . -38) 74991) ((-108 . -290) T) ((-223 . -23) T) ((-407 . -790) 74970) ((-407 . -787) 74949) ((-407 . -722) T) ((-500 . -288) 74924) ((-477 . -1051) 74889) ((-654 . -131) T) ((-619 . -614) 74858) ((-1107 . -514) 74791) ((-336 . -131) T) ((-169 . -402) 74770) ((-482 . -713) 74712) ((-811 . -286) 74689) ((-477 . -111) 74645) ((-649 . -1052) T) ((-1232 . -452) 74576) ((-1270 . -1077) T) ((-1269 . -1077) T) ((-1081 . -131) T) ((-1049 . -713) 74518) ((-778 . -131) T) ((-776 . -131) T) ((-571 . -452) T) ((-1023 . -514) 74451) ((-619 . -1045) T) ((-591 . -1094) T) ((-533 . -173) T) ((-461 . -131) T) ((-454 . -131) T) ((-45 . -1094) T) ((-385 . -713) 74421) ((-813 . -1094) T) ((-476 . -514) 74354) ((-463 . -514) 74287) ((-453 . -367) 74257) ((-45 . -608) 74236) ((-316 . -302) T) ((-477 . -614) 74186) ((-666 . -611) 74148) ((-59 . -846) 74127) ((-1223 . -309) 74012) ((-548 . -611) 73994) ((-1000 . -400) 73976) ((-811 . -602) 73953) ((-516 . -846) 73932) ((-496 . -846) 73911) ((-40 . -1213) T) ((-995 . -1034) 73807) ((-50 . -131) T) ((-581 . -131) T) ((-518 . -131) T) ((-294 . -644) 73667) ((-343 . -329) 73644) ((-343 . -363) T) ((-322 . -323) 73621) ((-319 . -286) 73606) ((-40 . -556) T) ((-379 . -1194) T) ((-379 . -1197) T) ((-1031 . -1185) 73581) ((-1182 . -235) 73531) ((-1161 . -231) 73483) ((-330 . -1094) T) ((-379 . -95) T) ((-379 . -35) T) ((-1031 . -107) 73429) ((-477 . -1045) T) ((-479 . -235) 73379) ((-1153 . -489) 73313) ((-1283 . -1051) 73297) ((-381 . -1051) 73281) ((-477 . -243) T) ((-812 . -102) T) ((-710 . -147) 73260) ((-710 . -145) 73239) ((-484 . -489) 73223) ((-485 . -335) 73192) ((-1283 . -111) 73171) ((-512 . -1094) T) ((-482 . -172) 73150) ((-995 . -377) 73134) ((-413 . -102) T) ((-381 . -111) 73113) ((-995 . -338) 73097) ((-279 . -979) 73081) ((-278 . -979) 73065) ((-1281 . -611) 73047) ((-1279 . -611) 73029) ((-110 . -514) NIL) ((-1166 . -1235) 73013) ((-850 . -848) 72997) ((-1172 . -1094) T) ((-103 . -1209) T) ((-948 . -945) 72958) ((-813 . -713) 72900) ((-1223 . -1145) NIL) ((-481 . -945) 72845) ((-1056 . -143) T) ((-60 . -102) 72823) ((-44 . -611) 72805) ((-78 . -611) 72787) ((-351 . -644) 72732) ((-1271 . -1094) T) ((-511 . -846) T) ((-343 . -1106) T) ((-295 . -1094) T) ((-995 . -896) 72691) ((-295 . -608) 72670) ((-1283 . -614) 72619) ((-1251 . -38) 72516) ((-1244 . -38) 72357) ((-1223 . -38) 72153) ((-487 . -1052) T) ((-381 . -614) 72137) ((-217 . -1052) T) ((-343 . -23) T) ((-152 . -611) 72119) ((-829 . -791) 72098) ((-829 . -788) 72077) ((-1208 . -614) 72058) ((-595 . -38) 72031) ((-594 . -38) 71928) ((-866 . -556) T) ((-223 . -131) T) ((-319 . -998) 71894) ((-79 . -611) 71876) ((-708 . -307) 71855) ((-294 . -722) 71757) ((-820 . -102) T) ((-860 . -840) T) ((-294 . -473) 71736) ((-1274 . -102) T) ((-40 . -363) T) ((-868 . -147) 71715) ((-868 . -145) 71694) ((-1152 . -489) 71676) ((-1283 . -1045) T) ((-482 . -514) 71609) ((-1140 . -1209) T) ((-960 . -611) 71591) ((-643 . -489) 71575) ((-630 . -489) 71506) ((-811 . -611) 71237) ((-48 . -27) T) ((-1172 . -713) 71134) ((-649 . -1094) T) ((-857 . -856) T) ((-436 . -364) 71108) ((-1096 . -102) T) ((-966 . -1094) T) ((-860 . -1094) T) ((-812 . -309) 71095) ((-533 . -527) T) ((-533 . -576) T) ((-1279 . -382) 71067) ((-1049 . -514) 71000) ((-1153 . -286) 70976) ((-240 . -231) 70945) ((-1271 . -713) 70915) ((-1160 . -93) T) ((-990 . -93) T) ((-813 . -172) 70894) ((-1206 . -490) 70871) ((-227 . -514) 70804) ((-619 . -791) 70783) ((-619 . -788) 70762) ((-1206 . -611) 70674) ((-222 . -1209) T) ((-671 . -611) 70606) ((-1150 . -1006) 70590) ((-939 . -102) 70540) ((-351 . -722) T) ((-857 . -611) 70522) ((-1223 . -400) 70474) ((-1107 . -489) 70458) ((-60 . -309) 70396) ((-331 . -102) T) ((-1203 . -21) T) ((-1203 . -25) T) ((-40 . -1106) T) ((-707 . -21) T) ((-625 . -611) 70378) ((-515 . -323) 70357) ((-707 . -25) T) ((-439 . -102) T) ((-108 . -286) NIL) ((-917 . -1106) T) ((-40 . -23) T) ((-767 . -1106) T) ((-564 . -1213) T) ((-495 . -1213) T) ((-319 . -611) 70339) ((-1000 . -231) 70321) ((-169 . -166) 70305) ((-580 . -556) T) ((-564 . -556) T) ((-495 . -556) T) ((-767 . -23) T) ((-1243 . -147) 70284) ((-1153 . -602) 70260) ((-1243 . -145) 70239) ((-1023 . -489) 70223) ((-1222 . -145) 70148) ((-1222 . -147) 70073) ((-1274 . -1280) 70052) ((-476 . -489) 70036) ((-463 . -489) 70020) ((-523 . -34) T) ((-649 . -713) 69990) ((-112 . -963) T) ((-658 . -846) 69969) ((-1172 . -172) 69920) ((-365 . -102) T) ((-240 . -238) 69899) ((-251 . -102) T) ((-250 . -102) T) ((-1232 . -945) 69868) ((-245 . -846) 69847) ((-812 . -38) 69696) ((-45 . -514) 69488) ((-1152 . -286) 69463) ((-214 . -1094) T) ((-1144 . -1094) T) ((-1144 . -608) 69442) ((-585 . -25) T) ((-585 . -21) T) ((-1096 . -309) 69380) ((-959 . -411) 69364) ((-695 . -1213) T) ((-630 . -286) 69339) ((-1081 . -637) 69287) ((-778 . -637) 69235) ((-776 . -637) 69183) ((-343 . -131) T) ((-289 . -611) 69165) ((-901 . -1094) T) ((-695 . -556) T) ((-129 . -614) 69147) ((-866 . -1106) T) ((-454 . -637) 69095) ((-901 . -899) 69079) ((-379 . -452) T) ((-487 . -1094) T) ((-939 . -309) 69017) ((-697 . -644) 69004) ((-549 . -840) T) ((-217 . -1094) T) ((-316 . -916) 68983) ((-313 . -916) T) ((-313 . -816) NIL) ((-390 . -716) T) ((-866 . -23) T) ((-116 . -644) 68970) ((-474 . -145) 68949) ((-418 . -411) 68933) ((-474 . -147) 68912) ((-110 . -489) 68894) ((-311 . -614) 68875) ((-2 . -611) 68857) ((-186 . -102) T) ((-1152 . -19) 68839) ((-1152 . -602) 68814) ((-654 . -21) T) ((-654 . -25) T) ((-592 . -1138) T) ((-1107 . -286) 68791) ((-336 . -25) T) ((-336 . -21) T) ((-495 . -363) T) ((-1274 . -38) 68761) ((-1136 . -1209) T) ((-630 . -602) 68736) ((-549 . -1094) T) ((-1081 . -25) T) ((-1081 . -21) T) ((-531 . -788) T) ((-531 . -791) T) ((-117 . -1213) T) ((-959 . -1052) T) ((-621 . -556) T) ((-778 . -25) T) ((-778 . -21) T) ((-776 . -21) T) ((-776 . -25) T) ((-731 . -1052) T) ((-711 . -1052) T) ((-666 . -1051) 68720) ((-517 . -1077) T) ((-461 . -25) T) ((-117 . -556) T) ((-461 . -21) T) ((-454 . -25) T) ((-454 . -21) T) ((-1281 . -1051) 68704) ((-1136 . -1034) 68600) ((-813 . -290) 68579) ((-1279 . -1051) 68563) ((-819 . -1094) T) ((-1243 . -1194) 68529) ((-962 . -963) T) ((-666 . -111) 68508) ((-295 . -514) 68300) ((-1243 . -1197) 68266) ((-1243 . -95) 68232) ((-1226 . -102) 68210) ((-251 . -309) 68148) ((-250 . -309) 68086) ((-1223 . -231) 68038) ((-1153 . -612) NIL) ((-1153 . -611) 68020) ((-1222 . -1194) 67986) ((-1222 . -1197) 67952) ((-1217 . -368) T) ((-96 . -93) T) ((-1214 . -840) T) ((-1136 . -377) 67936) ((-1114 . -816) T) ((-1114 . -916) T) ((-1107 . -602) 67913) ((-1074 . -612) 67897) ((-484 . -611) 67829) ((-811 . -288) 67806) ((-606 . -151) 67753) ((-418 . -1052) T) ((-487 . -713) 67703) ((-482 . -489) 67687) ((-327 . -846) 67666) ((-339 . -644) 67640) ((-50 . -21) T) ((-50 . -25) T) ((-217 . -713) 67590) ((-169 . -720) 67561) ((-174 . -644) 67493) ((-581 . -21) T) ((-581 . -25) T) ((-518 . -25) T) ((-518 . -21) T) ((-475 . -151) 67443) ((-1074 . -611) 67425) ((-1055 . -611) 67407) ((-989 . -102) T) ((-858 . -102) T) ((-795 . -411) 67371) ((-40 . -131) T) ((-695 . -363) T) ((-697 . -722) T) ((-697 . -790) T) ((-697 . -787) T) ((-212 . -891) T) ((-580 . -1106) T) ((-564 . -1106) T) ((-495 . -1106) T) ((-359 . -611) 67353) ((-353 . -611) 67335) ((-345 . -611) 67317) ((-66 . -396) T) ((-66 . -395) T) ((-108 . -612) 67247) ((-108 . -611) 67189) ((-211 . -891) T) ((-954 . -151) 67173) ((-767 . -131) T) ((-666 . -614) 67091) ((-134 . -722) T) ((-116 . -722) T) ((-1243 . -35) 67057) ((-1049 . -489) 67041) ((-580 . -23) T) ((-564 . -23) T) ((-495 . -23) T) ((-1222 . -95) 67007) ((-1222 . -35) 66973) ((-1166 . -102) T) ((-1119 . -102) T) ((-850 . -102) T) ((-227 . -489) 66957) ((-1281 . -111) 66936) ((-1279 . -111) 66915) ((-44 . -1051) 66899) ((-1232 . -1235) 66883) ((-851 . -848) 66867) ((-1172 . -290) 66846) ((-110 . -286) 66821) ((-1281 . -614) 66767) ((-128 . -151) 66749) ((-1136 . 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-\ No newline at end of file
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-514) 154599) ((-1246 . -646) 154496) ((-1225 . -646) 154366) ((-870 . -792) 154345) ((-870 . -789) 154324) ((-870 . -724) T) ((-487 . -23) T) ((-223 . -611) 154306) ((-174 . -452) T) ((-222 . -309) 154244) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1286 . -1279) 154223) ((-675 . -1036) 154207) ((-580 . -290) T) ((-564 . -290) T) ((-495 . -290) T) ((-136 . -470) 154162) ((-652 . -644) 154121) ((-48 . -1097) T) ((-710 . -231) 154105) ((-869 . -898) NIL) ((-1235 . -884) NIL) ((-887 . -102) T) ((-883 . -102) T) ((-388 . -1097) T) ((-169 . -377) 154089) ((-169 . -338) 154073) ((-1235 . -1036) 153953) ((-853 . -1036) 153849) ((-1139 . -102) T) ((-651 . -131) T) ((-117 . -514) 153757) ((-660 . -790) 153736) ((-660 . -793) 153715) ((-571 . -1036) 153697) ((-294 . -1269) 153667) ((-864 . -102) T) ((-961 . -556) 153646) ((-1206 . -1054) 153529) ((-1001 . -1049) 153474) ((-482 . -637) 153380) ((-902 . -1097) T) ((-1022 . -715) 153317) ((-709 . -1054) 153282) ((-1001 . -638) 153227) 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149299) ((-518 . -1054) 149244) ((-227 . -57) 149202) ((-453 . -23) T) ((-407 . -102) T) ((-263 . -102) T) ((-692 . -290) T) ((-864 . -38) 149172) ((-581 . -111) 149128) ((-518 . -111) 149057) ((-1084 . -614) 148793) ((-418 . -1109) T) ((-316 . -1055) 148683) ((-313 . -1055) T) ((-128 . -1212) T) ((-780 . -614) 148431) ((-778 . -614) 148197) ((-656 . -1047) T) ((-1290 . -1097) T) ((-454 . -614) 147982) ((-169 . -307) 147913) ((-418 . -23) T) ((-40 . -611) 147895) ((-40 . -612) 147879) ((-108 . -990) 147861) ((-116 . -867) 147845) ((-647 . -614) 147829) ((-48 . -514) 147795) ((-1198 . -1008) 147779) ((-1178 . -611) 147746) ((-1185 . -34) T) ((-952 . -611) 147712) ((-919 . -611) 147694) ((-1110 . -848) 147645) ((-769 . -611) 147627) ((-670 . -611) 147609) ((-1153 . -309) 147547) ((-479 . -34) T) ((-1089 . -1212) T) ((-477 . -452) T) ((-1138 . -34) T) ((-1084 . -1047) T) ((-50 . -614) 147516) ((-780 . -1047) T) ((-778 . -1047) T) ((-645 . -235) 147500) ((-630 . -235) 147446) ((-581 . 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. -724) T) ((-581 . -243) T) ((-581 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1123 . -556) 146573) ((-354 . -290) T) ((-645 . -693) 146557) ((-379 . -1036) 146517) ((-294 . -1049) 146438) ((-1117 . -1055) T) ((-103 . -125) 146422) ((-294 . -638) 146364) ((-797 . -23) T) ((-1284 . -1279) 146340) ((-1262 . -286) 146317) ((-407 . -309) 146282) ((-1282 . -1279) 146261) ((-1248 . -1097) T) ((-868 . -611) 146243) ((-834 . -1036) 146212) ((-203 . -785) T) ((-202 . -785) T) ((-201 . -785) T) ((-200 . -785) T) ((-199 . -785) T) ((-198 . -785) T) ((-197 . -785) T) ((-196 . -785) T) ((-195 . -785) T) ((-194 . -785) T) ((-547 . -611) 146194) ((-495 . -1000) T) ((-274 . -837) T) ((-273 . -837) T) ((-272 . -837) T) ((-271 . -837) T) ((-48 . -290) T) ((-270 . -837) T) ((-269 . -837) T) ((-268 . -837) T) ((-193 . -785) T) ((-610 . -848) T) ((-652 . -411) 146178) ((-223 . -614) 146140) ((-110 . -848) T) ((-651 . -21) T) ((-651 . -25) T) ((-1285 . -38) 146110) ((-117 . -286) 146061) ((-1262 . -19) 146045) ((-1262 . -602) 146022) ((-1275 . -1097) T) ((-351 . -1049) 145967) ((-1074 . -1097) T) ((-985 . -1097) T) ((-961 . -131) T) ((-735 . -1097) T) ((-351 . -638) 145912) ((-733 . -131) T) ((-713 . -131) T) ((-511 . -791) T) ((-511 . -792) T) ((-453 . -131) T) ((-407 . -1148) 145890) ((-223 . -1047) T) ((-294 . -102) 145672) ((-141 . -1097) T) ((-697 . -1000) T) ((-91 . -1212) T) ((-127 . -611) 145604) ((-121 . -611) 145536) ((-1290 . -172) T) ((-1170 . -363) 145515) ((-1164 . -363) 145494) ((-316 . -1097) T) ((-418 . -131) T) ((-313 . -1097) T) ((-407 . -38) 145446) ((-1130 . -102) T) ((-1248 . -715) 145338) ((-652 . -1055) T) ((-1132 . -1257) T) ((-319 . -145) 145317) ((-319 . -147) 145296) ((-136 . -1097) T) ((-139 . -1097) T) ((-114 . -1097) T) ((-856 . -102) T) ((-580 . -611) 145278) ((-564 . -612) 145177) ((-564 . -611) 145159) ((-495 . -611) 145141) ((-495 . -612) 145086) ((-485 . -23) T) ((-482 . -848) 145037) ((-487 . -637) 145019) ((-963 . -611) 145001) ((-217 . 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. -1049) 141312) ((-474 . -47) 141282) ((-134 . -102) T) ((-40 . -233) 141254) ((-40 . -243) T) ((-116 . -102) T) ((-594 . -556) 141233) ((-339 . -638) 141217) ((-692 . -612) 141125) ((-316 . -514) 141091) ((-174 . -638) 141023) ((-313 . -514) 140915) ((-1246 . -1036) 140899) ((-1225 . -1036) 140685) ((-997 . -411) 140669) ((-427 . -23) T) ((-1117 . -172) T) ((-1248 . -290) T) ((-652 . -715) 140639) ((-144 . -1097) T) ((-48 . -1000) T) ((-407 . -231) 140623) ((-295 . -235) 140573) ((-869 . -918) T) ((-869 . -818) NIL) ((-868 . -614) 140545) ((-862 . -848) T) ((-1225 . -338) 140515) ((-1225 . -377) 140485) ((-222 . -1118) 140469) ((-1262 . -288) 140446) ((-1206 . -646) 140371) ((-1001 . -644) 140301) ((-961 . -21) T) ((-961 . -25) T) ((-733 . -21) T) ((-733 . -25) T) ((-713 . -21) T) ((-713 . -25) T) ((-709 . -646) 140266) ((-453 . -21) T) ((-453 . -25) T) ((-339 . -102) T) ((-174 . -102) T) ((-997 . -1055) T) ((-868 . -1047) T) ((-772 . -102) T) ((-1247 . -363) 140245) ((-1246 . -898) 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-898) 135364) ((-247 . -898) 135341) ((-117 . -1047) T) ((-814 . -1109) T) ((-1084 . -724) T) ((-621 . -233) 135320) ((-619 . -102) T) ((-780 . -724) T) ((-778 . -724) T) ((-413 . -1109) T) ((-117 . -243) T) ((-40 . -368) NIL) ((-117 . -233) NIL) ((-1217 . -848) T) ((-454 . -724) T) ((-814 . -23) T) ((-729 . -25) T) ((-729 . -21) T) ((-1074 . -286) 135299) ((-78 . -396) T) ((-78 . -395) T) ((-533 . -765) 135281) ((-692 . -1054) 135231) ((-1254 . -131) T) ((-1247 . -131) T) ((-1226 . -131) T) ((-1171 . -25) T) ((-1139 . -411) 135215) ((-633 . -367) 135147) ((-605 . -367) 135079) ((-1153 . -1146) 135063) ((-103 . -1097) 135041) ((-1171 . -21) T) ((-1170 . -21) T) ((-863 . -611) 135023) ((-997 . -715) 134971) ((-223 . -646) 134938) ((-692 . -111) 134872) ((-50 . -724) T) ((-1170 . -25) T) ((-351 . -349) T) ((-1164 . -21) T) ((-1077 . -452) 134823) ((-1164 . -25) T) ((-710 . -514) 134770) ((-581 . -724) T) ((-518 . -724) T) ((-1123 . -21) T) ((-1123 . -25) T) ((-595 . -131) T) ((-294 . 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. -286) 132157) ((-1163 . -1080) T) ((-992 . -1080) T) ((-814 . -131) T) ((-117 . -793) NIL) ((-117 . -790) NIL) ((-355 . -307) T) ((-352 . -307) T) ((-344 . -307) T) ((-251 . -1109) 132067) ((-250 . -1109) 131977) ((-1022 . -1047) T) ((-1001 . -1055) T) ((-48 . -614) 131910) ((-343 . -646) 131855) ((-619 . -38) 131839) ((-1275 . -611) 131801) ((-1275 . -612) 131762) ((-1074 . -611) 131744) ((-1022 . -243) T) ((-354 . -1047) T) ((-813 . -1269) 131714) ((-251 . -23) T) ((-250 . -23) T) ((-985 . -611) 131696) ((-735 . -612) 131657) ((-735 . -611) 131639) ((-797 . -848) 131618) ((-1156 . -151) 131565) ((-997 . -514) 131477) ((-354 . -233) T) ((-354 . -243) T) ((-388 . -614) 131458) ((-1002 . -25) T) ((-141 . -611) 131440) ((-141 . -612) 131399) ((-908 . -307) T) ((-1002 . -21) T) ((-969 . -25) T) ((-912 . -21) T) ((-912 . -25) T) ((-427 . -21) T) ((-427 . -25) T) ((-841 . -411) 131383) ((-48 . -1047) T) ((-1284 . -1276) 131367) ((-1282 . -1276) 131351) ((-1033 . -602) 131326) ((-316 . 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-309) NIL) ((-72 . -395) T) ((-1110 . -102) 118725) ((-831 . -411) 118709) ((-1117 . -793) T) ((-1117 . -790) T) ((-699 . -1097) T) ((-578 . -611) 118691) ((-379 . -363) T) ((-169 . -493) 118669) ((-222 . -611) 118601) ((-134 . -1097) T) ((-116 . -1097) T) ((-48 . -724) T) ((-1044 . -489) 118566) ((-141 . -425) 118548) ((-141 . -368) T) ((-1025 . -102) T) ((-512 . -509) 118527) ((-710 . -614) 118283) ((-476 . -102) T) ((-463 . -102) T) ((-1032 . -1109) T) ((-1219 . -611) 118265) ((-1178 . -1036) 118201) ((-1171 . -35) 118167) ((-1171 . -95) 118133) ((-1171 . -1200) 118099) ((-1171 . -1197) 118065) ((-1155 . -309) NIL) ((-89 . -396) T) ((-89 . -395) T) ((-1077 . -1148) 118044) ((-1170 . -1197) 118010) ((-1170 . -1200) 117976) ((-1032 . -23) T) ((-1170 . -95) 117942) ((-571 . -493) T) ((-1170 . -35) 117908) ((-1164 . -1197) 117874) ((-1164 . -1200) 117840) ((-1164 . -95) 117806) ((-361 . -1109) T) ((-359 . -1148) 117785) ((-353 . -1148) 117764) ((-345 . -1148) 117743) ((-1164 . -35) 117709) ((-1123 . -35) 117675) ((-1123 . -95) 117641) ((-108 . -1148) T) ((-1123 . -1200) 117607) ((-831 . -1055) 117586) ((-645 . -309) 117524) ((-630 . -309) 117375) ((-1123 . -1197) 117341) ((-710 . -1047) T) ((-1059 . -637) 117323) ((-1077 . -38) 117191) ((-950 . -637) 117139) ((-1002 . -147) T) ((-1002 . -145) NIL) ((-379 . -1109) T) ((-324 . -25) T) ((-322 . -23) T) ((-941 . -848) 117118) ((-710 . -326) 117095) ((-481 . -637) 117043) ((-40 . -1036) 116931) ((-710 . -233) T) ((-699 . -715) 116918) ((-339 . -1097) T) ((-174 . -1097) T) ((-331 . -848) T) ((-418 . -452) 116868) ((-379 . -23) T) ((-359 . -38) 116833) ((-353 . -38) 116798) ((-345 . -38) 116763) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-834 . -1109) T) ((-108 . -38) 116713) ((-825 . -1109) T) ((-772 . -1097) T) ((-116 . -715) 116700) ((-670 . -1036) 116684) ((-610 . -102) T) ((-834 . -23) T) ((-825 . -23) T) ((-1153 . -286) 116661) ((-1110 . -309) 116599) ((-482 . -1049) 116496) ((-1099 . 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115251) ((-174 . -715) 115183) ((-407 . -286) 115141) ((-870 . -556) T) ((-108 . -400) 115123) ((-84 . -384) T) ((-84 . -395) T) ((-699 . -172) T) ((-615 . -611) 115105) ((-99 . -724) T) ((-482 . -102) 114895) ((-99 . -473) T) ((-116 . -172) T) ((-1284 . -644) 114854) ((-1282 . -644) 114813) ((-1110 . -38) 114783) ((-169 . -637) 114731) ((-1052 . -102) T) ((-997 . -614) 114621) ((-869 . -25) T) ((-813 . -238) 114600) ((-869 . -21) T) ((-816 . -102) T) ((-44 . -644) 114543) ((-414 . -102) T) ((-385 . -102) T) ((-110 . -309) NIL) ((-227 . -102) 114521) ((-127 . -1212) T) ((-121 . -1212) T) ((-815 . -1049) 114472) ((-815 . -638) 114414) ((-1032 . -131) T) ((-668 . -367) 114398) ((-152 . -644) 114357) ((-997 . -1047) T) ((-1235 . -637) 114305) ((-1101 . -611) 114287) ((-1001 . -611) 114269) ((-515 . -23) T) ((-510 . -23) T) ((-343 . -307) T) ((-508 . -23) T) ((-322 . -131) T) ((-3 . -1097) T) ((-1001 . -612) 114253) ((-997 . -243) 114232) ((-997 . -233) 114211) ((-1290 . -724) T) ((-1254 . 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112784) ((-1235 . -25) T) ((-1235 . -21) T) ((-853 . -25) T) ((-44 . -367) 112768) ((-853 . -21) T) ((-729 . -452) 112719) ((-1285 . -611) 112701) ((-1274 . -1049) 112671) ((-1052 . -309) 112609) ((-669 . -1080) T) ((-604 . -1080) T) ((-390 . -1097) T) ((-571 . -25) T) ((-571 . -21) T) ((-180 . -1080) T) ((-161 . -1080) T) ((-156 . -1080) T) ((-154 . -1080) T) ((-1274 . -638) 112579) ((-619 . -1097) T) ((-697 . -884) 112561) ((-1262 . -1212) T) ((-227 . -309) 112499) ((-144 . -368) T) ((-1044 . -612) 112441) ((-1044 . -611) 112384) ((-313 . -907) NIL) ((-1220 . -842) T) ((-697 . -1036) 112329) ((-709 . -918) T) ((-474 . -1216) 112308) ((-1170 . -452) 112287) ((-1164 . -452) 112266) ((-330 . -102) T) ((-870 . -1109) T) ((-319 . -644) 112148) ((-316 . -646) 111969) ((-313 . -646) 111898) ((-474 . -556) 111849) ((-339 . -514) 111815) ((-550 . -151) 111765) ((-40 . -307) T) ((-841 . -611) 111747) ((-699 . -290) T) ((-870 . -23) T) ((-379 . -493) T) ((-1077 . -231) 111717) ((-512 . -102) T) 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110500) ((-1254 . -95) 110466) ((-633 . -611) 110435) ((-605 . -611) 110404) ((-225 . -848) T) ((-1247 . -95) 110370) ((-1247 . -35) 110336) ((-1246 . -1109) T) ((-1117 . -646) 110323) ((-1226 . -95) 110289) ((-1225 . -1109) T) ((-592 . -151) 110271) ((-1077 . -349) 110250) ((-174 . -290) T) ((-117 . -377) 110227) ((-117 . -338) 110204) ((-1226 . -35) 110170) ((-868 . -307) T) ((-313 . -792) NIL) ((-313 . -789) NIL) ((-316 . -724) 110019) ((-313 . -724) T) ((-474 . -363) 109998) ((-359 . -349) 109977) ((-353 . -349) 109956) ((-345 . -349) 109935) ((-316 . -473) 109914) ((-1246 . -23) T) ((-1225 . -23) T) ((-716 . -1109) T) ((-712 . -131) T) ((-651 . -102) T) ((-477 . -715) 109879) ((-45 . -282) 109829) ((-105 . -1097) T) ((-68 . -611) 109811) ((-968 . -102) T) ((-862 . -102) T) ((-621 . -898) 109770) ((-1286 . -1097) T) ((-381 . -1097) T) ((-82 . -1212) T) ((-1211 . -1097) T) ((-1059 . -848) T) ((-117 . -898) NIL) ((-780 . -918) 109749) ((-711 . -848) T) ((-531 . -1097) T) ((-500 . -1097) T) ((-355 . -1216) T) ((-352 . -1216) T) ((-344 . -1216) T) ((-264 . -1216) 109728) ((-247 . -1216) 109707) ((-533 . -858) T) ((-1110 . -231) 109676) ((-1155 . -826) T) ((-1139 . -1054) 109660) ((-390 . -759) T) ((-692 . -1212) T) ((-689 . -1036) 109644) ((-355 . -556) T) ((-352 . -556) T) ((-344 . -556) T) ((-264 . -556) 109575) ((-247 . -556) 109506) ((-525 . -1080) T) ((-1139 . -111) 109485) ((-453 . -742) 109455) ((-864 . -1054) 109425) ((-815 . -38) 109367) ((-692 . -882) 109349) ((-692 . -884) 109331) ((-295 . -309) 109135) ((-908 . -1216) T) ((-1153 . -288) 109112) ((-1077 . -644) 109007) ((-668 . -411) 108991) ((-864 . -111) 108956) ((-1002 . -452) T) ((-692 . -1036) 108901) ((-908 . -556) T) ((-533 . -611) 108883) ((-581 . -918) T) ((-487 . -1049) 108833) ((-474 . -1109) T) ((-518 . -918) T) ((-912 . -452) T) ((-65 . -611) 108815) ((-217 . -1049) 108765) ((-487 . -638) 108715) ((-359 . -644) 108652) ((-353 . -644) 108589) ((-345 . -644) 108526) ((-630 . -229) 108472) 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95634) ((-673 . -514) 95567) ((-662 . -25) T) ((-662 . -21) T) ((-454 . -556) 95498) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -918) T) ((-117 . -818) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -614) 95480) ((-116 . -614) 95452) ((-1077 . -715) 95320) ((-1002 . -1049) 95270) ((-1002 . -638) 95220) ((-941 . -978) 95204) ((-912 . -638) 95156) ((-912 . -1049) 95108) ((-908 . -21) T) ((-908 . -25) T) ((-870 . -848) 95059) ((-864 . -646) 95019) ((-709 . -1109) T) ((-709 . -23) T) ((-289 . -172) T) ((-699 . -1047) T) ((-311 . -93) T) ((-699 . -233) T) ((-645 . -1097) 94997) ((-630 . -608) 94972) ((-630 . -1097) T) ((-581 . -1216) T) ((-581 . -556) T) ((-518 . -1216) T) ((-518 . -556) T) ((-487 . -644) 94922) ((-427 . -1049) 94906) ((-427 . -638) 94890) ((-359 . -715) 94842) ((-353 . -715) 94794) ((-339 . -1054) 94778) ((-345 . -715) 94730) ((-339 . 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-1197) T) ((-531 . -611) 93381) ((-520 . -309) 93319) ((-500 . -611) 93301) ((-500 . -612) 93283) ((-1211 . -611) 93249) ((-1164 . -1148) NIL) ((-1025 . -1068) 93218) ((-1025 . -1097) T) ((-1002 . -102) T) ((-969 . -102) T) ((-912 . -102) T) ((-891 . -1036) 93195) ((-1139 . -724) T) ((-1001 . -646) 93140) ((-476 . -1097) T) ((-463 . -1097) T) ((-585 . -23) T) ((-571 . -35) T) ((-571 . -95) T) ((-427 . -102) T) ((-1060 . -229) 93086) ((-1171 . -38) 92983) ((-864 . -724) T) ((-692 . -918) T) ((-511 . -25) T) ((-507 . -21) T) ((-507 . -25) T) ((-1170 . -38) 92824) ((-339 . -1047) T) ((-1164 . -38) 92620) ((-1077 . -172) T) ((-174 . -1047) T) ((-1123 . -38) 92517) ((-710 . -47) 92494) ((-359 . -172) T) ((-353 . -172) T) ((-519 . -57) 92468) ((-497 . -57) 92418) ((-351 . -1281) 92395) ((-225 . -452) T) ((-319 . -290) 92346) ((-345 . -172) T) ((-174 . -243) T) ((-1225 . -848) 92245) ((-108 . -172) T) ((-870 . -990) 92229) ((-656 . -1109) T) ((-581 . -363) T) ((-581 . -329) 92216) ((-518 . 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. -1109) T) ((-1206 . -131) T) ((-1022 . -918) T) ((-1001 . -724) T) ((-841 . -646) 90474) ((-710 . -884) NIL) ((-595 . -1049) 90447) ((-581 . -1109) T) ((-518 . -1109) T) ((-594 . -1049) 90330) ((-1164 . -400) 90282) ((-1002 . -309) NIL) ((-813 . -489) 90266) ((-595 . -638) 90239) ((-354 . -918) T) ((-594 . -638) 90136) ((-1153 . -34) T) ((-407 . -646) 90088) ((-50 . -23) T) ((-709 . -131) T) ((-710 . -1036) 89968) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 89939) ((-1137 . -1097) T) ((-1277 . -1276) 89923) ((-699 . -793) T) ((-699 . -790) T) ((-1117 . -307) T) ((-379 . -147) T) ((-280 . -611) 89905) ((-1225 . -990) 89875) ((-48 . -918) T) ((-673 . -489) 89859) ((-251 . -1269) 89829) ((-250 . -1269) 89799) ((-1173 . -848) T) ((-1110 . -172) 89778) ((-1117 . -1020) T) ((-1044 . -34) T) ((-834 . -147) 89757) ((-834 . -145) 89736) ((-735 . -107) 89720) ((-610 . -132) T) ((-482 . -1097) 89510) ((-1175 . -1055) T) ((-869 . -452) T) ((-85 . -1212) T) ((-240 . -38) 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. -23) T) ((-116 . -646) 80504) ((-474 . -145) 80483) ((-418 . -411) 80467) ((-474 . -147) 80446) ((-110 . -489) 80428) ((-311 . -614) 80409) ((-2 . -611) 80391) ((-186 . -102) T) ((-1155 . -19) 80373) ((-1155 . -602) 80348) ((-656 . -21) T) ((-656 . -25) T) ((-592 . -1141) T) ((-1110 . -286) 80325) ((-336 . -25) T) ((-336 . -21) T) ((-240 . -644) 80075) ((-495 . -363) T) ((-1277 . -38) 80045) ((-1169 . -1049) 79868) ((-1139 . -1212) T) ((-1122 . -1049) 79711) ((-852 . -1049) 79695) ((-630 . -602) 79670) ((-1169 . -638) 79499) ((-1122 . -638) 79348) ((-852 . -638) 79318) ((-1284 . -1054) 79302) ((-1282 . -1054) 79286) ((-549 . -1097) T) ((-1084 . -25) T) ((-1084 . -21) T) ((-531 . -790) T) ((-531 . -793) T) ((-117 . -1216) T) ((-961 . -1055) T) ((-621 . -556) T) ((-780 . -25) T) ((-780 . -21) T) ((-778 . -21) T) ((-778 . -25) T) ((-733 . -1055) T) ((-713 . -1055) T) ((-668 . -1054) 79270) ((-517 . -1080) T) ((-461 . -25) T) ((-117 . -556) T) ((-461 . -21) T) ((-454 . -25) T) ((-454 . 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-111) 77044) ((-1217 . -1097) T) ((-1178 . -1257) T) ((-1163 . -490) 77025) ((-1163 . -611) 76991) ((-668 . -1047) T) ((-1155 . -612) NIL) ((-1155 . -611) 76973) ((-1060 . -608) 76948) ((-1060 . -1097) T) ((-992 . -490) 76929) ((-74 . -441) T) ((-74 . -395) T) ((-992 . -611) 76895) ((-152 . -1054) 76879) ((-668 . -233) 76858) ((-571 . -554) 76842) ((-355 . -147) 76821) ((-355 . -145) 76772) ((-352 . -147) 76751) ((-352 . -145) 76702) ((-344 . -147) 76681) ((-344 . -145) 76632) ((-264 . -145) 76611) ((-264 . -147) 76590) ((-251 . -38) 76560) ((-247 . -147) 76539) ((-117 . -363) T) ((-247 . -145) 76518) ((-250 . -38) 76488) ((-152 . -111) 76467) ((-1001 . -1036) 76355) ((-1164 . -846) NIL) ((-692 . -1216) T) ((-797 . -1055) T) ((-697 . -1109) T) ((-1282 . -1047) T) ((-1153 . -1212) T) ((-1001 . -377) 76332) ((-908 . -145) T) ((-908 . -147) 76314) ((-868 . -131) T) ((-813 . -1054) 76211) ((-697 . -23) T) ((-692 . -556) T) ((-225 . -1049) 76176) ((-645 . -611) 76108) ((-645 . -612) 76069) 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+\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 39afecb3..65327070 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3452645031)            
-(4410 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3452782367)            
+(4413 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -226,10 +226,11 @@
  |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&|
  |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage|
  |RationalFunctionLimitPackage| |LinearDependence|
- |LinearlyExplicitRingOver| |ListToMap| |ListFunctions2|
- |ListFunctions3| |List| |Literal| |ListMultiDictionary| |LeftModule|
- |ListMonoidOps| |LinearAggregate&| |LinearAggregate|
- |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator1|
+ |LinearlyExplicitRingOver| |LinearSet| |ListToMap| |ListFunctions2|
+ |ListFunctions3| |List| |Literal| |LeftLinearSet|
+ |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&|
+ |LinearAggregate| |ElementaryFunctionLODESolver|
+ |LinearOrdinaryDifferentialOperator1|
  |LinearOrdinaryDifferentialOperator2|
  |LinearOrdinaryDifferentialOperatorCategory&|
  |LinearOrdinaryDifferentialOperatorCategory|
@@ -380,10 +381,10 @@
  |RandomFloatDistributions| |RationalFunctionFactor|
  |RationalFunctionFactorizer| |RationalFunction| |RGBColorModel|
  |RGBColorSpace| |RegularChain| |RandomIntegerDistributions| |Ring&|
- |Ring| |RationalInterpolation| |RectangularMatrixCategory&|
- |RectangularMatrixCategory| |RectangularMatrix|
- |RectangularMatrixCategoryFunctions2| |RightModule| |Rng|
- |RealNumberSystem&| |RealNumberSystem|
+ |Ring| |RationalInterpolation| |RightLinearSet|
+ |RectangularMatrixCategory&| |RectangularMatrixCategory|
+ |RectangularMatrix| |RectangularMatrixCategoryFunctions2|
+ |RightModule| |Rng| |RealNumberSystem&| |RealNumberSystem|
  |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable|
  |RecursivePolynomialCategory&| |RecursivePolynomialCategory|
  |RepeatAst| |RealRootCharacterizationCategory&|
@@ -477,661 +478,659 @@
  |XPolynomial| |XPolynomialRing| |XRecursivePolynomial|
  |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
  |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping|
- |Record| |Union| |height| |inR?| |complexLimit| |s21bdf|
- |splitConstant| |coordinate| |deleteProperty!| |quadraticForm|
- |quadratic?| |isPlus| |setCondition!| |e01sef| |front| |lift|
- |radPoly| |leftOne| |multiEuclidean| |countRealRootsMultiple| |cAtanh|
- |convert| |s15adf| |rk4| |unaryFunction| |OMread| |reduce|
- |subResultantChain| |cosIfCan| |repeatUntilLoop| |tanIfCan|
- |screenResolution| |knownInfBasis| |totalDifferential| |ScanRoman|
- |nthExpon| |symmetricPower| |fortranLiteralLine| |blankSeparate|
- |ddFact| |discriminant| |generalizedEigenvector| |definingInequation|
- |maxdeg| |OMconnInDevice| |split| |someBasis| |e02dff|
- |generalizedContinuumHypothesisAssumed| |prime?|
- |exprHasWeightCosWXorSinWX| |symbol| |printCode| |transform|
- |brillhartTrials| |sparsityIF| |matrixConcat3D| |OMUnknownSymbol?|
- |factorPolynomial| |unitsColorDefault| |expression| |graeffe|
- |testModulus| |thenBranch| |isTerm| |f04faf| |completeEval|
- |sech2cosh| |heapSort| |integer| |perfectSqrt| |cycleRagits|
- |zeroSquareMatrix| |prinpolINFO| |rational?| |numberOfPrimitivePoly|
- |getRef| |makeFloatFunction| |any?| |slash| |palgint| |vconcat|
- |getGoodPrime| |ip4Address| |cTanh| |shiftRoots| |fTable|
- |OMsetEncoding| |OMsupportsSymbol?| |deriv| |simplify| |getMeasure|
- |stopMusserTrials| |OMgetBVar| |monicDivide|
- |basisOfCommutingElements| |rk4qc| |paren| |inverseLaplace| |divide|
- |declare| |shanksDiscLogAlgorithm| |simpson| |dominantTerm| |e02baf|
- |f02wef| |acosIfCan| |noLinearFactor?| |relerror| |algSplitSimple|
- |addMatch| |randomR| |euclideanNormalForm| |tail| |resetNew| |port|
- |mathieu12| |imagK| |makeSketch| |polarCoordinates| |hyperelliptic|
- |axes| |complexSolve| |nullary| |karatsuba| ** |iidprod| |iiacosh|
- |rootKerSimp| |rdHack1| |byte| |cot2trig| |rootNormalize|
- |subResultantsChain| |lifting1| |rootPoly| |callForm?| |t|
- |outputList| |karatsubaDivide| |leftQuotient| |label| |rules| |error|
- |clearDenominator| |getCode| |primitive?| |e02bcf| |lfunc| |pdct|
- |setRow!| |rightUnits| |balancedBinaryTree| |unknown| |assert|
- |rowEchLocal| |secIfCan| |readInt8!| |linearMatrix| |readable?|
- |getOperator| |coth2tanh| |int| |leader| |hcrf| |s17aef|
- |semiResultantEuclidean2| |binarySearchTree| |sequences|
- |invmultisect| |OMgetString| |stosePrepareSubResAlgo| |beauzamyBound|
- |linSolve| |OMencodingUnknown| |shellSort| |select!| |predicates|
- |linkToFortran| |crest| |mindeg| |primitiveElement|
- |structuralConstants| |imagI| |pointPlot| |thetaCoord| |OMopenFile|
- |queue| |coerceP| |clearTheIFTable| |rectangularMatrix| |complexForm|
- |iiacsc| |pushdterm| |iterationVar| |palgLODE0| |binaryTournament|
- |reflect| |li| |roughBase?| |selectOptimizationRoutines| |constructor|
- |collectQuasiMonic| |s17dhf| |zero?| |showIntensityFunctions|
- |endOfFile?| |max| |littleEndian| |asinhIfCan| |schwerpunkt|
- |symmetricProduct| |rowEchelonLocal| |option| |OMgetVariable|
- |pushdown| |lieAlgebra?| |hconcat| |nonSingularModel| |deepExpand|
- |cscIfCan| |pointColor| |balancedFactorisation| |patternMatch|
- |tubeRadius| |genericLeftTrace| |dimensionOfIrreducibleRepresentation|
- |unitNormalize| |rangePascalTriangle| |exp1| |groebner| |taylorRep|
- |rootBound| |degreeSubResultant| |f04maf| |ellipticCylindrical|
- |pair?| |groebgen| |checkPrecision| |nthCoef| |monicCompleteDecompose|
- |rootPower| |s18aff| |dioSolve| |updatF| |atanIfCan|
- |createGenericMatrix| |rightTrim| |iiatan| |sizePascalTriangle|
- |determinant| |viewPhiDefault| |commutator| |e01sff| |bumptab1|
- |alphanumeric?| |leftTrim| |parents| |integral| |trigs| |bat1|
- |qualifier| |setMinPoints| |shallowExpand| |members|
- |explicitlyFinite?| |hessian| |PDESolve| |getButtonValue| |unary?|
- |fortranDoubleComplex| |implies| |relativeApprox| |index?| |hdmpToDmp|
- |printInfo| |splitDenominator| |binaryTree| |degree|
- |resultantReduitEuclidean| |romberg| |permanent| |factors| |test|
- |ef2edf| |column| |setRealSteps| |ldf2lst| |drawComplexVectorField|
- |OMlistSymbols| |toseSquareFreePart| |bernoulli| |lexico|
- |principalIdeal| |rationalApproximation| |dark|
- |exprHasAlgebraicWeight| |bombieriNorm| |firstNumer|
- |numberOfImproperPartitions| |safeCeiling| |perfectNthRoot| |fill!|
- |qPot| |triangular?| |binary| |modularGcd| |rightQuotient| |string?|
- |dihedralGroup| |hMonic| |generate| |stFunc1| |leftExtendedGcd|
- |close| |makeViewport3D| |eq| |laguerre| |appendPoint| |OMlistCDs|
- |interactiveEnv| |kind| |OMputBVar| |OMwrite| |mappingAst| |rarrow|
- |iter| |c06gcf| |d01akf| |prefix| |imagJ| |nextIrreduciblePoly|
- |zeroDimensional?| |digit| |incrementBy| |f01qcf| |op| |minrank|
- |cotIfCan| |pattern| |display| |flatten| |setProperties|
- |extendedResultant| |OMgetBind| |matrixDimensions| |rCoord|
- |readInt32!| |monomialIntPoly| |selectfirst| |taylorIfCan| |expand|
- |padicallyExpand| |lazyPseudoDivide| |gcdPrimitive|
- |bezoutDiscriminant| |integralAtInfinity?| |OMgetError| |collectUnder|
- |filterWhile| |f04mcf| |flexibleArray| |cyclicEqual?|
- |commutativeEquality| |exportedOperators| |dn| |semicolonSeparate|
- |curryRight| |filterUntil| |OMputEndApp| |unitNormal| |trunc| |rquo|
- |f04mbf| |message| |dmp2rfi| |null?| |select| |shiftRight| |cos2sec|
- |mapCoef| |perspective| |gradient| |input| |listRepresentation|
- |node?| |read!| |s21bcf| |symbolTable| |rowEchelon| |largest| |fi2df|
- |union| |aQuadratic| |reductum| |iibinom| |library| |fractionPart|
- |nextPrimitivePoly| |exp| |prinb| |makingStats?| |initTable!|
- |palgintegrate| |multiset| |forLoop| |semiDegreeSubResultantEuclidean|
- |infieldint| |check| |stFunc2| |euclideanSize| |f02agf| |hermite|
- |createIrreduciblePoly| |OMReadError?| |numberOfNormalPoly| |style|
- |aspFilename| |hypergeometric0F1| |truncate| |infix| |maxPoints|
- |outerProduct| |laplace| |bitTruth| |preprocess| |checkRur|
- |numerator| |cons| |lfinfieldint| |atoms| |whileLoop| |makeRecord|
- |squareFreeFactors| |set| |computeCycleEntry| |drawToScale|
- |perfectNthPower?| |postfix| |ode1| |d01anf| |Beta| |internal?|
- |rotate| |genericLeftDiscriminant| |makeCos| |midpoints| |totalDegree|
- |smith| |genericPosition| |inputBinaryFile| |crushedSet| |pmintegrate|
- |quote| |pol| |drawCurves| |showTheRoutinesTable| |multiplyExponents|
- |eigenvector| |nthExponent| |f04asf| |explogs2trigs| |f01qdf|
- |charpol| |sumOfSquares| |writable?| |generic?| |fullDisplay|
- |subNode?| |stop| |cAsec| |divisor| |quickSort|
- |ScanFloatIgnoreSpaces| |has?| |rightRegularRepresentation|
- |leadingIdeal| |solid| |inHallBasis?| |s17ahf| |prod| |red| |second|
- |diagonal| |rightTrace| |cardinality| |setlast!| |bringDown| |bsolve|
- |cyclotomicFactorization| |fortranComplex| |e02dcf|
- |prepareSubResAlgo| |third| |indiceSubResultantEuclidean| |color|
- |genericRightDiscriminant| |c05nbf| |e04dgf| |signature| |isOr|
- |pureLex| |insertRoot!| |iicsc| |euclideanGroebner| |minRowIndex|
- |horizConcat| |green| |generateIrredPoly| |s20acf| |toroidal|
- |besselJ| |factorAndSplit| |iiabs| |rightAlternative?| |boundOfCauchy|
- |outputArgs| |factorFraction| |palginfieldint| |compactFraction|
- |trace2PowMod| |e02agf| |reduction| |lhs| |resetVariableOrder| |cAcot|
- |algebraic?| |FormatRoman| |mainForm| |lowerCase?|
- |expressIdealMember| |dequeue!| |clipPointsDefault| |optimize|
- |rootOfIrreduciblePoly| |complex?| |reducedDiscriminant| |rhs|
- |explicitEntries?| |normalizedDivide| |singRicDE| |slex|
- |algintegrate| |moebius| |collectUpper| |pseudoQuotient| |void|
- |vertConcat| |exponent| |f04axf| |wordInStrongGenerators| |leaf?|
- |cycle| |pseudoRemainder| |central?| |besselI| |nextItem|
- |LyndonWordsList| |systemCommand| |tanhIfCan| |partialDenominators|
- |ignore?| |innerSolve1| |OMgetEndAttr| |euler| |e01bff| |OMreadStr|
- |lfintegrate| |copy!| |bumptab| |before?| |script| |idealiserMatrix|
- |bag| |accuracyIF| |purelyAlgebraic?| |mainCoefficients| |twoFactor|
- |tanQ| |kmax| |sequence| |minGbasis| |transcendent?| |lieAdmissible?|
- |selectAndPolynomials| |OMencodingSGML| |size?| |basisOfLeftNucloid|
- |inverseIntegralMatrixAtInfinity| |readInt16!| |readByte!| |Hausdorff|
- |Nul| |cCosh| |retractable?| |primPartElseUnitCanonical| |setrest!|
- |normal| |arrayStack| |ldf2vmf| |partialFraction| |fortranInteger|
- |mathieu22| |critB| |elRow2!| |drawComplex| |meshFun2Var| |s17acf|
- |coerceListOfPairs| |tex| |edf2fi| |key| |basisOfMiddleNucleus|
- |unravel| |redpps| |clipBoolean| |heap| |mr| UP2UTS |singularitiesOf|
- |wronskianMatrix| |leftDivide| |rischDEsys| |s17ajf| |mapBivariate|
- |shallowCopy| |primintfldpoly| |mergeDifference| |trapezoidalo|
- |subTriSet?| |octon| |leftExactQuotient| |prefixRagits|
- |lazyPremWithDefault| |delta| |setErrorBound| |filename| |numerators|
- |depth| |headReduced?| |createNormalElement| |lepol| |rationalPoints|
- |pointLists| |cond| |hspace| |repeating| |whitePoint| |cyclicEntries|
- |factorByRecursion| |minPoly| |getlo| |derivationCoordinates| |f01rcf|
- |anticoord| |remove!| |extendedSubResultantGcd|
- |algebraicCoefficients?| |mapExponents| |linearDependence|
- |getConstant| |parse| |setAttributeButtonStep| |insertBottom!|
- |clearFortranOutputStack| |rightTraceMatrix| |minIndex| |fractRadix|
- |isTimes| |pointSizeDefault| |leftDiscriminant| |makeCrit|
- |infiniteProduct| |reducedQPowers| |numberOfFactors| |writeBytes!|
- |prem| |extensionDegree| |roughUnitIdeal?| |doubleRank| |curveColor|
- |iisqrt3| |totolex| |resetBadValues| |f02awf| |numberOfComponents|
- |empty?| |cycleEntry| |evaluateInverse| |roughBasicSet| |irreducible?|
- |createNormalPrimitivePoly| |digits| |coleman| |substring?|
- |singleFactorBound| |factorial| |bits| |solve1|
- |constantCoefficientRicDE| |rur| |prevPrime| |stirling1| |d01alf|
- |semiSubResultantGcdEuclidean2| |invertibleElseSplit?| |isList|
- |alternating| |isOp| |tryFunctionalDecomposition| |e01sbf| |rightZero|
- |integralBasisAtInfinity| |setleft!| |lambda| |numFunEvals|
- |diagonalMatrix| |coefficient| |suffix?| |rotatey| |call|
- |computeBasis| |curve| |e02zaf| |monomRDE| |possiblyNewVariety?|
- |getDatabase| |getZechTable| |const| |ranges| |binomial| |e01baf|
- |super| |iitan| |internalDecompose| |expextendedint| |pop!|
- |create3Space| |moduloP| |duplicates?| |lo| UTS2UP |choosemon|
- |constantLeft| |showTheIFTable| EQ |gcdcofactprim|
- |factorSquareFreePolynomial| |constantKernel| |unmakeSUP| |supRittWu?|
- |patternMatchTimes| |groebnerIdeal| |minimumDegree|
- |numberOfFractionalTerms| |ref| |oneDimensionalArray| |basis|
- |functionIsOscillatory| |setFieldInfo| |s15aef| |aQuartic| |scale|
- |fixedPointExquo| |factorSquareFreeByRecursion| |defineProperty|
- |numberOfComputedEntries| |viewport2D| |iomode| |po| |compBound|
- |weierstrass| |mkPrim| |birth| |quartic| |eigenMatrix| |arg1|
- |alternatingGroup| |addPoint| |leftRegularRepresentation| |integrate|
- |rightRemainder| |f02bjf| |complementaryBasis| |e02ajf| |entries|
- |constantIfCan| |arg2| |OMputString| |radicalSolve| |listOfMonoms|
- |youngGroup| |leadingExponent| |index| |lcm| |difference|
- |rightExtendedGcd| |merge!| |quoted?| |selectOrPolynomials|
- |totalGroebner| |scripted?| |exprHasLogarithmicWeights| |e02adf|
- |rewriteSetByReducingWithParticularGenerators| |cyclicCopy|
- |multiEuclideanTree| |irreducibleRepresentation| |f01brf| |subPolSet?|
- |conditions| |normalizeAtInfinity| |getVariableOrder|
- |basisOfRightNucleus| |SFunction| |leftPower| |nonLinearPart| |append|
- |KrullNumber| |satisfy?| |linearPolynomials| |addmod|
- |lineColorDefault| |match| |delete| |listConjugateBases| |lighting|
- |e02gaf| |standardBasisOfCyclicSubmodule| |associates?| |pair|
- |outputSpacing| |inf| |gcd| |setPrologue!| |rightFactorIfCan|
- |toseLastSubResultant| |SturmHabichtSequence| |value| |result|
- |tracePowMod| |karatsubaOnce| |chiSquare| |lprop|
- |characteristicPolynomial| |semiResultantEuclidean1| |false|
- |palgextint| |radicalEigenvalues| |find| |rightMinimalPolynomial|
- |range| |powmod| |corrPoly| |createThreeSpace| |debug3D|
- |lastSubResultant| |extractTop!| |repeating?| |symmetricRemainder|
- |cubic| |commutative?| |limitedIntegrate| |reset| |bivariate?|
- |composites| |stoseInternalLastSubResultant| |socf2socdf|
- |parabolicCylindrical| |wrregime| |cAcos| |uniform01| |randomLC|
- |hasoln| |localReal?| |medialSet| |typeLists| |eof?| |computePowers|
- |traverse| |directSum| |quotedOperators| |innerSolve| |pow| |write|
- |setLegalFortranSourceExtensions| |transcendentalDecompose| |ratpart|
- |getIdentifier| |integral?| |box| |#| |lintgcd| |interpolate|
- |fractRagits| |tree| |save| |outputFixed| |OMgetEndError|
- |leviCivitaSymbol| |swapColumns!| |coefChoose| |round| |exponential1|
- |LiePolyIfCan| |scaleRoots| |expintfldpoly| |extension| |dec|
- |setStatus| |OMputInteger| |commonDenominator| |chainSubResultants|
- |htrigs| |principal?| |squareMatrix| |uncouplingMatrices| |cCoth|
- |showTypeInOutput| |rightGcd| |monomials| |subNodeOf?| |totalLex|
- |OMputEndObject| |zCoord| |ReduceOrder| |rischNormalize|
- |normInvertible?| |leftZero| |complexNormalize| |droot| |meatAxe|
- |interReduce| |mathieu23| |checkForZero| |pointColorDefault|
- |separateFactors| |lastSubResultantElseSplit| |factorsOfDegree|
- |factorList| |symbol?| |fortranTypeOf| |objectOf| |iisec| |precision|
- |raisePolynomial| |d02bhf| |OMserve| |roughSubIdeal?|
- |createMultiplicationTable| |f02aef| |resultantEuclideannaif|
- |legendreP| |simplifyExp| |wordsForStrongGenerators| |arbitrary|
- |tablePow| |df2ef| |reduceByQuasiMonic| |generator| |numFunEvals3D|
- |delete!| |constant?| |denomRicDE| |LazardQuotient| |setsubMatrix!|
- |escape| |tan2cot| |comment| |pack!| |elementary| |makeYoungTableau|
- |log10| |cAcosh| |sturmSequence| |unrankImproperPartitions1|
- |viewZoomDefault| |newReduc| |block| |iiasinh| |traceMatrix|
- |removeRoughlyRedundantFactorsInContents| |printInfo!| |bitand|
- |HenselLift| |sylvesterSequence| |primes| |qqq| |level| |reseed|
- |rightCharacteristicPolynomial| |abelianGroup| |identity|
- |maxRowIndex| |bitior| |mapMatrixIfCan| |roman| |maxColIndex| |tanAn|
- |var2Steps| |isMult| |midpoint| |getExplanations| |eigenvectors|
- |listBranches| |palgRDE0| |exQuo| |interval| |rightDivide| |cyclic|
- |chiSquare1| |mesh?| |stripCommentsAndBlanks| |Lazard|
- |numberOfComposites| |divisors| F |setValue!| |allRootsOf| |rename|
- |problemPoints| |nextColeman| |increment| |lastSubResultantEuclidean|
- |cPower| |intChoose| |iiasech| |unvectorise| |adaptive| |open|
- |mapExpon| |critpOrder| |matrix| |numer| |polygon?| |mapUnivariate|
- |lazyPseudoRemainder| |search| |chineseRemainder| |hasSolution?|
- |leftUnits| |characteristicSet| |regime| |morphism| |integralMatrix|
- |rightNorm| |denom| |create| |fortran| |null| |symmetricDifference|
- |startPolynomial| |part?| |constantToUnaryFunction| |saturate|
- |d01amf| |maxrow| |bipolar| |useNagFunctions| |primextendedint|
- |modTree| |not| |taylorQuoByVar| |OMputSymbol| |nthFlag|
- |normalizeIfCan| |HermiteIntegrate| |closedCurve?| |and| |Lazard2|
- |mapmult| |cap| |coth2trigh| |associatorDependence|
- |extendedIntegrate| |solveLinearlyOverQ| |operations| |realSolve|
- |exprToGenUPS| |digamma| |cyclotomicDecomposition| |e02aef| |or|
- |vark| |categories| |symmetricSquare| |log2| |cyclePartition|
- |leftRecip| |weakBiRank| |any| |setOfMinN| |controlPanel| |nullSpace|
- |positive?| |xor| |doublyTransitive?| |padecf| |colorFunction|
- |direction| |diophantineSystem| |iisin| |hexDigit?| |f04adf|
- |upperCase?| |double?| |case| |f07aef| |selectsecond| |branchPoint?|
- |subresultantSequence| |sylvesterMatrix| |exactQuotient!| |Zero|
- |ListOfTerms| |removeZero| |stirling2| |withPredicates| |singular?|
- |OMgetInteger| |shift| |changeWeightLevel| |signatureAst|
- |infinityNorm| |wordInGenerators| |leftTrace| |linearlyDependent?|
- |One| |setScreenResolution3D| |airyBi| |charthRoot| |compound?|
- |rotatez| |coerce| |bernoulliB| Y |f02akf| |adaptive3D?| |iprint|
- |newSubProgram| |mainCharacterization| |symFunc| |applyRules|
- |denominators| |quadratic| |construct| |degreePartition| |quoByVar|
- |trailingCoefficient| |viewSizeDefault| |normalDeriv| |torsion?|
- |polynomialZeros| |extractProperty| |useSingleFactorBound|
- |approximants| |minPoints3D| |iteratedInitials| |csch2sinh| |cAsech|
- |rationalIfCan| |elem?| |commaSeparate| |c06ecf| |outputForm|
- |datalist| |outputGeneral| |integralBasis| |linGenPos|
- |setMaxPoints3D| |cycleElt| |contains?| |top| |nullary?| |writeLine!|
- |f07fef| |real?| |bezoutResultant| |inc| |intcompBasis| |d01asf|
- |f07adf| |equiv| |irreducibleFactors| |e01bgf| |graphCurves|
- |inrootof| |linearDependenceOverZ| |showSummary| |packageCall|
- |putColorInfo| |parseString| |complexIntegrate| |ScanArabic| |sort|
- |fillPascalTriangle| |makeTerm| |rootSimp| |OMputEndBind|
- |removeRoughlyRedundantFactorsInPols| |obj| |OMreceive|
- |identityMatrix| |mainExpression| |decreasePrecision| |setClosed|
- |continue| |numberOfMonomials| |geometric| |norm| |completeHermite|
- |henselFact| |partialQuotients| |dualSignature|
- |createLowComplexityNormalBasis| |trim| |contract| |cache|
- |showAttributes| |squareFreeLexTriangular| |iiacos| |mat| |spherical|
- |integer?| |rank| |removeCoshSq| |functionIsFracPolynomial?| |bytes|
- |setTopPredicate| |wholeRagits| |normalize| |subset?| |list|
- |OMputApp| |arity| |B1solve| |polygon| |laplacian| |digit?| |e04fdf|
- |categoryFrame| |primeFactor| |fixedDivisor| |extendIfCan| |random|
- |car| |closedCurve| |var1StepsDefault| |changeNameToObjf|
- |measure2Result| |inverse| |maxrank| |elliptic| |asinIfCan|
- |curveColorPalette| |iisinh| |cdr| |sin?| |setStatus!|
- |rationalPoint?| |idealiser| |derivative| |stopTableInvSet!|
- |rational| |extract!| |indiceSubResultant| |tubePlot| |legendre|
- |setDifference| |subst| |localAbs| |llprop| |name| |reverse!|
- |consnewpol| |isAnd| |insert!| |leftGcd|
- |genericLeftMinimalPolynomial| |deref| |enqueue!| |primitivePart|
- |setIntersection| |convergents| |updatD| |body|
- |differentialVariables| |collect| |zeroSetSplit| |minimumExponent|
- |permutationGroup| |length| |infRittWu?| |logpart| |showAll?|
- |setUnion| |totalfract| |upperCase!| |stiffnessAndStabilityOfODEIF|
- |isNot| |lowerCase!| |remove| |PollardSmallFactor| |rootDirectory|
- |expintegrate| |scripts| |d03faf| |expandLog| |apply| |f04atf| |low|
- |rewriteIdealWithHeadRemainder| |cycleSplit!| |lists| |besselY| RF2UTS
- |oblateSpheroidal| |rightLcm| |swap| |btwFact| |f02abf|
- |viewPosDefault| |groebnerFactorize| |distFact| |iicot| |last|
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- |antisymmetricTensors| |cCos| |componentUpperBound| |center| |polCase|
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- |addMatchRestricted| |trace| |acsc| |ipow| |pomopo!|
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- |halfExtendedSubResultantGcd1| |sup| |sin2csc| |tanh| |tan2trig|
- |logGamma| |mpsode| |noKaratsuba| |associatedEquations| |reshape|
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- |inv| |acosh| |lazyPrem| |critT| |bandedJacobian| |constantRight|
- |paraboloidal| |update| |ground?| |nextsousResultant2| |maxint|
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- |iiatanh| |f02bbf| |s17dlf| |ground| |primlimintfrac|
- |roughEqualIdeals?| |pushup| |acothIfCan|
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- |sort!| |mesh| |selectSumOfSquaresRoutines| |highCommonTerms|
- |scalarTypeOf| |typeList| |OMputAtp| |normalise| |leadingMonomial|
- |asech| |distribute| |fortranReal| |e04naf| |writeInt8!| |equality|
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- |numericalOptimization| |rightExactQuotient| |quotientByP| |s13adf|
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- |frobenius| |univariateSolve| |BasicMethod| |hclf| |debug| |hash|
- |definingEquations| |OMputEndAttr| |outputBinaryFile| |sncndn|
- |regularRepresentation| |nextNormalPoly| |child?| |realElementary|
- |OMconnectTCP| |count| D |double| |algebraicDecompose| |f2df|
- |varselect| |generalTwoFactor| |e01saf| |errorInfo| |remainder|
- |lowerPolynomial| |hermiteH| |binding| |bezoutMatrix| |tubePoints|
- |e04jaf| |ocf2ocdf| |write!| |sample| |semiLastSubResultantEuclidean|
- |setchildren!| |createLowComplexityTable| |npcoef| |trapezoidal| |row|
- |cCot| |addBadValue| |revert| |content| |blue| |zeroDimPrimary?|
- |conjug| |tanh2coth| |rangeIsFinite| |stoseInvertibleSetreg| |headAst|
- |moduleSum| |monicRightFactorIfCan| |quasiRegular| |changeVar|
- |byteBuffer| |alternative?| |normalForm| |scanOneDimSubspaces|
- |s01eaf| |lquo| |iiperm| |edf2ef| |pushuconst| |lflimitedint| |one?|
- |mkIntegral| |graphStates| |dimensionsOf| |changeBase| |yellow|
- |e02bbf| |zerosOf| |limitPlus| |s18def| |zero| |e02bdf|
- |numberOfChildren| |oddintegers| |putGraph| |bindings| |refine|
- |declare!| |iilog| |iiacsch| |showFortranOutputStack| |cRationalPower|
- |stiffnessAndStabilityFactor| |nativeModuleExtension|
- |genericRightTrace| |readUInt8!| |predicate| |tab1| |elliptic?|
- |modularFactor| |And| |subscript| |lyndonIfCan| |principalAncestors|
- |integerIfCan| |OMmakeConn| |inverseIntegralMatrix| |lfextlimint|
- |hex| |palglimint| |primPartElseUnitCanonical!| |Or| |se2rfi|
- |expenseOfEvaluationIF| |specialTrigs| |subresultantVector|
- |internalIntegrate0| |rombergo| |outputFloating| |extendedint|
- |pascalTriangle| |Not| |rubiksGroup| |minus!| |binaryFunction|
- |indicialEquation| |palgint0| |univariatePolynomialsGcds| |bottom!|
- |decrease| |getMatch| |domainOf| |finiteBound| |completeSmith|
- |OMgetType| |radicalEigenvector| |backOldPos| |curry|
- |startTableInvSet!| |stoseSquareFreePart| |safetyMargin|
- |internalSubPolSet?| |coord| |epilogue| |conjugates| |cycles|
- |univariatePolynomials| |OMunhandledSymbol| |divergence| |supersub|
- |solveLinearPolynomialEquation| |isPower| |segment| |dmpToHdmp|
- |trigs2explogs| |printHeader| |wholePart| |squareFreePolynomial|
- |removeSuperfluousCases| |reify| |elements| |inputOutputBinaryFile|
- |semiResultantEuclideannaif| |overset?| |makeVariable| |gensym|
- |aLinear| |parameters| |recur| |listYoungTableaus|
- |variationOfParameters| |stopTable!| |useEisensteinCriterion?| |id|
- |OMputEndBVar| |closed?| |iicsch| |stoseInvertibleSetsqfreg|
- |clipParametric| |setright!| |coercePreimagesImages|
- |currentCategoryFrame| |permutations| |coordinates| |s21baf|
- |characteristicSerie| |shufflein| |fixedPoint| |viewDeltaYDefault|
- |table| |operator| |safeFloor| |diff| |hasPredicate?| |bfEntry|
- |alphanumeric| |new| |symmetric?| |diag| |initiallyReduce| |polyRicDE|
- |pole?| |composite| |basisOfCentroid| |e02bef| |loadNativeModule|
- |insert| |selectNonFiniteRoutines| |strongGenerators| |ode|
- |quasiMonic?| |algebraicSort| |leftCharacteristicPolynomial|
- |discreteLog| |solve| |bitLength| |OMUnknownCD?| |invertible?|
- |leftScalarTimes!| |selectMultiDimensionalRoutines| |SturmHabicht|
- |iExquo| |options| |setfirst!| |setButtonValue| |mapSolve|
- |OMgetEndBind| |mainPrimitivePart| |clearTheSymbolTable|
- |extractBottom!| |subQuasiComponent?| |d01apf| |pi| |mirror| |recolor|
- |reducedSystem| |iiacoth| |sPol| |sh| |rk4f| |infinity|
- |SturmHabichtCoefficients| |retractIfCan| |extractClosed| |c05pbf|
- |tRange| |assign| |terms| |pushucoef| |iitanh| |acschIfCan| |string|
- |extractPoint| |limitedint| |complexExpand| |nonQsign| |extractIndex|
- |quasiRegular?| |pseudoDivide| |firstSubsetGray| |coshIfCan|
- |userOrdered?| |mindegTerm| |sum| |ptree| |iflist2Result|
- |genericLeftNorm| |kernel| |generalSqFr| |minset| |jordanAlgebra?|
- |doubleComplex?| |nextPrimitiveNormalPoly| |elRow1!| |draw|
- |rightRankPolynomial| |d02kef| |particularSolution| |subspace|
- |power!| |patternVariable| |option?| |evenlambert| |makeResult|
- |polyPart| |dimension| |left| |exprex| |cyclicGroup| |cSec| |rotate!|
- |exprToXXP| |representationType| |triangulate| |realEigenvalues|
- |right| |isQuotient| |contractSolve| |fintegrate| |pushNewContour|
- |laurentIfCan| |pToHdmp| |factorOfDegree| |intPatternMatch|
- |setProperty!| |lp| |explicitlyEmpty?| |BumInSepFFE|
- |nthFractionalTerm| |getOrder| |reducedForm| |makeObject| |signAround|
- |removeSquaresIfCan| |stoseInvertible?sqfreg| |map|
- |radicalEigenvectors| |usingTable?| |numberOfHues| |components|
- |iiacot| |d01gaf| |csubst| |countRealRoots| |elt| |currentEnv|
- |OMconnOutDevice| |expt| |OMencodingXML| |oddInfiniteProduct|
- |linearAssociatedLog| |tableForDiscreteLogarithm| |c06fuf| |nthFactor|
- |coef| |every?| |showArrayValues| |resize| |d01aqf| |schema|
- |OMgetAtp| |e02ahf| |isobaric?| |rename!| |exteriorDifferential|
- |push| |nil| |infinite| |arbitraryExponent| |approximate| |complex|
- |shallowMutable| |canonical| |noetherian| |central|
- |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed|
- |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation|
- |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation|
- |finiteAggregate| |shallowlyMutable| |commutative|) 
-\ No newline at end of file
+ |Record| |Union| |height| |refine| |localAbs| |tableau|
+ |internalZeroSetSplit| |ord| |paren| |gderiv| |transform| |s20adf|
+ |list?| |leftUnit| |pseudoRemainder| |lift| |associatorDependence|
+ |components| |clip| |ScanFloatIgnoreSpacesIfCan| |parseString|
+ |convert| |principalIdeal| |singularitiesOf| |setOrder| |SFunction|
+ |iFTable| |reduce| |logGamma| |drawComplexVectorField| |euler|
+ |coth2tanh| |acotIfCan| |branchPoint?| |getZechTable| |elColumn2!|
+ |mathieu12| |move| |coshIfCan| |antisymmetric?| |connect|
+ |reducedQPowers| |lllip| |cylindrical| |submod| |flagFactor|
+ |semiIndiceSubResultantEuclidean| |predicates| |LazardQuotient|
+ |iiasin| |solve1| |moduleSum| |reverseLex| |rightScalarTimes!|
+ |symbol| |expandLog| |associative?| |OMreadStr| |sturmSequence|
+ |rischDEsys| |front| |basisOfRightAnnihilator| |f01bsf|
+ |normalizedAssociate| |expression| |tRange|
+ |tryFunctionalDecomposition| |viewpoint| |coefChoose| |algebraic?|
+ |primitiveElement| |selectIntegrationRoutines| |bumptab| |digit|
+ |integer| |patternMatchTimes| |domainOf| |iicsch| |FormatArabic|
+ |headReduce| |f02aff| |showTheRoutinesTable| |UpTriBddDenomInv|
+ |lazyPrem| |localUnquote| |constantLeft| |getMeasure| |ignore?| |abs|
+ |B1solve| |Si| |create3Space| |complexSolve| |complexRoots|
+ |unitCanonical| |outputArgs| |conjugate| |badValues| |revert|
+ |cyclic?| |rightRankPolynomial| |normal01| |middle| |doubleResultant|
+ |variable?| |minimumDegree| |rationalFunction| |nextPrimitivePoly|
+ |useSingleFactorBound| |declare| |implies| |f04atf| |addPoint|
+ |iExquo| |showAllElements| |c06eaf| |printingInfo?|
+ |differentialVariables| |s21bcf| |s17acf| |rdHack1| |split|
+ |initiallyReduce| |tail| |OMopenString| |port|
+ |removeRedundantFactorsInPols| |quotient| |aQuartic|
+ |powerAssociative?| |expandTrigProducts| |curry| |complexEigenvalues|
+ |drawToScale| |order| |push!| ** |rroot| |thenBranch| |buildSyntax|
+ |validExponential| |mightHaveRoots| |byte| |lowerCase|
+ |solveLinearPolynomialEquationByFractions| |difference| |e02def|
+ |denomLODE| |root?| |t| |outputList| |cycleTail| |label| |maxPoints|
+ |rules| |hostPlatform| |error| |completeEval| |shanksDiscLogAlgorithm|
+ |f01qef| |OMgetEndBVar| |lllp| |leftRank| |dequeue!|
+ |fortranDoubleComplex| |acscIfCan| |principalAncestors| |prindINFO|
+ |assert| |unknown| |s20acf| |rotate| |exists?| |setprevious!|
+ |totalLex| |hessian| |prime?| |int| |leader| |modulus| |makeCos|
+ |inverseColeman| |extractBottom!| |sumOfSquares|
+ |coercePreimagesImages| |oddlambert| |extractTop!| |largest| |orbit|
+ |idealiser| |innerEigenvectors| |besselI| |adaptive?| |imports|
+ |dmpToHdmp| |bezoutResultant| |wronskianMatrix| |leftTrace|
+ |permutationRepresentation| |outputAsScript| |removeZero| |OMgetApp|
+ |inHallBasis?| |roughUnitIdeal?| |bits| |makingStats?|
+ |leftTraceMatrix| |bipolar| |leastMonomial| |multiplyCoefficients|
+ |getSyntaxFormsFromFile| |determinant| |setrest!| |iiperm| |smith|
+ |generalizedContinuumHypothesisAssumed| |PollardSmallFactor|
+ |viewPhiDefault| |li| |children| |constructor| |lex| |hasPredicate?|
+ |palgextint| |rightExactQuotient| |genericRightTrace| |stFunc2| |max|
+ |gbasis| |leftPower| |is?| |extensionDegree| |repSq| |option|
+ |compdegd| |raisePolynomial| |const| |qinterval| |blue|
+ |subtractIfCan| |useSingleFactorBound?| |padicFraction|
+ |semiLastSubResultantEuclidean| |printTypes| |shiftLeft| |graphCurves|
+ |showTheFTable| UTS2UP |getMultiplicationMatrix| |expressIdealMember|
+ |cycleRagits| |sh| |clearTable!| |bfKeys| |factorByRecursion| |e04gcf|
+ |rk4qc| |doubleComplex?| |bezoutDiscriminant| |alternatingGroup|
+ |goodnessOfFit| |checkPrecision| |leftQuotient| |ParCondList|
+ |exactQuotient| |float?| |bumptab1| |balancedBinaryTree| |chvar|
+ |tValues| |constant?| |rightTrim| |minGbasis| |setFormula!|
+ |tanh2trigh| |zCoord| |coleman| |solveid| |Is| |isTimes| |realSolve|
+ |leftTrim| |parents| |quadratic| |integralDerivationMatrix|
+ |complexNormalize| |alternative?| |perfectNthPower?| |argscript|
+ |increasePrecision| |yCoord| |exprHasLogarithmicWeights| |ddFact|
+ |updateStatus!| |printHeader| |permutation| |over| |bivariate?|
+ |strongGenerators| |tan2trig| |outputFixed| |just| |OMputEndAttr|
+ |printInfo| |reduced?| |numerators| |removeConstantTerm|
+ |LagrangeInterpolation| |lifting1| |commonDenominator| |cotIfCan|
+ |test| |OMwrite| |d01gaf| |e02bcf| |rootRadius|
+ |semiDiscriminantEuclidean| |cyclotomicFactorization| |infieldint|
+ |c02aff| |nextNormalPrimitivePoly| |enterPointData| |hclf| |solve|
+ |leftDiscriminant| |minimumExponent| |fillPascalTriangle| |d01aqf|
+ |changeName| |e01sff| |generalizedInverse| |listOfLists| |fprindINFO|
+ |connectTo| |createNormalElement| |returnTypeOf| |nonLinearPart|
+ |listexp| |showTypeInOutput| |geometric| |expIfCan| |cCosh| |pack!|
+ |e02agf| |setCondition!| |generate| |close| |eq| |f2st| |eigenvector|
+ |factorSquareFreePolynomial| |primes| |kind| |pile| |real?| |before?|
+ |diagonals| |iter| |coerceP| |contains?| |setelt!| |prefix|
+ |setClipValue| |pushNewContour| |number?| |anfactor| |incrementBy|
+ |op| |cycles| |getGraph| |pattern| |display| |flatten| |option?|
+ |Lazard2| |cosSinInfo| |host| |dimensions| |clipPointsDefault|
+ |gcdcofactprim| |crest| |dmpToP| |expand| |chebyshevT| |medialSet|
+ |df2ef| |increase| |partialDenominators| |leftOne| |filterWhile|
+ |unexpand| |atrapezoidal| |hermiteH| |var1StepsDefault|
+ |infieldIntegrate| |ldf2vmf| |fglmIfCan| |cyclotomic| |filterUntil|
+ |writeLine!| |primintegrate| |checkRur| |thetaCoord|
+ |nativeModuleExtension| |factor1| |vertConcat| |message| |select|
+ |intensity| |outlineRender| |coerceL| |insertTop!| |s13acf|
+ |solveInField| |input| |coerceS| |definingEquations|
+ |numericalIntegration| |readBytes!| |compiledFunction| |symbolTable|
+ |rischDE| |noLinearFactor?| |iisin| |union| |reductum|
+ |changeNameToObjf| |outputFloating| |library| |setProperty!| |exp|
+ |divergence| |resultantReduit| |truncate| |leadingIdeal| |f04adf|
+ |algintegrate| |getExplanations| |groebSolve| |vedf2vef| |back|
+ |noncommutativeJordanAlgebra?| |zeroDimPrime?| |lfintegrate| |LiePoly|
+ |quasiComponent| |product| |isNot| |changeBase| |newTypeLists|
+ |OMconnectTCP| |pop!| |outerProduct| |modularGcdPrimitive| |f02axf|
+ |indicialEquations| |collect| |cons| |backOldPos| |cSec| |makeRecord|
+ |set| |extractSplittingLeaf| |superscript| |sorted?| |curveColor|
+ |antisymmetricTensors| |modularGcd| |multisect| |univariatePolynomial|
+ |monomials| |qualifier| |swap!| |dfRange| |rCoord| |inverseLaplace|
+ |leftCharacteristicPolynomial| |drawStyle| |digamma| |nthRoot|
+ |elements| |palgRDE0| |OMlistSymbols| |univariatePolynomials| |expPot|
+ |quote| |qPot| |mat| |csc2sin| |expextendedint| |skewSFunction|
+ |point?| |curryRight| |bsolve| |stop| |exp1| |scalarTypeOf|
+ |reduction| |copies| |position!| |rspace| |qfactor| |gramschmidt|
+ |ocf2ocdf| |f02aef| |heap| |second| |denominators| |OMgetAttr|
+ |isPlus| |primeFactor| |subResultantGcd| |btwFact| |s18aff| |third|
+ |viewSizeDefault| |escape| |f01mcf| |subPolSet?| |signature|
+ |compound?| |s17ajf| |isEquiv| |probablyZeroDim?| |OMsupportsCD?|
+ |algebraicSort| |removeIrreducibleRedundantFactors| |iicoth|
+ |reduceByQuasiMonic| |light| |queue| |superHeight| |bottom!| |maxrank|
+ |ref| |toScale| |removeSquaresIfCan| |rootPoly| |expt|
+ |functionIsOscillatory| |lhs| |nonSingularModel| |radicalRoots|
+ |goodPoint| |updatF| |lfextlimint| |toseSquareFreePart|
+ |generalPosition| |optimize| |lifting| |rhs| |scripted?| |iisech|
+ |discriminant| |node?| |relerror| |f02ajf| |OMmakeConn| |tanIfCan|
+ |void| |factorOfDegree| |multiEuclidean| |getProperties| |makeSin|
+ |reducedContinuedFraction| |tracePowMod| |makeFR| |systemCommand|
+ |toseInvertible?| |removeCoshSq| |makeop| |idealiserMatrix| |kmax|
+ |bit?| |recur| |resize| |associatedEquations| |maxPoints3D|
+ |OMgetVariable| |infLex?| |script| |iflist2Result| |brillhartTrials|
+ |inputOutputBinaryFile| |zeroDim?| |viewZoomDefault| |intcompBasis|
+ |partitions| |monomialIntegrate| |viewWriteAvailable| |extractPoint|
+ |symFunc| |nthExponent| |sumSquares| |OMputEndBVar|
+ |viewDeltaYDefault| |green| |mathieu22| |linearDependence| |f01rdf|
+ |OMgetEndError| |lexico| |normal| |lazy?| |linearMatrix| |exprToXXP|
+ |part?| |byteBuffer| |explimitedint| |SturmHabichtMultiple|
+ |monicDecomposeIfCan| |nullary| |tex| |OMsend| |key| |ode|
+ |oddInfiniteProduct| |scan| |exprToUPS| |mr| |hexDigit?| |baseRDE|
+ |weight| |numericalOptimization| |elem?| |hspace| |setColumn!|
+ |tablePow| |diagonalProduct| |integralRepresents|
+ |selectNonFiniteRoutines| |stoseInvertible?sqfreg| |diagonal| |delta|
+ |filename| |mainSquareFreePart| |sqfrFactor| |depth| |OMgetError|
+ |showTheSymbolTable| |rightDiscriminant| |decrease| |cond| |makeMulti|
+ |fullDisplay| |removeDuplicates!| |compBound| |setAttributeButtonStep|
+ |pole?| |poisson| |matrixDimensions| |getGoodPrime| |lookup|
+ |splitNodeOf!| |parse| |nullary?| |palgLODE0| |incrementKthElement|
+ |exprHasAlgebraicWeight| |factorsOfCyclicGroupSize| |commutative?|
+ |numberOfComputedEntries| |pointColorDefault| |updatD| |elliptic|
+ |legendre| |s19adf| |iCompose| |OMputVariable| |hasTopPredicate?|
+ |cothIfCan| |tableForDiscreteLogarithm| |bracket| |factorFraction|
+ |binomThmExpt| |imagj| |presub| |ParCond| |round| |substring?| |iiabs|
+ |genericRightNorm| |rewriteSetWithReduction| |sample| |d01gbf|
+ |squareFree| |LyndonWordsList| |perspective| |graphs| |prevPrime|
+ |univariate?| |regularRepresentation| |sylvesterMatrix|
+ |nextSubsetGray| |lambda| |startTableInvSet!| |trailingCoefficient|
+ |suffix?| |uncouplingMatrices| |call| |imagk| |htrigs| |ffactor|
+ |exportedOperators| |solveLinear| |pureLex| |moreAlgebraic?| |super|
+ |lepol| |generalizedContinuumHypothesisAssumed?| |Beta| |stirling1|
+ |fortranInteger| |lo| |subresultantSequence| |vspace|
+ |infiniteProduct| EQ |OMUnknownSymbol?| |mapCoef| |rightPower|
+ |edf2ef| |setright!| |moduloP| |limit| |indiceSubResultantEuclidean|
+ |removeSinhSq| |prinb| |modTree| |resultant| |lfextendedint|
+ |deleteRoutine!| |polygon?| |mapExponents| |createNormalPrimitivePoly|
+ |chiSquare1| |printInfo!| |iiasech| |cCoth| |quartic| |arg1|
+ |leftNorm| |f04axf| |redPo| |unit?| |jordanAdmissible?| |binaryTree|
+ |minIndex| |rk4a| |arg2| |aspFilename| |monicModulo| |e01bgf| |e02gaf|
+ |index| |euclideanSize| |lcm| |safetyMargin| |cCos|
+ |reciprocalPolynomial| |multinomial| |nullity| |iibinom| |polygamma|
+ |genericLeftMinimalPolynomial| |nextNormalPoly| |genericLeftNorm|
+ |algebraicOf| |conditions| |bezoutMatrix| |irreducible?|
+ |identityMatrix| |composite| |append| |coordinates| |optional?|
+ |scaleRoots| |trapezoidalo| |integralCoordinates| |match| |delete|
+ |rightUnits| |delay| |semiResultantEuclideannaif| |cfirst| |pair|
+ |s17dgf| |gcd| |oddintegers| |newSubProgram| |expandPower| |isOp|
+ |value| |result| |reverse!| |firstUncouplingMatrix| |makeVariable|
+ |nextPartition| |OMputBVar| |false| |rightUnit| |cardinality|
+ |localReal?| |rootProduct| |lastSubResultantEuclidean| |adaptive|
+ |makeSUP| |laplace| |FormatRoman| |coefficient| |associates?| |iifact|
+ |sdf2lst| |reset| |stiffnessAndStabilityFactor| |sech2cosh|
+ |extractIndex| |alphabetic?| |removeRedundantFactors| |direction|
+ |generalizedEigenvector| |multMonom| |basisOfCommutingElements|
+ |ratpart| |s17adf| |prod| |makeViewport2D| |viewPosDefault| |every?|
+ |write| |nthFactor| |mainCoefficients| |SturmHabichtCoefficients|
+ |makeEq| |#| |groebner| |maximumExponent| |setPredicates| |tree|
+ |save| |numberOfCycles| |internalDecompose| |exponents| |discreteLog|
+ |distance| |e04jaf| |cot2trig| |findBinding| |setleft!| |dec|
+ |stoseInvertibleSetsqfreg| |iiasinh| |figureUnits| |mindeg| |contract|
+ |lighting| |LowTriBddDenomInv| |rootSplit| |karatsubaOnce|
+ |jacobiIdentity?| |setlast!| |s21baf| |d02bbf| |sincos| |OMgetBVar|
+ |pushuconst| |internalSubQuasiComponent?| |xn| |wholeRadix| |colorDef|
+ |symmetricSquare| |rightRemainder| |permutations| |startPolynomial|
+ |genericPosition| |contractSolve| |rationalPower| |precision| |f04mcf|
+ |mulmod| |patternVariable| |partialNumerators| |clearTheFTable|
+ |ScanFloatIgnoreSpaces| |stoseInvertible?reg| |s18def| |addBadValue|
+ |evaluate| |box| |invmod| |mapmult| |subMatrix| |generator|
+ |polyRicDE| |clipSurface| |e02bbf| |ode2| |comment| |hostByteOrder|
+ |fortranLogical| |nlde| |OMencodingBinary| |log10| |asimpson| |imagK|
+ |socf2socdf| |unitsColorDefault| |OMgetObject| |recolor| |s19aaf|
+ |radicalSolve| |bitand| |degreeSubResultant| |taylorRep| |ip4Address|
+ |quoByVar| |level| |symmetricProduct| |stoseInvertibleSetreg|
+ |separateDegrees| |bitior| |f01rcf| |f02adf| |leviCivitaSymbol|
+ |firstDenom| |norm| |d03eef| |OMputApp| |supDimElseRittWu?|
+ |polynomialZeros| |coth2trigh| |leftMult| |currentCategoryFrame|
+ |lowerCase!| |s13adf| |laurentIfCan| |ranges| |yCoordinates|
+ |matrixGcd| |basicSet| |c06gqf| F |genericLeftDiscriminant| |separant|
+ |s14baf| |OMgetBind| |sort!| |algebraicVariables| |open| |harmonic|
+ |jacobian| |matrix| |numer| |preprocess| |particularSolution| |search|
+ |setAdaptive| |semiResultantEuclidean2| |normalizeIfCan|
+ |resetBadValues| |integralBasisAtInfinity| |s17aff| |denom| |fortran|
+ |cyclicEqual?| |divisor| |null| |drawComplex| |OMputSymbol|
+ |headReduced?| |tubePointsDefault| |rootBound| |remove!| |cot2tan|
+ |hcrf| |not| |balancedFactorisation| |e01baf| |e04ycf|
+ |coerceListOfPairs| |createMultiplicationTable| |OMputFloat| |and|
+ |clipWithRanges| |viewport3D| |iiacsch| |complexElementary|
+ |operations| |areEquivalent?| |sylvesterSequence| |airyBi| |f02bbf|
+ |or| |fracPart| |categories| |acschIfCan| |lieAdmissible?| |curryLeft|
+ |any| |eyeDistance| |rangeIsFinite| |cyclicParents|
+ |LyndonCoordinates| |xor| |diff| |reseed|
+ |functionIsContinuousAtEndPoints| |bernoulliB| |createGenericMatrix|
+ |invertIfCan| |viewport2D| |pointLists| |case| |fullPartialFraction|
+ |e02dcf| |OMbindTCP| |nor| |extendedint| |enqueue!| |Zero|
+ |bandedJacobian| |fortranLinkerArgs| |mapdiv| |monomial?| |shift|
+ |dominantTerm| |chainSubResultants| |trigs| |subHeight| |One|
+ |var1Steps| |radicalEigenvector| |sumOfDivisors| |stopTableInvSet!|
+ |coerce| |algSplitSimple| Y |conjug| |nextColeman|
+ |setScreenResolution| |complexIntegrate| |nthRootIfCan|
+ |createPrimitiveNormalPoly| |listConjugateBases| |construct|
+ |palglimint0| |toseLastSubResultant| |invertibleSet| |printStats!|
+ |getStream| |degreeSubResultantEuclidean| |normalizedDivide|
+ |rightQuotient| |nthCoef| |readByte!| |cyclicGroup| |extractIfCan|
+ |s21bdf| |gcdPolynomial| |addMatch| |tan2cot| |rk4f| |invmultisect|
+ |datalist| |belong?| |d02cjf| |primPartElseUnitCanonical!| |fibonacci|
+ |showScalarValues| |top| |computePowers| |e01sbf| |iiatan|
+ |numberOfPrimitivePoly| |inc| |OMgetAtp| |numFunEvals3D|
+ |numberOfChildren| |reopen!| |airyAi| |numericIfCan| |romberg|
+ |e02daf| |leaf?| |showSummary| |definingInequation| |critM|
+ |OMputError| |seriesSolve| |derivationCoordinates| |sort|
+ |genericLeftTraceForm| |reducedDiscriminant| |leftScalarTimes!|
+ |c05adf| |getButtonValue| |obj| |iilog| |cLog| |fixedPoints|
+ |linearAssociatedExp| |intChoose| |continue| |clipParametric|
+ |unaryFunction| |s18aef| |outputAsTex| |laguerre| |cartesian| |df2fi|
+ |double?| |cAtan| |selectAndPolynomials| |cache| |showAttributes|
+ |pmintegrate| |Ci| |limitPlus| |whileLoop| |realEigenvectors|
+ |rotatey| |rank| |rightZero| |getMatch| |satisfy?| |stFunc1|
+ |OMgetEndBind| |mathieu24| |list| |accuracyIF| |complexEigenvectors|
+ |complexNumericIfCan| |nextsousResultant2| |randomLC| |makeSketch|
+ |exprToGenUPS| |alphanumeric?| |d01alf| |Aleph| |digit?| |random|
+ |car| |sub| |completeEchelonBasis| |clearFortranOutputStack|
+ |resultantnaif| |charthRoot| |laurentRep| |setnext!| |extractClosed|
+ |jordanAlgebra?| |stoseSquareFreePart| |cdr| |iomode|
+ |monicRightFactorIfCan| |has?| |toroidal| |chebyshevU| |setEmpty!|
+ |intersect| |patternMatch| |mainForm| |kroneckerDelta| |palgextint0|
+ |setDifference| |subst| |evaluateInverse| |nthr| |name| |select!|
+ |repeating?| |dioSolve| |pmComplexintegrate| |infix| |frst|
+ |fixedDivisor| |fractRagits| |generalInfiniteProduct|
+ |setIntersection| |createZechTable| |subTriSet?| |body| |frobenius|
+ |linearDependenceOverZ| |edf2df| |nilFactor|
+ |resultantReduitEuclidean| |length| |OMreadFile| |shellSort| |f04maf|
+ |setUnion| |elseBranch| |separate| |selectODEIVPRoutines|
+ |mainContent| |overlap| |remove| |scripts| |mainMonomials| |plotPolar|
+ |tanh2coth| |radPoly| |leftFactorIfCan| |apply| |fixPredicate|
+ |endOfFile?| |cosIfCan| |showRegion| |lists| |uniform|
+ |rationalPoint?| |alphanumeric| |modifyPointData| |subSet| |qqq|
+ |finiteBound| |po| |setPosition| |integers| |integralLastSubResultant|
+ |last| |formula| |henselFact| |c06fuf| |setMaxPoints| |even?|
+ |headRemainder| |size| |splitConstant| |e02aef| |charpol| |rootOf|
+ |trunc| |assoc| |close!| |eof?| |output| |explicitlyFinite?| |csubst|
+ |nonQsign| |isOr| |setref| |objects| |explicitlyEmpty?| |positive?|
+ |freeOf?| |scalarMatrix| |showFortranOutputStack| |factorSquareFree|
+ |d01anf| |monomRDEsys| |mapUp!| |UnVectorise| |base| |newReduc|
+ |enumerate| |listBranches| |qelt| |getIdentifier| |makeUnit|
+ |rootDirectory| |cSin| |e04fdf| |first| |bipolarCylindrical| |isAnd|
+ |binary| |purelyTranscendental?| |s17dhf| |qsetelt| |rightRecip|
+ |OMgetString| |overset?| |nrows| |copyInto!| |simplifyExp| |rest|
+ |f04qaf| |crushedSet| |polarCoordinates| |finite?| |pomopo!| |xRange|
+ |iisqrt2| |leftLcm| |ncols| |countRealRoots| |writable?| |concat!|
+ |substitute| |aQuadratic| |viewWriteDefault| |isOpen?|
+ |continuedFraction| |cAcosh| |yRange| |quotientByP| |debug3D|
+ |selectsecond| |dictionary| |quasiMonicPolynomials| |removeDuplicates|
+ |OMgetEndApp| |subCase?| |nextPrimitiveNormalPoly| |drawCurves| |row|
+ |zRange| |radicalSimplify| |leftDivide| |RemainderList| |c06fpf|
+ |monic?| |edf2fi| |tab| |euclideanGroebner| |laplacian| |iisec| |next|
+ |map!| |irreducibleRepresentation| |fortranCompilerName| |generic?| BY
+ |denominator| |dot| |corrPoly| |d01apf| |nodes| |showClipRegion|
+ |cschIfCan| |qsetelt!| |makeResult| |rewriteIdealWithRemainder|
+ |leaves| |contours| |callForm?| |myDegree| |signAround|
+ |symmetricDifference| |errorInfo| |RittWuCompare| |resetVariableOrder|
+ |cyclicSubmodule| |wrregime| |taylorIfCan| |rightMinimalPolynomial|
+ |e01saf| |s17dlf| |nodeOf?| |legendreP| |divideIfCan|
+ |createLowComplexityTable| |applyQuote| |hitherPlane| |factors|
+ |bivariatePolynomials| |iiexp| |printCode| |subResultantsChain|
+ |lexGroebner| |semiSubResultantGcdEuclidean2| |pdct| |commaSeparate|
+ |cyclic| |nthExpon| |setImagSteps| |kovacic| |realElementary|
+ |replace| |pquo| |userOrdered?| |minPoly| |internalSubPolSet?|
+ |createPrimitiveElement| |point| |monicLeftDivide| |isList|
+ |retractable?| |bounds| |terms| |multiset| |defineProperty| |previous|
+ |gensym| |removeRoughlyRedundantFactorsInPols| |LyndonBasis| |linears|
+ |flexible?| |acsch| |ellipticCylindrical| |invertible?| |d01asf|
+ |ruleset| |critBonD| |factorset| |jacobi| |insertionSort!| |conical|
+ |deref| |nextsubResultant2| NOT |fill!| |clipBoolean| |c06gcf|
+ |extendedIntegrate| |exponent| |bigEndian| |HenselLift| |imagJ|
+ |OMputEndObject| |acosIfCan| OR |series| |nil?| |appendPoint| |any?|
+ |OMreceive| |toseInvertibleSet| |expintfldpoly| |pushucoef| |dark|
+ |viewDeltaXDefault| |acothIfCan| AND |computeBasis| |zeroMatrix|
+ |addMatchRestricted| |suchThat| |computeCycleEntry| |entries| |f01qdf|
+ |mathieu23| |firstNumer| |subresultantVector| |tanQ| |inspect|
+ |rightFactorCandidate| |numberOfHues| |mapExpon| |bandedHessian|
+ |prefix?| |integerBound| |arguments| |singleFactorBound| |sPol|
+ |merge| |quasiRegular?| |qroot| |initials| |setProperties!| |epilogue|
+ |birth| |points| |mkcomm| |f01qcf| |boundOfCauchy| |incr| |exQuo|
+ |PDESolve| |vark| |min| |characteristic| |readIfCan!| |OMputBind|
+ |floor| |forLoop| |companionBlocks| |tryFunctionalDecomposition?|
+ |OMconnOutDevice| |sec2cos| |karatsuba| |sin2csc| |swapColumns!|
+ |doublyTransitive?| |lSpaceBasis| |axesColorDefault| |unravel|
+ |swapRows!| |weights| |hi| |degree| |member?| |addPoint2|
+ |mainDefiningPolynomial| |times!| |c02agf| |topPredicate|
+ |chineseRemainder| |mapSolve| |element?| |mkAnswer| |intPatternMatch|
+ |semiResultantEuclidean1| |tanhIfCan| |algebraicDecompose| |unparse|
+ |setleaves!| |char| |normalDeriv| |OMencodingXML| |exponential|
+ |tanNa| |semiSubResultantGcdEuclidean1| |getPickedPoints|
+ |perfectNthRoot| |sts2stst| |sn| |argumentList!| |generalTwoFactor|
+ |f02bjf| |basisOfCentroid| |dflist| |complex?| |mesh| |headAst|
+ |infix?| |heapSort| |plusInfinity| |directory| |setClosed|
+ |conditionsForIdempotents| RF2UTS |upperCase!| |choosemon| |mask|
+ |blankSeparate| |e02zaf| |indiceSubResultant| |monomialIntPoly|
+ |OMlistCDs| |minusInfinity| |log2| |low| |graphImage|
+ |standardBasisOfCyclicSubmodule| |genericRightMinimalPolynomial| *
+ |numberOfFractionalTerms| |quadratic?| |screenResolution3D| |key?|
+ |untab| |print| |atoms| |condition| |calcRanges| |powers| |permanent|
+ |inGroundField?| |iiacot| |rem| |normalized?| |resolve| |string?|
+ |OMencodingUnknown| |roughBase?| |OMread| |fixedPointExquo|
+ |basisOfLeftNucleus| |derivative| |createNormalPoly| |cRationalPower|
+ |omError| |constant| |quo| |hypergeometric0F1| |float| |knownInfBasis|
+ |divideExponents| |lagrange| |tubeRadiusDefault| |hex| |leastPower|
+ |nextSublist| |subset?| |HermiteIntegrate| |copy!| =
+ |setVariableOrder| |arbitrary| |partialQuotients| |iitan| |diagonal?|
+ |groebnerIdeal| |hconcat| |df2mf| |rational?| |div| |mesh?|
+ |att2Result| |noKaratsuba| |pointColor| |ran| |roughEqualIdeals?|
+ |iteratedInitials| |type| |linearAssociatedLog| |cAtanh| |evenlambert|
+ |radicalEigenvalues| |fortranTypeOf| |exquo| < |closedCurve?|
+ |lastSubResultant| |d02raf| |rightLcm| |f04faf| |fractionPart| |cap|
+ |stiffnessAndStabilityOfODEIF| |f02wef| ~= > |cross|
+ |diophantineSystem| |wordsForStrongGenerators| |bat1| |stopTable!|
+ |fmecg| |iroot| |ODESolve| |integralMatrix| ~ |generators|
+ |antiCommutator| |showArrayValues| <= |factorPolynomial|
+ |tanintegrate| |d01fcf| |charClass| |s17agf| |cCot| |withPredicates|
+ |nextPrime| |returnType!| |iicot| |meshPar2Var| >= |hermite| |parts|
+ |homogeneous?| |e04ucf| |gcdPrimitive| |acoshIfCan|
+ |createIrreduciblePoly| |e01sef| |morphism| |brillhartIrreducible?|
+ |iiasec| |zeroOf| |sinh2csch| |outputMeasure| |addPointLast| |setRow!|
+ |squareFreePolynomial| |zero?| |mainKernel| |someBasis|
+ |factorGroebnerBasis| |status| |constantKernel| |/\\| |sign|
+ |cycleSplit!| |varList| GE |cExp| |zag| |spherical| |scopes|
+ |leadingBasisTerm| |symmetricRemainder| |cAsin| |OMgetEndAtp| |\\/|
+ |empty| |halfExtendedSubResultantGcd1| + |cosh2sech| GT |maxColIndex|
+ |setPrologue!| |iiacsc| |fortranCarriageReturn| |constantOpIfCan|
+ |rationalApproximation| |distFact| |factorAndSplit|
+ |numberOfOperations| |s18acf| - |transcendent?| LE |c05pbf|
+ |removeSuperfluousCases| |pushFortranOutputStack| |lyndon|
+ |removeCosSq| |f02fjf| |besselK| |axes| / |rur| |internal?| LT
+ |e01bff| |squareMatrix| |popFortranOutputStack| |s18adf| |getOperands|
+ |cCsc| |squareFreeFactors| |isConnected?| |readable?|
+ |characteristicPolynomial| |denomRicDE| |postfix| |binarySearchTree|
+ |insertMatch| |iiGamma| |readInt8!| |minPol| |outputAsFortran|
+ |compile| |cubic| |column| |symbolIfCan|
+ |halfExtendedSubResultantGcd2| |generic| |multiple?| |retract|
+ |pushup| |symbol?| |plot| |ridHack1| |leadingExponent|
+ |commutativeEquality| |cyclicEntries| |upperCase?| |groebnerFactorize|
+ |setRealSteps| |hasSolution?| |infinityNorm| |pToHdmp| |var2Steps|
+ |OMReadError?| |rightTraceMatrix| |halfExtendedResultant1| |remainder|
+ |e02adf| |shiftRight| |limitedint| |wholeRagits| |property|
+ |leftFactor| |schema| |factorSquareFreeByRecursion| |maxRowIndex|
+ |arity| |polar| |simplifyPower| |findConstructor| |lazyIntegrate|
+ |quasiMonic?| |ode1| |sin?| |roman| |exprex|
+ |initializeGroupForWordProblem| |paraboloidal| |complexZeros|
+ |printStatement| |alphabetic| |setvalue!| |numerator| |tensorProduct|
+ |palgint0| |internalIntegrate| |repeatUntilLoop| |odd?| |applyRules|
+ |mindegTerm| |permutationGroup| |SturmHabicht| |f07aef|
+ |monicRightDivide| |units| |dimensionOfIrreducibleRepresentation|
+ |semicolonSeparate| |f2df| |mapUnivariate| |associator| |setStatus|
+ |changeMeasure| |totalGroebner| |isTerm| |alternating| |groebgen|
+ |removeRedundantFactorsInContents| |iitanh| |subResultantChain|
+ |changeThreshhold| |exactQuotient!| |curve| |basisOfNucleus|
+ |squareFreeLexTriangular| |primitivePart!| |recip|
+ |functionIsFracPolynomial?| |selectPolynomials| |basisOfLeftNucloid|
+ |parabolic| |decimal| |quadraticNorm| |exteriorDifferential|
+ |processTemplate| |atanIfCan| |collectQuasiMonic| |reverse| |plus|
+ |ricDsolve| |internalInfRittWu?| |clearCache| |BumInSepFFE| |cSinh|
+ |transcendentalDecompose| |lintgcd| |meshFun2Var| |d01bbf|
+ |zeroSetSplitIntoTriangularSystems| |absolutelyIrreducible?| |c06ecf|
+ |genus| |partialFraction| |anticoord| |zoom| |sparsityIF| |cAsec|
+ |bytes| |deepestInitial| |approxNthRoot| |dimensionsOf| |subNode?|
+ |identity| |groebner?| |mapDown!| |iiacoth| |binding| |setMinPoints3D|
+ |code| GF2FG |realEigenvalues| |setsubMatrix!| |setPoly|
+ |createLowComplexityNormalBasis| |rightMult| |collectUpper| |rotatez|
+ |leftZero| |countable?| |nextItem| |linearPolynomials| |llprop|
+ |vector| |bright| |makeSeries| |startTable!| |comp| |shallowCopy|
+ |traceMatrix| |f07fef| |times| |numberOfImproperPartitions|
+ |elementary| |f02abf| |computeCycleLength| |initial| |integer?|
+ |differentiate| |unitNormalize| |s01eaf| |ldf2lst| |critMonD1|
+ |inrootof| |slex| |innerSolve1| |insert!| |delete!|
+ |sizePascalTriangle| |supersub| |se2rfi| |credPol| |iicsc|
+ |conjugates| |dn| |function| |palgLODE| |mkPrim| |safeFloor|
+ |prinshINFO| |gethi| |makeViewport3D| |closedCurve|
+ |basisOfRightNucleus| |neglist| |pointPlot| |primextintfrac|
+ |purelyAlgebraicLeadingMonomial?| |rightCharacteristicPolynomial|
+ |module| |changeWeightLevel| |rightExtendedGcd| |failed| |interval|
+ |weakBiRank| |sizeMultiplication| |read!| |monom| |eval| |cAsinh|
+ |check| |dom| |lazyPquo| |rightRank| |cycle| |intermediateResultsIF|
+ |startTableGcd!| |s15aef| |secIfCan| |OMgetSymbol| |complexForm|
+ |rule| |rischNormalize| |inRadical?| |radicalOfLeftTraceForm|
+ |divideIfCan!| |abelianGroup| |members| |upperCase| |radix|
+ |transcendenceDegree| |distribute| |lazyVariations| |palgintegrate|
+ |e04dgf| |positiveSolve| |linearlyDependent?| |sinIfCan|
+ |setScreenResolution3D| |primitivePart| |unvectorise| |common|
+ |leftExtendedGcd| |leftUnits| |mdeg| |biRank| |innerSolve| |find|
+ |bubbleSort!| |split!| |iisinh| |OMputObject| |external?| |prem|
+ |e01bef| |f02agf| |cAcsch| |ceiling| |hue| |overlabel|
+ |multiplyExponents| |semiDegreeSubResultantEuclidean| |readLineIfCan!|
+ |cyclotomicDecomposition| |notelem| |mainExpression| |fTable|
+ |linearlyDependentOverZ?| |saturate| |plus!| |title|
+ |nextIrreduciblePoly| |ideal| |definingPolynomial| |cup| |build|
+ |clearDenominator| |expr| |plenaryPower| |rightGcd| |flexibleArray|
+ |exptMod| |normalElement| |mvar| |logical?| |atom?| |interactiveEnv|
+ |getDatabase| |reflect| |overbar| |possiblyInfinite?| |mirror|
+ |quatern| |symbolTableOf| |OMserve| |usingTable?| |removeSinSq|
+ |rangePascalTriangle| |inf| |curveColorPalette| |operator|
+ |completeSmith| |addiag| |binomial| |stFuncN| |e| |coerceImages|
+ |fortranCharacter| |latex| |lyndon?| |trivialIdeal?| |f01ref|
+ |zeroVector| |readUInt32!| |LiePolyIfCan| |createRandomElement|
+ |csch2sinh| |measure2Result| |bumprow| |setProperty| |putColorInfo|
+ |f02awf| |variable| |power!| |true| |operators| |negative?|
+ |trace2PowMod| |s17def| |linear| |iterationVar| |elRow1!|
+ |eigenvalues| |pascalTriangle| |s19abf| |iterators| |writeBytes!|
+ |imagi| |head| |moebius| |d03faf| |nothing| |lazyGintegrate|
+ |initiallyReduced?| |redPol| |integerIfCan| |inverseIntegralMatrix|
+ |deepestTail| |outputGeneral| |splitDenominator| |palgRDE|
+ |prefixRagits| |polynomial| |f04arf| |startStats!| |getlo|
+ |doubleFloatFormat| |readUInt16!| |findCycle| |init| |null?|
+ |createThreeSpace| |s17ahf| |mainVariables| |mergeFactors|
+ |factorList| |OMgetInteger| |basisOfCenter| |readUInt8!| |hexDigit|
+ |d02gaf| |musserTrials| |lineColorDefault|
+ |setLegalFortranSourceExtensions| |OMencodingSGML|
+ |createPrimitivePoly| |nthFractionalTerm| |completeHermite| |d02bhf|
+ |stosePrepareSubResAlgo| |meshPar1Var| |extract!| |pdf2df| |imagI|
+ |BasicMethod| |dihedralGroup| |keys| |ratPoly| |swap| |fortranDouble|
+ |maxdeg| |powmod| |cycleLength| |distdfact| |primextendedint|
+ |constantOperator| |lazyPremWithDefault| |properties| |changeVar|
+ |scanOneDimSubspaces| |wreath| |f04asf| |c06frf| |width| |s14abf|
+ |decompose| |sqfree| |sturmVariationsOf| |deleteProperty!|
+ |complexExpand| |argument| |translate| |mainPrimitivePart| |elliptic?|
+ |maxIndex| |minordet| |operation| |primitive?| |logIfCan| |f01brf|
+ |merge!| |rename!| |isAbsolutelyIrreducible?| |setErrorBound|
+ |lazyPseudoDivide| |hMonic| |iprint| |dihedral| |dAndcExp| |badNum|
+ |pseudoDivide| |orthonormalBasis| |eigenvectors|
+ |nextLatticePermutation| |entry?| |constDsolve| |rootsOf| |expint|
+ |solveLinearlyOverQ| |rewriteIdealWithHeadRemainder| |sayLength|
+ |algDsolve| |GospersMethod| |readLine!| |restorePrecision|
+ |evenInfiniteProduct| |normalizeAtInfinity| |integralAtInfinity?|
+ |createMultiplicationMatrix| |lowerPolynomial|
+ |useEisensteinCriterion?| |exponential1| |antiCommutative?|
+ |internalLastSubResultant| |SturmHabichtSequence| |more?| |mix|
+ |twoFactor| |infinite?| |loopPoints| |iiacosh| |slash| |tubePoints|
+ |useEisensteinCriterion| |constantRight| |roughBasicSet|
+ |genericLeftTrace| |dimension| |OMputAttr| |expenseOfEvaluation|
+ |youngGroup| |triangularSystems| |primlimitedint| |rightDivide|
+ |schwerpunkt| |ReduceOrder| |simpleBounds?| |cAcot| |symmetricGroup|
+ |optional| |OMsetEncoding| |finiteBasis| |setchildren!| |writeInt8!|
+ |minRowIndex| |pr2dmp| |stoseLastSubResultant| |computeInt| |meatAxe|
+ |representationType| |autoReduced?| |oblateSpheroidal| |s13aaf|
+ |solid| |root| |interpret| |algebraicCoefficients?| |monicDivide|
+ |region| |stack| |pointData| |doubleRank| |stopMusserTrials| |twist|
+ |aromberg| |nthFlag| |removeRoughlyRedundantFactorsInContents|
+ |pdf2ef| |e02ajf| |c05nbf| |removeZeroes| |rightNorm|
+ |makeFloatFunction| |OMputEndError| |closeComponent| |safeCeiling|
+ |quotedOperators| |variationOfParameters| |assign| |s15adf| |rarrow|
+ |setLabelValue| |iiatanh| |tower| |leftExactQuotient| |sup| |surface|
+ |numeric| |cAsech| |OMgetType| |firstSubsetGray| |randomR|
+ |rightAlternative?| |setTopPredicate| |imaginary| |d02ejf| FG2F
+ |idealSimplify| |radical| |getMultiplicationTable| |messagePrint|
+ |diagonalMatrix| |KrullNumber| |removeRoughlyRedundantFactorsInPol|
+ |iicosh| |tubePlot| |normalDenom| |dim| |inR?| |numberOfComposites|
+ |fixedPoint| |constantCoefficientRicDE| |checkForZero|
+ |factorsOfDegree| |lexTriangular| |screenResolution| |normal?|
+ |d02kef| |relationsIdeal| |solveLinearPolynomialEquationByRecursion|
+ SEGMENT |fortranLiteral| |cPower| |nil| |listOfMonoms| |graphState|
+ |leftAlternative?| |s19acf| |trueEqual| |less?|
+ |numberOfIrreduciblePoly| |setButtonValue| |xCoord| |d01amf|
+ |setAdaptive3D| |palginfieldint| |complexNumeric| |curve?|
+ |factorSFBRlcUnit| |viewDefaults| |unit| |iicos| |bombieriNorm|
+ |cycleElt| |signatureAst| |cAcsc| |parametric?| |center| |principal?|
+ |lambert| |numberOfVariables| |replaceKthElement| |typeList|
+ |lyndonIfCan| |approximate| |putGraph| |kernels| |insertBottom!|
+ |Hausdorff| |testModulus| |primeFrobenius| |e02dff| |complex|
+ |endSubProgram| |isExpt| |log| |normFactors| |polygon| |univariate|
+ |ramifiedAtInfinity?| |cSech| |addmod| |subscript| |integralBasis|
+ |minPoints3D| |node| |Frobenius| |univariatePolynomialsGcds|
+ |modifyPoint| F2FG |shufflein| |simpson| |mergeDifference| |asinIfCan|
+ |reduceLODE| |generalLambert| |lfinfieldint| |weighted| |erf|
+ |rightRegularRepresentation| |conditionP| |unitVector| |c06ebf|
+ |simplify| |duplicates?| |OMgetEndObject| |factor| |failed?|
+ |clearTheSymbolTable| |sncndn| |prepareSubResAlgo| |constantIfCan|
+ |setEpilogue!| |create| |concat| |setStatus!| |readInt16!| |linGenPos|
+ |sqrt| |dmp2rfi| |besselY| |inverseIntegralMatrixAtInfinity|
+ |singRicDE| |matrixConcat3D| |trapezoidal| |symmetricPower| |dilog|
+ |viewThetaDefault| |minrank| |upDateBranches| |possiblyNewVariety?|
+ |real| |initTable!| |hasHi| |polyRDE| |pow| |transpose| |setValue!|
+ |factorials| |branchPointAtInfinity?| |rombergo|
+ |resultantEuclideannaif| |sin| |imag| |systemSizeIF| |subspace|
+ |mantissa| |controlPanel| |directProduct| |top!| |setOfMinN|
+ |lflimitedint| |limitedIntegrate| |monomRDE| |normalise| |ListOfTerms|
+ |cos| |isImplies| |quickSort| |collectUnder| |size?|
+ |seriesToOutputForm| |associatedSystem| |singular?| |setFieldInfo|
+ |elRow2!| |wholePart| |tan| |squareTop| |LyndonWordsList1|
+ |rowEchelonLocal| |hyperelliptic| |outputSpacing| |getCurve|
+ |approxSqrt| |consnewpol| |rowEchLocal| |OMsupportsSymbol?| |brace|
+ |cot| |d01akf| |besselJ| |empty?| |leftMinimalPolynomial| |varselect|
+ |logpart| |listYoungTableaus| |extendIfCan| |adaptive3D?| |destruct|
+ |sec| |explicitEntries?| |OMgetFloat| |rdregime| |getRef| |source|
+ |objectOf| |unknownEndian| |countRealRootsMultiple| |optpair|
+ |getOrder| |central?| |csc| |getConstant| |minPoints| |unmakeSUP|
+ |getCode| |combineFeatureCompatibility| |sortConstraints|
+ |useNagFunctions| |cAcoth| |opeval| |laguerreL| |asin| |category|
+ |power| |bringDown| |critT| |ptFunc| |optAttributes| |bitCoef|
+ |c06ekf| |commutator| |writeByte!| |equation| |inconsistent?| |acos|
+ |domain| |getProperty| |prinpolINFO| |characteristicSet|
+ |stoseIntegralLastSubResultant| |irreducibleFactor| |primlimintfrac|
+ |e02ddf| |generalSqFr| |compactFraction| |monomial| |prepareDecompose|
+ |atan| |mkIntegral| |entry| |mainValue| |package| |beauzamyBound|
+ |e02akf| |weierstrass| |polyred| |asinhIfCan| |tanAn| |show|
+ |selectFiniteRoutines| |coordinate| |multivariate| |acot|
+ |convergents| |Vectorise| |f07adf| |resultantEuclidean| |target|
+ |basisOfLeftAnnihilator| |cTanh| |baseRDEsys| |traverse|
+ |unrankImproperPartitions1| |variables| |asec| |extend| |increment|
+ |subscriptedVariables| |rectangularMatrix| |whatInfinity| |space|
+ |gradient| |rowEch| |univcase| |leftGcd| |localIntegralBasis| |trace|
+ |acsc| |e02bef| |sinhcosh| |infRittWu?| |child?| |rotatex|
+ |fortranReal| |degreePartition| |s14aaf| |parametersOf| |shuffle|
+ |sinh| |style| |rootNormalize| |pushdown| |stronglyReduced?|
+ |linearPart| |cn| |d02gbf| |deriv| |e01daf| |setMinPoints|
+ |rationalIfCan| |cosh| |innerint| |rename| |rquo| |bindings| |ravel|
+ |zeroDimPrimary?| |c06fqf| |OMclose| |cycleEntry| |coefficients|
+ |janko2| |tanh| |minset| |basisOfRightNucloid| |categoryFrame|
+ |binaryTournament| |ef2edf| |critMTonD1| |reshape| |mapMatrixIfCan|
+ |hdmpToDmp| |tube| |aCubic| |coth| |taylor| |minColIndex|
+ |writeUInt8!| |LazardQuotient2| |clearTheIFTable| |divisors|
+ |mappingAst| |shade| |regime| |square?| |stoseInvertibleSet| |sech|
+ |laurent| |setelt| |linkToFortran| |newLine| |complement| |e02baf|
+ |iidsum| |extendedEuclidean| |reorder| |outputBinaryFile|
+ |lazyPseudoRemainder| |showAll?| |csch| |puiseux| |univariateSolve|
+ |OMunhandledSymbol| |red| |midpoints| |range| |problemPoints|
+ |rubiksGroup| |rk4| |interpolate| |adjoint| |asinh| |copy|
+ |invertibleElseSplit?| |positiveRemainder| |linSolve| |parent|
+ |minimize| |ScanArabic| |cyclicCopy| |compose| |relativeApprox| |inv|
+ |triangulate| |acosh| |d03edf| |OMputEndApp|
+ |stoseInternalLastSubResultant| |lowerCase?| |digits| |tubeRadius|
+ |update| |ground?| |asecIfCan| |stronglyReduce| |OMputAtp| |partition|
+ |atanh| |padicallyExpand| |polCase| |makeprod|
+ |selectSumOfSquaresRoutines| |constantToUnaryFunction| |ground|
+ |pushdterm| |numberOfMonomials| |f02xef| |purelyAlgebraic?|
+ |OMputInteger| |acoth| |autoCoerce| |OMgetEndAttr| |normalize|
+ |OMputString| |droot| |equality| |dequeue| |identitySquareMatrix|
+ |minimalPolynomial| |minus!| |torsion?| |leadingMonomial| |asech|
+ |shrinkable| |one?| |errorKind| |f02aaf| |leftRankPolynomial|
+ |completeHensel| |fractRadix| |leadingSupport| LODO2FUN |c06gbf|
+ |leadingCoefficient| |trigs2explogs| |rightFactorIfCan| |quasiRegular|
+ |numberOfDivisors| |setLength!| |push| |universe| |mpsode|
+ |generateIrredPoly| |interReduce| |multiple| |primitiveMonomials|
+ |sinhIfCan| |graeffe| |binaryFunction| |measure| |position|
+ |semiResultantReduitEuclidean| |totolex| |normalForm| |dualSignature|
+ |shiftRoots| |interpretString| |recoverAfterFail| |composites| |say|
+ |showTheIFTable| |stripCommentsAndBlanks| |numberOfFactors| |padecf|
+ |euclideanNormalForm| |perfectSqrt| |e02ahf| |testDim| |indices|
+ |match?| |child| |critB| |powerSum| |cCsch| |in?| |perfectSquare?|
+ |makeCrit| |octon| |componentUpperBound| |randnum| |bernoulli|
+ |sizeLess?| |psolve| |summation| |decomposeFunc|
+ |generalizedEigenvectors| |basisOfMiddleNucleus| |e01bhf|
+ |internalIntegrate0| |bitLength| |shallowExpand| |froot| |ScanRoman|
+ |selectfirst| |sequence| |quoted?| |quasiAlgebraicSet| |asechIfCan|
+ |makeYoungTableau| |content| |setTex!| |directSum| |indicialEquation|
+ |debug| |hash| |rational| |Gamma| |pseudoQuotient| |OMParseError?|
+ |divisorCascade| |unitNormal| |Ei| |lieAlgebra?| |midpoint| |count| D
+ |double| |component| |polyPart| |Lazard| |leadingIndex| |rootSimp|
+ |vconcat| |graphStates| |Nul| |tanSum| |totalDegree| |bothWays|
+ |outputForm| |reindex| |setfirst!| |removeSuperfluousQuasiComponents|
+ |externalList| |packageCall| |palgint| |sechIfCan| |OMputEndBind|
+ |movedPoints| |hasoln| |stoseInvertible?| |approximants|
+ |leftRegularRepresentation| |solid?| |eulerPhi| |radicalEigenvectors|
+ |integral?| |c06gsf| |whitePoint| |pade| |separateFactors| |f02akf|
+ |mapBivariate| |wordInGenerators| |getVariableOrder| |moebiusMu|
+ |phiCoord| |ksec| |UP2ifCan| |f01maf| |getBadValues| |rightOne|
+ |explogs2trigs| |setProperties| |fortranComplex| |lquo|
+ |solveLinearPolynomialEquation| |mainMonomial| |multiEuclideanTree|
+ |closed?| |zerosOf| |primPartElseUnitCanonical|
+ |exprHasWeightCosWXorSinWX| |realRoots| |d01ajf| |zero|
+ |splitSquarefree| |deepExpand| |goto| |integrate| |s17dcf|
+ |showIntensityFunctions| |declare!| |inputBinaryFile| |virtualDegree|
+ |readInt32!| |certainlySubVariety?| |capacity| |subQuasiComponent?|
+ |f07fdf| |pastel| |predicate| |mainVariable?| |taylorQuoByVar|
+ |cyclePartition| |simpsono| |And| |leftRecip|
+ |subResultantGcdEuclidean| |e04mbf| |redpps| |symmetric?|
+ |lazyResidueClass| |iidprod| |currentSubProgram| |complementaryBasis|
+ |Or| |subNodeOf?| |prime| |leftRemainder| |lprop| |fractionFreeGauss!|
+ |deepCopy| |reify| |makeTerm| |write!| |Not| |index?| |argumentListOf|
+ |integralMatrixAtInfinity| |karatsubaDivide| |bitTruth|
+ |leadingCoefficientRicDE| |irreducibleFactors| |iipow|
+ |numberOfComponents| |setMaxPoints3D| |nary?| |reducedForm|
+ |linearAssociatedOrder| |complexLimit| |vectorise| |allRootsOf| |bat|
+ |lastSubResultantElseSplit| |decreasePrecision| |OMopenFile|
+ |unprotectedRemoveRedundantFactors| |rotate!| |realZeros| |inverse|
+ |highCommonTerms| |rationalPoints| |antiAssociative?| |currentScope|
+ |parabolicCylindrical| |extension| |oneDimensionalArray|
+ |pointSizeDefault| |segment| |e02bdf| |eisensteinIrreducible?|
+ |halfExtendedResultant2| |sumOfKthPowerDivisors| |colorFunction|
+ |color| |mainVariable| |primaryDecomp| |s17aef| |totalDifferential|
+ |iiacos| |extendedResultant| |returns| |parameters| |trim|
+ |internalAugment| |maxint| |coHeight| |pointColorPalette| |nsqfree|
+ |simplifyLog| |id| |normInvertible?| |specialTrigs| |npcoef| |seed|
+ |rootPower| |selectPDERoutines| |physicalLength| |OMconnInDevice|
+ |zeroSetSplit| |mathieu11| |typeLists| |imagE| |doubleDisc|
+ |stirling2| |wordInStrongGenerators| |redmat| |isMult| |clikeUniv|
+ |table| |quadraticForm| |bivariateSLPEBR| |represents| |pair?|
+ |integral| |character?| UP2UTS |zeroSquareMatrix| |new| |cscIfCan|
+ |pol| |monicCompleteDecompose| |identification| |maxrow| |high|
+ |leadingTerm| |zeroDimensional?| |loadNativeModule| |ramified?|
+ |insert| |rowEchelon| |isobaric?| |numFunEvals| |insertRoot!| |diag|
+ |littleEndian| |eq?| |lazyPseudoQuotient| |normDeriv2|
+ |indicialEquationAtInfinity| |cAcos| |extractProperty| |fintegrate|
+ |hdmpToP| |lazyIrreducibleFactors| |genericRightDiscriminant|
+ |options| |e04naf| |eigenMatrix| |ratDsolve| |atanhIfCan| |gcdprim|
+ |eulerE| |unrankImproperPartitions0| |basis| |solveRetract| |pi|
+ |listLoops| |rewriteIdealWithQuasiMonicGenerators| |yellow|
+ |pleskenSplit| |chiSquare| |resetAttributeButtons| |comparison| |ipow|
+ |palglimint| |infinity| |triangSolve| |nand| |retractIfCan|
+ |torsionIfCan| |rightTrace| |f04mbf| |modularFactor|
+ |discriminantEuclidean| |routines| |splitLinear| |nullSpace| |string|
+ |algint| |var2StepsDefault| |makeGraphImage| |repeating| |pToDmp|
+ |triangular?| |tab1| |totalfract| |unary?| |equiv|
+ |expenseOfEvaluationIF| |lfunc| |rootOfIrreduciblePoly| |sum| |ptree|
+ |factorial| |resetNew| |kernel| |supRittWu?| |prologue| |sequences|
+ |rst| |isPower| |mapUnivariateIfCan| |primintfldpoly| |draw| |s21bbf|
+ |reducedSystem| |squareFreePart| |mapGen| |complete| |ratDenom|
+ |OMputEndAtp| |physicalLength!| |coord| |expintegrate|
+ |prolateSpheroidal| |augment| |left| |topFortranOutputStack|
+ |leastAffineMultiple| |mainCharacterization| |fi2df| |s18dcf| |f04jgf|
+ |exponentialOrder| |horizConcat| |reduceBasisAtInfinity| |right|
+ |rootKerSimp| |enterInCache| |isQuotient| |listRepresentation| |cTan|
+ |OMUnknownCD?| |symmetricTensors| |bfEntry| |genericRightTraceForm|
+ |linear?| |lp| |characteristicSerie| |edf2efi| |aLinear|
+ |singularAtInfinity?| |scale| |makeObject| |orbits| |lazyEvaluate|
+ |selectOrPolynomials| |squareFreePrim| |map|
+ |selectMultiDimensionalRoutines| |s17akf| |structuralConstants|
+ |presuper| |powern| |branchIfCan| |uniform01|
+ |selectOptimizationRoutines| |cos2sec| |elt| |arrayStack| |An|
+ |rewriteSetByReducingWithParticularGenerators| |magnitude|
+ |currentEnv| |stopTableGcd!| |roughSubIdeal?| |divide| |open?| |coef|
+ |numberOfNormalPoly| |block| |duplicates| |getOperator| |critpOrder|
+ |gcdcofact| |extendedSubResultantGcd| |bag| |df2st| |iisqrt3|
+ |fortranLiteralLine| |OMcloseConn| |nil| |infinite|
+ |arbitraryExponent| |approximate| |complex| |shallowMutable|
+ |canonical| |noetherian| |central| |partiallyOrderedSet|
+ |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors|
+ |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown|
+ |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate|
+ |shallowlyMutable| |commutative|) 
+\ No newline at end of file
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index e2378a89..6ccb511b 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5309 +1,5324 @@
 
-(3205083 . 3452645053)       
-((-3833 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-3963 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3904 ((|#2| $ (-564) |#2|) NIL) ((|#2| $ (-1226 (-564)) |#2|) 43)) (-2563 (($ $) 80)) (-1316 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 51) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 49) ((|#2| (-1 |#2| |#2| |#2|) $) 48)) (-3998 (((-564) (-1 (-112) |#2|) $) 27) (((-564) |#2| $) NIL) (((-564) |#2| $ (-564)) 96)) (-3035 (((-641 |#2|) $) 13)) (-3669 (($ (-1 (-112) |#2| |#2|) $ $) 63) (($ $ $) NIL)) (-2714 (($ (-1 |#2| |#2|) $) 37)) (-4357 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 59)) (-4248 (($ |#2| $ (-564)) NIL) (($ $ $ (-564)) 66)) (-2139 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29)) (-4377 (((-112) (-1 (-112) |#2|) $) 23)) (-4366 ((|#2| $ (-564) |#2|) NIL) ((|#2| $ (-564)) NIL) (($ $ (-1226 (-564))) 65)) (-2114 (($ $ (-564)) 75) (($ $ (-1226 (-564))) 74)) (-4062 (((-767) (-1 (-112) |#2|) $) 34) (((-767) |#2| $) NIL)) (-3806 (($ $ $ (-564)) 68)) (-3926 (($ $) 67)) (-2435 (($ (-641 |#2|)) 72)) (-3696 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 87) (($ (-641 $)) 85)) (-2423 (((-858) $) 92)) (-1368 (((-112) (-1 (-112) |#2|) $) 22)) (-2974 (((-112) $ $) 95)) (-2999 (((-112) $ $) 99))) 
-(((-18 |#1| |#2|) (-10 -8 (-15 -2974 ((-112) |#1| |#1|)) (-15 -2423 ((-858) |#1|)) (-15 -2999 ((-112) |#1| |#1|)) (-15 -3963 (|#1| |#1|)) (-15 -3963 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2563 (|#1| |#1|)) (-15 -3806 (|#1| |#1| |#1| (-564))) (-15 -3833 ((-112) |#1|)) (-15 -3669 (|#1| |#1| |#1|)) (-15 -3998 ((-564) |#2| |#1| (-564))) (-15 -3998 ((-564) |#2| |#1|)) (-15 -3998 ((-564) (-1 (-112) |#2|) |#1|)) (-15 -3833 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3669 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3904 (|#2| |#1| (-1226 (-564)) |#2|)) (-15 -4248 (|#1| |#1| |#1| (-564))) (-15 -4248 (|#1| |#2| |#1| (-564))) (-15 -2114 (|#1| |#1| (-1226 (-564)))) (-15 -2114 (|#1| |#1| (-564))) (-15 -4366 (|#1| |#1| (-1226 (-564)))) (-15 -4357 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3696 (|#1| (-641 |#1|))) (-15 -3696 (|#1| |#1| |#1|)) (-15 -3696 (|#1| |#2| |#1|)) (-15 -3696 (|#1| |#1| |#2|)) (-15 -2435 (|#1| (-641 |#2|))) (-15 -2139 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -1316 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1316 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1316 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4366 (|#2| |#1| (-564))) (-15 -4366 (|#2| |#1| (-564) |#2|)) (-15 -3904 (|#2| |#1| (-564) |#2|)) (-15 -4062 ((-767) |#2| |#1|)) (-15 -3035 ((-641 |#2|) |#1|)) (-15 -4062 ((-767) (-1 (-112) |#2|) |#1|)) (-15 -4377 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -1368 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2714 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4357 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3926 (|#1| |#1|))) (-19 |#2|) (-1209)) (T -18)) 
+(3219914 . 3452782389)       
+((-1757 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-2239 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3877 ((|#2| $ (-564) |#2|) NIL) ((|#2| $ (-1229 (-564)) |#2|) 43)) (-2087 (($ $) 80)) (-1320 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 51) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 49) ((|#2| (-1 |#2| |#2| |#2|) $) 48)) (-3979 (((-564) (-1 (-112) |#2|) $) 27) (((-564) |#2| $) NIL) (((-564) |#2| $ (-564)) 96)) (-2936 (((-642 |#2|) $) 13)) (-2740 (($ (-1 (-112) |#2| |#2|) $ $) 63) (($ $ $) NIL)) (-2613 (($ (-1 |#2| |#2|) $) 37)) (-4358 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 59)) (-4238 (($ |#2| $ (-564)) NIL) (($ $ $ (-564)) 66)) (-3254 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29)) (-2121 (((-112) (-1 (-112) |#2|) $) 23)) (-4368 ((|#2| $ (-564) |#2|) NIL) ((|#2| $ (-564)) NIL) (($ $ (-1229 (-564))) 65)) (-2073 (($ $ (-564)) 75) (($ $ (-1229 (-564))) 74)) (-4043 (((-769) (-1 (-112) |#2|) $) 34) (((-769) |#2| $) NIL)) (-2568 (($ $ $ (-564)) 68)) (-3901 (($ $) 67)) (-2337 (($ (-642 |#2|)) 72)) (-3651 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 87) (($ (-642 $)) 85)) (-2327 (((-860) $) 92)) (-2710 (((-112) (-1 (-112) |#2|) $) 22)) (-2872 (((-112) $ $) 95)) (-2897 (((-112) $ $) 99))) 
+(((-18 |#1| |#2|) (-10 -8 (-15 -2872 ((-112) |#1| |#1|)) (-15 -2327 ((-860) |#1|)) (-15 -2897 ((-112) |#1| |#1|)) (-15 -2239 (|#1| |#1|)) (-15 -2239 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2087 (|#1| |#1|)) (-15 -2568 (|#1| |#1| |#1| (-564))) (-15 -1757 ((-112) |#1|)) (-15 -2740 (|#1| |#1| |#1|)) (-15 -3979 ((-564) |#2| |#1| (-564))) (-15 -3979 ((-564) |#2| |#1|)) (-15 -3979 ((-564) (-1 (-112) |#2|) |#1|)) (-15 -1757 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -2740 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3877 (|#2| |#1| (-1229 (-564)) |#2|)) (-15 -4238 (|#1| |#1| |#1| (-564))) (-15 -4238 (|#1| |#2| |#1| (-564))) (-15 -2073 (|#1| |#1| (-1229 (-564)))) (-15 -2073 (|#1| |#1| (-564))) (-15 -4368 (|#1| |#1| (-1229 (-564)))) (-15 -4358 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3651 (|#1| (-642 |#1|))) (-15 -3651 (|#1| |#1| |#1|)) (-15 -3651 (|#1| |#2| |#1|)) (-15 -3651 (|#1| |#1| |#2|)) (-15 -2337 (|#1| (-642 |#2|))) (-15 -3254 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -1320 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1320 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1320 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4368 (|#2| |#1| (-564))) (-15 -4368 (|#2| |#1| (-564) |#2|)) (-15 -3877 (|#2| |#1| (-564) |#2|)) (-15 -4043 ((-769) |#2| |#1|)) (-15 -2936 ((-642 |#2|) |#1|)) (-15 -4043 ((-769) (-1 (-112) |#2|) |#1|)) (-15 -2121 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2710 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2613 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4358 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3901 (|#1| |#1|))) (-19 |#2|) (-1212)) (T -18)) 
 NIL 
-(-10 -8 (-15 -2974 ((-112) |#1| |#1|)) (-15 -2423 ((-858) |#1|)) (-15 -2999 ((-112) |#1| |#1|)) (-15 -3963 (|#1| |#1|)) (-15 -3963 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2563 (|#1| |#1|)) (-15 -3806 (|#1| |#1| |#1| (-564))) (-15 -3833 ((-112) |#1|)) (-15 -3669 (|#1| |#1| |#1|)) (-15 -3998 ((-564) |#2| |#1| (-564))) (-15 -3998 ((-564) |#2| |#1|)) (-15 -3998 ((-564) (-1 (-112) |#2|) |#1|)) (-15 -3833 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3669 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3904 (|#2| |#1| (-1226 (-564)) |#2|)) (-15 -4248 (|#1| |#1| |#1| (-564))) (-15 -4248 (|#1| |#2| |#1| (-564))) (-15 -2114 (|#1| |#1| (-1226 (-564)))) (-15 -2114 (|#1| |#1| (-564))) (-15 -4366 (|#1| |#1| (-1226 (-564)))) (-15 -4357 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3696 (|#1| (-641 |#1|))) (-15 -3696 (|#1| |#1| |#1|)) (-15 -3696 (|#1| |#2| |#1|)) (-15 -3696 (|#1| |#1| |#2|)) (-15 -2435 (|#1| (-641 |#2|))) (-15 -2139 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -1316 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1316 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1316 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4366 (|#2| |#1| (-564))) (-15 -4366 (|#2| |#1| (-564) |#2|)) (-15 -3904 (|#2| |#1| (-564) |#2|)) (-15 -4062 ((-767) |#2| |#1|)) (-15 -3035 ((-641 |#2|) |#1|)) (-15 -4062 ((-767) (-1 (-112) |#2|) |#1|)) (-15 -4377 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -1368 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2714 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4357 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3926 (|#1| |#1|))) 
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-(((-19 |#1|) (-140) (-1209)) (T -19)) 
+(-10 -8 (-15 -2872 ((-112) |#1| |#1|)) (-15 -2327 ((-860) |#1|)) (-15 -2897 ((-112) |#1| |#1|)) (-15 -2239 (|#1| |#1|)) (-15 -2239 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2087 (|#1| |#1|)) (-15 -2568 (|#1| |#1| |#1| (-564))) (-15 -1757 ((-112) |#1|)) (-15 -2740 (|#1| |#1| |#1|)) (-15 -3979 ((-564) |#2| |#1| (-564))) (-15 -3979 ((-564) |#2| |#1|)) (-15 -3979 ((-564) (-1 (-112) |#2|) |#1|)) (-15 -1757 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -2740 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3877 (|#2| |#1| (-1229 (-564)) |#2|)) (-15 -4238 (|#1| |#1| |#1| (-564))) (-15 -4238 (|#1| |#2| |#1| (-564))) (-15 -2073 (|#1| |#1| (-1229 (-564)))) (-15 -2073 (|#1| |#1| (-564))) (-15 -4368 (|#1| |#1| (-1229 (-564)))) (-15 -4358 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3651 (|#1| (-642 |#1|))) (-15 -3651 (|#1| |#1| |#1|)) (-15 -3651 (|#1| |#2| |#1|)) (-15 -3651 (|#1| |#1| |#2|)) (-15 -2337 (|#1| (-642 |#2|))) (-15 -3254 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -1320 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -1320 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1320 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4368 (|#2| |#1| (-564))) (-15 -4368 (|#2| |#1| (-564) |#2|)) (-15 -3877 (|#2| |#1| (-564) |#2|)) (-15 -4043 ((-769) |#2| |#1|)) (-15 -2936 ((-642 |#2|) |#1|)) (-15 -4043 ((-769) (-1 (-112) |#2|) |#1|)) (-15 -2121 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2710 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2613 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4358 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3901 (|#1| |#1|))) 
+((-2907 (((-112) $ $) 19 (|has| |#1| (-1097)))) (-1765 (((-1267) $ (-564) (-564)) 41 (|has| $ (-6 -4411)))) (-1757 (((-112) (-1 (-112) |#1| |#1|) $) 99) (((-112) $) 93 (|has| |#1| (-848)))) (-2239 (($ (-1 (-112) |#1| |#1|) $) 90 (|has| $ (-6 -4411))) (($ $) 89 (-12 (|has| |#1| (-848)) (|has| $ (-6 -4411))))) (-2383 (($ (-1 (-112) |#1| |#1|) $) 100) (($ $) 94 (|has| |#1| (-848)))) (-3697 (((-112) $ (-769)) 8)) (-3877 ((|#1| $ (-564) |#1|) 53 (|has| $ (-6 -4411))) ((|#1| $ (-1229 (-564)) |#1|) 59 (|has| $ (-6 -4411)))) (-1700 (($ (-1 (-112) |#1|) $) 76 (|has| $ (-6 -4410)))) (-1976 (($) 7 T CONST)) (-2087 (($ $) 91 (|has| $ (-6 -4411)))) (-3115 (($ $) 101)) (-2595 (($ $) 79 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410))))) (-2490 (($ |#1| $) 78 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410)))) (($ (-1 (-112) |#1|) $) 75 (|has| $ (-6 -4410)))) (-1320 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) 77 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410)))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) 74 (|has| $ (-6 -4410))) ((|#1| (-1 |#1| |#1| |#1|) $) 73 (|has| $ (-6 -4410)))) (-2625 ((|#1| $ (-564) |#1|) 54 (|has| $ (-6 -4411)))) (-2551 ((|#1| $ (-564)) 52)) (-3979 (((-564) (-1 (-112) |#1|) $) 98) (((-564) |#1| $) 97 (|has| |#1| (-1097))) (((-564) |#1| $ (-564)) 96 (|has| |#1| (-1097)))) (-2936 (((-642 |#1|) $) 31 (|has| $ (-6 -4410)))) (-4227 (($ (-769) |#1|) 70)) (-3462 (((-112) $ (-769)) 9)) (-2040 (((-564) $) 44 (|has| (-564) (-848)))) (-2755 (($ $ $) 88 (|has| |#1| (-848)))) (-2740 (($ (-1 (-112) |#1| |#1|) $ $) 102) (($ $ $) 95 (|has| |#1| (-848)))) (-3234 (((-642 |#1|) $) 30 (|has| $ (-6 -4410)))) (-2776 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410))))) (-3421 (((-564) $) 45 (|has| (-564) (-848)))) (-1520 (($ $ $) 87 (|has| |#1| (-848)))) (-2613 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4411)))) (-4358 (($ (-1 |#1| |#1|) $) 36) (($ (-1 |#1| |#1| |#1|) $ $) 65)) (-3576 (((-112) $ (-769)) 10)) (-3315 (((-1155) $) 22 (|has| |#1| (-1097)))) (-4238 (($ |#1| $ (-564)) 61) (($ $ $ (-564)) 60)) (-3997 (((-642 (-564)) $) 47)) (-4145 (((-112) (-564) $) 48)) (-4033 (((-1117) $) 21 (|has| |#1| (-1097)))) (-2557 ((|#1| $) 43 (|has| (-564) (-848)))) (-3254 (((-3 |#1| "failed") (-1 (-112) |#1|) $) 72)) (-2696 (($ $ |#1|) 42 (|has| $ (-6 -4411)))) (-2121 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4410)))) (-3215 (($ $ (-642 (-294 |#1|))) 27 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ (-294 |#1|)) 26 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097)))) (($ $ (-642 |#1|) (-642 |#1|)) 24 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097))))) (-4245 (((-112) $ $) 14)) (-3441 (((-112) |#1| $) 46 (-12 (|has| $ (-6 -4410)) (|has| |#1| (-1097))))) (-2724 (((-642 |#1|) $) 49)) (-3719 (((-112) $) 11)) (-2972 (($) 12)) (-4368 ((|#1| $ (-564) |#1|) 51) ((|#1| $ (-564)) 50) (($ $ (-1229 (-564))) 64)) (-2073 (($ $ (-564)) 63) (($ $ (-1229 (-564))) 62)) (-4043 (((-769) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4410))) (((-769) |#1| $) 29 (-12 (|has| |#1| (-1097)) (|has| $ (-6 -4410))))) (-2568 (($ $ $ (-564)) 92 (|has| $ (-6 -4411)))) (-3901 (($ $) 13)) (-1314 (((-536) $) 80 (|has| |#1| (-612 (-536))))) (-2337 (($ (-642 |#1|)) 71)) (-3651 (($ $ |#1|) 69) (($ |#1| $) 68) (($ $ $) 67) (($ (-642 $)) 66)) (-2327 (((-860) $) 18 (|has| |#1| (-611 (-860))))) (-1648 (((-112) $ $) 23 (|has| |#1| (-1097)))) (-2710 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4410)))) (-2934 (((-112) $ $) 85 (|has| |#1| (-848)))) (-2908 (((-112) $ $) 84 (|has| |#1| (-848)))) (-2872 (((-112) $ $) 20 (|has| |#1| (-1097)))) (-2922 (((-112) $ $) 86 (|has| |#1| (-848)))) (-2897 (((-112) $ $) 83 (|has| |#1| (-848)))) (-2127 (((-769) $) 6 (|has| $ (-6 -4410))))) 
+(((-19 |#1|) (-140) (-1212)) (T -19)) 
 NIL 
-(-13 (-373 |t#1|) (-10 -7 (-6 -4408))) 
-(((-34) . T) ((-102) -2807 (|has| |#1| (-1094)) (|has| |#1| (-846))) ((-611 (-858)) -2807 (|has| |#1| (-1094)) (|has| |#1| (-846)) (|has| |#1| (-611 (-858)))) ((-151 |#1|) . T) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-286 #0=(-564) |#1|) . T) ((-288 #0# |#1|) . T) ((-309 |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) ((-373 |#1|) . T) ((-489 |#1|) . T) ((-602 #0# |#1|) . T) ((-514 |#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) ((-647 |#1|) . T) ((-846) |has| |#1| (-846)) ((-1094) -2807 (|has| |#1| (-1094)) (|has| |#1| (-846))) ((-1209) . T)) 
-((-4012 (((-3 $ "failed") $ $) 12)) (-3082 (($ $) NIL) (($ $ $) 9)) (* (($ (-917) $) NIL) (($ (-767) $) 16) (($ (-564) $) 26))) 
-(((-20 |#1|) (-10 -8 (-15 * (|#1| (-564) |#1|)) (-15 -3082 (|#1| |#1| |#1|)) (-15 -3082 (|#1| |#1|)) (-15 -4012 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-767) |#1|)) (-15 * (|#1| (-917) |#1|))) (-21)) (T -20)) 
+(-13 (-373 |t#1|) (-10 -7 (-6 -4411))) 
+(((-34) . T) ((-102) -2706 (|has| |#1| (-1097)) (|has| |#1| (-848))) ((-611 (-860)) -2706 (|has| |#1| (-1097)) (|has| |#1| (-848)) (|has| |#1| (-611 (-860)))) ((-151 |#1|) . T) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-286 #0=(-564) |#1|) . T) ((-288 #0# |#1|) . T) ((-309 |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097))) ((-373 |#1|) . T) ((-489 |#1|) . T) ((-602 #0# |#1|) . T) ((-514 |#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097))) ((-649 |#1|) . T) ((-848) |has| |#1| (-848)) ((-1097) -2706 (|has| |#1| (-1097)) (|has| |#1| (-848))) ((-1212) . T)) 
+((-1532 (((-3 $ "failed") $ $) 12)) (-2987 (($ $) NIL) (($ $ $) 9)) (* (($ (-919) $) NIL) (($ (-769) $) 16) (($ (-564) $) 26))) 
+(((-20 |#1|) (-10 -8 (-15 -2987 (|#1| |#1| |#1|)) (-15 -2987 (|#1| |#1|)) (-15 * (|#1| (-564) |#1|)) (-15 -1532 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-769) |#1|)) (-15 * (|#1| (-919) |#1|))) (-21)) (T -20)) 
 NIL 
-(-10 -8 (-15 * (|#1| (-564) |#1|)) (-15 -3082 (|#1| |#1| |#1|)) (-15 -3082 (|#1| |#1|)) (-15 -4012 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-767) |#1|)) (-15 * (|#1| (-917) |#1|))) 
-((-3009 (((-112) $ $) 7)) (-1494 (((-112) $) 17)) (-4012 (((-3 $ "failed") $ $) 20)) (-4080 (($) 18 T CONST)) (-2766 (((-1152) $) 10)) (-4052 (((-1114) $) 11)) (-2423 (((-858) $) 12)) (-1860 (((-112) $ $) 9)) (-2403 (($) 19 T CONST)) (-2974 (((-112) $ $) 6)) (-3082 (($ $) 23) (($ $ $) 22)) (-3070 (($ $ $) 15)) (* (($ (-917) $) 14) (($ (-767) $) 16) (($ (-564) $) 21))) 
+(-10 -8 (-15 -2987 (|#1| |#1| |#1|)) (-15 -2987 (|#1| |#1|)) (-15 * (|#1| (-564) |#1|)) (-15 -1532 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-769) |#1|)) (-15 * (|#1| (-919) |#1|))) 
+((-2907 (((-112) $ $) 7)) (-2952 (((-112) $) 17)) (-1532 (((-3 $ "failed") $ $) 20)) (-1976 (($) 18 T CONST)) (-3315 (((-1155) $) 10)) (-4033 (((-1117) $) 11)) (-2327 (((-860) $) 12)) (-1648 (((-112) $ $) 9)) (-2312 (($) 19 T CONST)) (-2872 (((-112) $ $) 6)) (-2987 (($ $) 23) (($ $ $) 22)) (-2974 (($ $ $) 15)) (* (($ (-919) $) 14) (($ (-769) $) 16) (($ (-564) $) 24))) 
 (((-21) (-140)) (T -21)) 
-((-3082 (*1 *1 *1) (-4 *1 (-21))) (-3082 (*1 *1 *1 *1) (-4 *1 (-21))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-21)) (-5 *2 (-564))))) 
-(-13 (-131) (-10 -8 (-15 -3082 ($ $)) (-15 -3082 ($ $ $)) (-15 * ($ (-564) $)))) 
-(((-23) . T) ((-25) . T) ((-102) . T) ((-131) . T) ((-611 (-858)) . T) ((-1094) . T)) 
-((-1494 (((-112) $) 10)) (-4080 (($) 15)) (* (($ (-917) $) 14) (($ (-767) $) 19))) 
-(((-22 |#1|) (-10 -8 (-15 * (|#1| (-767) |#1|)) (-15 -1494 ((-112) |#1|)) (-15 -4080 (|#1|)) (-15 * (|#1| (-917) |#1|))) (-23)) (T -22)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-767) |#1|)) (-15 -1494 ((-112) |#1|)) (-15 -4080 (|#1|)) (-15 * (|#1| (-917) |#1|))) 
-((-3009 (((-112) $ $) 7)) (-1494 (((-112) $) 17)) (-4080 (($) 18 T CONST)) (-2766 (((-1152) $) 10)) (-4052 (((-1114) $) 11)) (-2423 (((-858) $) 12)) (-1860 (((-112) $ $) 9)) (-2403 (($) 19 T CONST)) (-2974 (((-112) $ $) 6)) (-3070 (($ $ $) 15)) (* (($ (-917) $) 14) (($ (-767) $) 16))) 
+((-2987 (*1 *1 *1) (-4 *1 (-21))) (-2987 (*1 *1 *1 *1) (-4 *1 (-21)))) 
+(-13 (-131) (-644 (-564)) (-10 -8 (-15 -2987 ($ $)) (-15 -2987 ($ $ $)))) 
+(((-23) . T) ((-25) . T) ((-102) . T) ((-131) . T) ((-611 (-860)) . T) ((-644 (-564)) . T) ((-1097) . T)) 
+((-2952 (((-112) $) 10)) (-1976 (($) 15)) (* (($ (-919) $) 14) (($ (-769) $) 19))) 
+(((-22 |#1|) (-10 -8 (-15 * (|#1| (-769) |#1|)) (-15 -2952 ((-112) |#1|)) (-15 -1976 (|#1|)) (-15 * (|#1| (-919) |#1|))) (-23)) (T -22)) 
+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 
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 NIL 
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 (((-93) (-140)) (T -93)) 
 NIL 
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 NIL 
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 (((-95) (-140)) (T -95)) 
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 NIL 
 (((-98) (-140)) (T -98)) 
 NIL 
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-((-3009 (((-112) $ $) 10))) 
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-NIL 
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-((-3009 (((-112) $ $) 7)) (-2974 (((-112) $ $) 6))) 
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+((-2269 (*1 *2 *3 *4) (-12 (-5 *4 (-642 *3)) (-4 *3 (-1238 *5)) (-4 *5 (-13 (-452) (-147))) (-5 *2 (-418 *3)) (-5 *1 (-100 *5 *3)))) (-2269 (*1 *2 *3 *3) (-12 (-4 *4 (-13 (-452) (-147))) (-5 *2 (-418 *3)) (-5 *1 (-100 *4 *3)) (-4 *3 (-1238 *4))))) 
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+((-2907 (((-112) $ $) 10))) 
+(((-101 |#1|) (-10 -8 (-15 -2907 ((-112) |#1| |#1|))) (-102)) (T -101)) 
+NIL 
+(-10 -8 (-15 -2907 ((-112) |#1| |#1|))) 
+((-2907 (((-112) $ $) 7)) (-2872 (((-112) $ $) 6))) 
 (((-102) (-140)) (T -102)) 
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-NIL 
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 (((-139) (-13 (-185) (-611 (-187)))) (T -139)) 
 NIL 
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+(((-151 |#1|) (-140) (-1212)) (T -151)) 
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+(((-34) . T) ((-102) |has| |#1| (-1097)) ((-611 (-860)) -2706 (|has| |#1| (-1097)) (|has| |#1| (-611 (-860)))) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-309 |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097))) ((-489 |#1|) . T) ((-514 |#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1097))) ((-1097) |has| |#1| (-1097)) ((-1212) . T)) 
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+(((-154) (-13 (-1080) (-10 -8 (-15 -3342 ((-642 (-1132)) $)) (-15 -2474 ((-1132) $))))) (T -154)) 
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+(-13 (-1080) (-10 -8 (-15 -3342 ((-642 (-1132)) $)) (-15 -2474 ((-1132) $)))) 
+((-3067 (((-642 (-169 |#2|)) |#1| |#2|) 50))) 
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+((-3067 (*1 *2 *3 *4) (-12 (-5 *2 (-642 (-169 *4))) (-5 *1 (-155 *3 *4)) (-4 *3 (-1238 (-169 (-564)))) (-4 *4 (-13 (-363) (-846)))))) 
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+((-2907 (((-112) $ $) NIL)) (-1843 (((-1211) $) 12)) (-1833 (((-1132) $) 9)) (-3315 (((-1155) $) NIL)) (-4033 (((-1117) $) NIL)) (-2327 (((-860) $) 19) (($ (-1178)) NIL) (((-1178) $) NIL)) (-1648 (((-112) $ $) NIL)) (-2872 (((-112) $ $) NIL))) 
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-(((-193) (-783)) (T -193)) 
-NIL 
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 NIL 
 (-13 (-235 |t#1|)) 
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-NIL 
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-NIL 
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-NIL 
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(((-769) $) NIL (|has| $ (-6 -4410))))) 
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 NIL 
 (-238 |#1| |#2|) 
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-NIL 
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+NIL 
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 (((-243) (-140)) (T -243)) 
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 NIL 
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-NIL 
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-NIL 
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-(((-102) . T) ((-614 |#1|) . T) ((-611 (-858)) . T) ((-846) . T) ((-1034 |#1|) . T) ((-1094) . T)) 
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-(((-268) (-835)) (T -268)) 
-NIL 
-(-835) 
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-(((-269) (-835)) (T -269)) 
-NIL 
-(-835) 
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-(((-270) (-835)) (T -270)) 
-NIL 
-(-835) 
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-NIL 
-(-835) 
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-NIL 
-(-835) 
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-(((-273) (-835)) (T -273)) 
-NIL 
-(-835) 
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-(((-274) (-835)) (T -274)) 
-NIL 
-(-835) 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
+(-837) 
+((-2907 (((-112) $ $) NIL)) (-1916 (((-1033) (-2 (|:| |lfn| (-642 (-316 (-225)))) (|:| -3366 (-642 (-225))))) NIL) (((-1033) (-2 (|:| |fn| (-316 (-225))) (|:| -3366 (-642 (-225))) (|:| |lb| (-642 (-841 (-225)))) (|:| |cf| (-642 (-316 (-225)))) (|:| |ub| (-642 (-841 (-225)))))) 95)) (-3978 (((-2 (|:| -3978 (-379)) (|:| |explanations| (-1155))) (-1060) (-2 (|:| |fn| (-316 (-225))) (|:| -3366 (-642 (-225))) (|:| |lb| (-642 (-841 (-225)))) (|:| |cf| (-642 (-316 (-225)))) (|:| |ub| (-642 (-841 (-225)))))) 32) (((-2 (|:| -3978 (-379)) (|:| |explanations| (-1155))) (-1060) (-2 (|:| |lfn| (-642 (-316 (-225)))) (|:| -3366 (-642 (-225))))) NIL)) (-3315 (((-1155) $) NIL)) (-4033 (((-1117) $) NIL)) (-2327 (((-860) $) NIL)) (-1648 (((-112) $ $) NIL)) (-2872 (((-112) $ $) NIL))) 
+(((-274) (-837)) (T -274)) 
+NIL 
+(-837) 
+((-2907 (((-112) $ $) NIL)) (-2755 (($ $ $) NIL)) (-1520 (($ $ $) NIL)) (-3315 (((-1155) $) NIL)) (-4033 (((-1117) $) NIL)) (-2135 (((-642 (-564)) $) 29)) (-2775 (((-769) $) 27)) (-2327 (((-860) $) 36) (($ (-642 (-564))) 23)) (-1648 (((-112) $ $) NIL)) (-4053 (($ (-769)) 33)) (-2934 (((-112) $ $) NIL)) (-2908 (((-112) $ $) NIL)) (-2872 (((-112) $ $) 9)) (-2922 (((-112) $ $) NIL)) (-2897 (((-112) $ $) 17))) 
+(((-275) (-13 (-848) (-10 -8 (-15 -2327 ($ (-642 (-564)))) (-15 -2775 ((-769) $)) (-15 -2135 ((-642 (-564)) $)) (-15 -4053 ($ (-769)))))) (T -275)) 
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+(-13 (-848) (-10 -8 (-15 -2327 ($ (-642 (-564)))) (-15 -2775 ((-769) $)) (-15 -2135 ((-642 (-564)) $)) (-15 -4053 ($ (-769))))) 
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*3) (-1000))))) (-1820 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3096 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3551 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3257 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2979 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2945 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2844 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2365 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-4188 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-1342 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3189 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2611 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2932 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2876 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3588 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-1716 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2390 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-2651 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-4388 (*1 *2) (-12 (-4 *2 (-13 (-430 *3) (-1000))) (-5 *1 (-276 *3 *2)) (-4 *3 (-556)))) (-2577 (*1 *2) (-12 (-4 *2 (-13 (-430 *3) (-1000))) (-5 *1 (-276 *3 *2)) (-4 *3 (-556)))) (-3307 (*1 *2 *2) (-12 (-5 *2 (-114)) (-4 *3 (-556)) (-5 *1 (-276 *3 *4)) (-4 *4 (-13 (-430 *3) (-1000))))) (-2357 (*1 *2 *3) (-12 (-5 *3 (-114)) (-4 *4 (-556)) (-5 *2 (-112)) (-5 *1 (-276 *4 *5)) (-4 *5 (-13 (-430 *4) (-1000))))) (-4265 (*1 *2) (-12 (-4 *2 (-13 (-430 *3) (-1000))) (-5 *1 (-276 *3 *2)) (-4 *3 (-556)))) (-2683 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3951 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3938 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3926 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3913 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3900 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3888 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3875 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3863 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3851 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3839 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3827 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3816 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3803 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3791 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3776 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3763 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3750 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3739 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3727 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3716 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3704 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3693 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3679 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-3612 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000))))) (-1723 (*1 *2 *2) (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-1000)))))) 
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+(((-277 |#1| |#2|) (-10 -7 (-15 -3941 (|#2| |#2|)) (-15 -3941 (|#2| |#2| (-1173))) (-15 -3229 ((-2 (|:| |func| |#2|) (|:| |kers| (-642 (-610 |#2|))) (|:| |vals| (-642 |#2|))) |#2| (-1173))) (-15 -2662 (|#2| |#2|)) (-15 -2662 (|#2| |#2| (-1173))) (-15 -1433 ((-3 |#2| "failed") (-642 (-610 |#2|)) |#2| (-1173))) (-15 -3829 (|#2| |#2| (-610 |#2|))) (-15 -2729 (|#2| (-407 (-564)) |#2|))) (-13 (-556) (-1036 (-564)) (-637 (-564))) (-13 (-27) (-1197) (-430 |#1|))) (T -277)) 
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 ((** (($ $ $) 10))) 
 (((-283 |#1|) (-10 -8 (-15 ** (|#1| |#1| |#1|))) (-284)) (T -283)) 
 NIL 
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-NIL 
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+NIL 
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 (((-286 |#1| |#2|) . T)) 
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 (((-290) (-140)) (T -290)) 
 NIL 
-(-13 (-1045) (-111 $ $) (-10 -7 (-6 -4400))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-111 $ $) . T) ((-131) . T) ((-614 (-564)) . T) ((-611 (-858)) . T) ((-644 $) . T) ((-722) . T) ((-1051 $) . T) ((-1045) . T) ((-1052) . T) ((-1106) . T) ((-1094) . T)) 
-((-4346 (($ (-506) (-506) (-1098) $) 19)) (-2772 (($ (-506) (-641 (-961)) $) 23)) (-3931 (((-641 (-1079)) $) 10)) (-1610 (($) 25)) (-3136 (((-687 (-1098)) (-506) (-506) $) 18)) (-3190 (((-641 (-961)) (-506) $) 22)) (-2994 (($) 7)) (-4367 (($) 24)) (-2423 (((-858) $) 29)) (-2530 (($) 26))) 
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-NIL 
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 NIL 
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 NIL 
 (-329 |#1|) 
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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 (-637 |t#1|) (-10 -7 (IF (|has| |t#1| (-637 (-564))) (-6 (-637 (-564))) |%noBranch|))) 
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+NIL 
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 (((-387) (-140)) (T -387)) 
 NIL 
-(-13 (-556) (-846) (-1034 (-564))) 
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 (((-388) (-389)) (T -388)) 
 NIL 
 (-389) 
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 (((-389) (-140)) (T -389)) 
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-(((-102) . T) ((-614 #0=(-1152)) . T) ((-611 (-858)) . T) ((-611 #0#) . T) ((-490 #0#) . T) ((-1094) . T)) 
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-NIL 
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+NIL 
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 (((-452) (-140)) (T -452)) 
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-NIL 
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-NIL 
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-((-4274 (*1 *1) (-5 *1 (-477)))) 
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+((-4265 (*1 *1) (-5 *1 (-477)))) 
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+((-1833 (*1 *2 *1) (-12 (-5 *2 (-1132)) (-5 *1 (-478)))) (-1843 (*1 *2 *1) (-12 (-5 *2 (-1132)) (-5 *1 (-478))))) 
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 NIL 
 (-238 |#1| |#2|) 
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 NIL 
 (-335 |#1| |#2| |#3| |#4|) 
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 NIL 
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-NIL 
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 NIL 
 (-19 |#1|) 
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 NIL 
 (-57 |#1| (-496 |#1| |#3|) (-496 |#1| |#2|)) 
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 NIL 
 (-13 (-21) (-509 |#1| |#2|)) 
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 NIL 
 (-13 (-23) (-509 |#1| |#2|)) 
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-(((-510 |#1| |#2|) (-13 (-788) (-509 |#1| |#2|)) (-788) (-846)) (T -510)) 
-NIL 
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-(((-511 |#1| |#2|) (-13 (-789) (-509 |#1| |#2|)) (-789) (-846)) (T -511)) 
-NIL 
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+NIL 
+(-13 (-790) (-509 |#1| |#2|)) 
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+(((-511 |#1| |#2|) (-13 (-791) (-509 |#1| |#2|)) (-791) (-848)) (T -511)) 
+NIL 
+(-13 (-791) (-509 |#1| |#2|)) 
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 NIL 
 (-509 |#1| |#2|) 
-((-3291 (($ $ (-641 |#2|) (-641 |#3|)) NIL) (($ $ |#2| |#3|) 12))) 
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+((-3215 (($ $ (-642 |#2|) (-642 |#3|)) NIL) (($ $ |#2| |#3|) 12))) 
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 NIL 
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-((-3291 (($ $ (-641 |#1|) (-641 |#2|)) 7) (($ $ |#1| |#2|) 6))) 
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+(((-515 |#1| |#2| |#3|) (-323 |#1| |#2|) (-1097) (-131) |#2|) (T -515)) 
 NIL 
 (-323 |#1| |#2|) 
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-(-13 (-1077) (-10 -8 (-15 -2940 ((-1129) $)) (-15 -1353 ((-1129) $)) (-15 -3603 ((-1129) $)))) 
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 NIL 
 (-329 (-581 |#1|)) 
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+(((-519 |#1| |#2| |#3| |#4| |#5|) (-57 |#1| |#4| |#5|) (-1212) (-564) (-564) (-373 |#1|) (-373 |#1|)) (T -519)) 
 NIL 
 (-57 |#1| |#4| |#5|) 
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(|has| $ (-6 -4408)))) (-4082 (($ $ (-641 $)) NIL (|has| $ (-6 -4408)))) (-1466 (($ (-1 (-112) |#1|) $) NIL)) (-1667 (($ (-1 (-112) |#1|) $) NIL (|has| $ (-6 -4407)))) (-1772 ((|#1| $) NIL)) (-4080 (($) NIL T CONST)) (-2563 (($ $) 28 (|has| $ (-6 -4408)))) (-3200 (($ $) 29)) (-2671 (($ $) 18) (($ $ (-767)) 35)) (-2679 (($ $) 66 (|has| |#1| (-1094)))) (-2696 (($ $) NIL (-12 (|has| $ (-6 -4407)) (|has| |#1| (-1094))))) (-1945 (($ |#1| $) NIL (|has| |#1| (-1094))) (($ (-1 (-112) |#1|) $) NIL)) (-2591 (($ (-1 (-112) |#1|) $) NIL (|has| $ (-6 -4407))) (($ |#1| $) NIL (-12 (|has| $ (-6 -4407)) (|has| |#1| (-1094))))) (-1316 ((|#1| (-1 |#1| |#1| |#1|) $) NIL (|has| $ (-6 -4407))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) NIL (|has| $ (-6 -4407))) ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) NIL (-12 (|has| $ (-6 -4407)) (|has| |#1| (-1094))))) (-2726 ((|#1| $ (-564) |#1|) NIL (|has| $ (-6 -4408)))) (-2652 ((|#1| $ (-564)) NIL)) (-2643 (((-112) $) NIL)) (-3998 (((-564) |#1| $ (-564)) NIL (|has| |#1| 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(($) 16)) (-4366 ((|#1| $ "value") NIL) ((|#1| $ "first") 15) (($ $ "rest") 20) ((|#1| $ "last") NIL) (($ $ (-1226 (-564))) NIL) ((|#1| $ (-564)) NIL) ((|#1| $ (-564) |#1|) NIL)) (-3277 (((-564) $ $) NIL)) (-2251 (($ $ (-1226 (-564))) NIL) (($ $ (-564)) NIL)) (-2114 (($ $ (-1226 (-564))) NIL) (($ $ (-564)) NIL)) (-3206 (((-112) $) 39)) (-3068 (($ $) NIL)) (-2602 (($ $) NIL (|has| $ (-6 -4408)))) (-3004 (((-767) $) NIL)) (-1977 (($ $) 44)) (-4062 (((-767) (-1 (-112) |#1|) $) NIL (|has| $ (-6 -4407))) (((-767) |#1| $) NIL (-12 (|has| $ (-6 -4407)) (|has| |#1| (-1094))))) (-3806 (($ $ $ (-564)) NIL (|has| $ (-6 -4408)))) (-3926 (($ $) 40)) (-1311 (((-536) $) NIL (|has| |#1| (-612 (-536))))) (-2435 (($ (-641 |#1|)) 26)) (-3634 (($ $ $) 65) (($ $ |#1|) NIL)) (-3696 (($ $ $) NIL) (($ |#1| $) 10) (($ (-641 $)) NIL) (($ $ |#1|) NIL)) (-2423 (((-858) $) 54 (|has| |#1| (-611 (-858))))) (-3154 (((-641 $) $) NIL)) (-4059 (((-112) $ $) NIL (|has| |#1| (-1094)))) (-1860 (((-112) $ $) NIL (|has| |#1| (-1094)))) (-1368 (((-112) (-1 (-112) |#1|) $) NIL (|has| $ (-6 -4407)))) (-3034 (((-112) $ $) NIL (|has| |#1| (-846)))) (-3011 (((-112) $ $) NIL (|has| |#1| (-846)))) (-2974 (((-112) $ $) 58 (|has| |#1| (-1094)))) (-3023 (((-112) $ $) NIL (|has| |#1| (-846)))) (-2999 (((-112) $ $) NIL (|has| |#1| (-846)))) (-2181 (((-767) $) 9 (|has| $ (-6 -4407))))) 
-(((-520 |#1| |#2|) (-662 |#1|) (-1209) (-564)) (T -520)) 
-NIL 
-(-662 |#1|) 
-((-1679 ((|#4| |#4|) 37)) (-2514 (((-767) |#4|) 46)) (-2907 (((-767) |#4|) 47)) (-2383 (((-641 |#3|) |#4|) 57 (|has| |#3| (-6 -4408)))) (-2540 (((-3 |#4| "failed") |#4|) 71)) (-3108 ((|#4| |#4|) 63)) (-1540 ((|#1| |#4|) 62))) 
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-((-2540 (*1 *2 *2) (|partial| -12 (-4 *3 (-363)) (-4 *4 (-373 *3)) (-4 *5 (-373 *3)) (-5 *1 (-521 *3 *4 *5 *2)) (-4 *2 (-683 *3 *4 *5)))) (-3108 (*1 *2 *2) (-12 (-4 *3 (-363)) (-4 *4 (-373 *3)) (-4 *5 (-373 *3)) (-5 *1 (-521 *3 *4 *5 *2)) (-4 *2 (-683 *3 *4 *5)))) (-1540 (*1 *2 *3) (-12 (-4 *4 (-373 *2)) (-4 *5 (-373 *2)) (-4 *2 (-363)) (-5 *1 (-521 *2 *4 *5 *3)) (-4 *3 (-683 *2 *4 *5)))) (-2383 (*1 *2 *3) (-12 (|has| *6 (-6 -4408)) (-4 *4 (-363)) (-4 *5 (-373 *4)) (-4 *6 (-373 *4)) (-5 *2 (-641 *6)) (-5 *1 (-521 *4 *5 *6 *3)) (-4 *3 (-683 *4 *5 *6)))) (-2907 (*1 *2 *3) (-12 (-4 *4 (-363)) (-4 *5 (-373 *4)) (-4 *6 (-373 *4)) (-5 *2 (-767)) (-5 *1 (-521 *4 *5 *6 *3)) (-4 *3 (-683 *4 *5 *6)))) (-2514 (*1 *2 *3) (-12 (-4 *4 (-363)) (-4 *5 (-373 *4)) (-4 *6 (-373 *4)) (-5 *2 (-767)) (-5 *1 (-521 *4 *5 *6 *3)) (-4 *3 (-683 *4 *5 *6)))) (-1679 (*1 *2 *2) (-12 (-4 *3 (-363)) (-4 *4 (-373 *3)) (-4 *5 (-373 *3)) (-5 *1 (-521 *3 *4 *5 *2)) (-4 *2 (-683 *3 *4 *5))))) 
-(-10 -7 (-15 -1679 (|#4| |#4|)) (-15 -2514 ((-767) |#4|)) (-15 -2907 ((-767) |#4|)) (IF (|has| |#3| (-6 -4408)) (-15 -2383 ((-641 |#3|) |#4|)) |%noBranch|) (-15 -1540 (|#1| |#4|)) (-15 -3108 (|#4| |#4|)) (-15 -2540 ((-3 |#4| "failed") |#4|))) 
-((-1679 ((|#8| |#4|) 20)) (-2383 (((-641 |#3|) |#4|) 29 (|has| |#7| (-6 -4408)))) (-2540 (((-3 |#8| "failed") |#4|) 23))) 
-(((-522 |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (-10 -7 (-15 -1679 (|#8| |#4|)) (-15 -2540 ((-3 |#8| "failed") |#4|)) (IF (|has| |#7| (-6 -4408)) (-15 -2383 ((-641 |#3|) |#4|)) |%noBranch|)) (-556) (-373 |#1|) (-373 |#1|) (-683 |#1| |#2| |#3|) (-988 |#1|) (-373 |#5|) (-373 |#5|) (-683 |#5| |#6| |#7|)) (T -522)) 
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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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 (((-173) . T)) 
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-((-1624 (((-1 |#1| |#1|) |#1|) 11)) (-2312 (((-1 |#1| |#1|)) 10))) 
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-(((-531 |#1|) (-13 (-789) (-509 (-767) |#1|)) (-846)) (T -531)) 
-NIL 
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-((-1988 (((-641 |#2|) (-1166 |#1|) |#3|) 98)) (-3208 (((-641 (-2 (|:| |outval| |#2|) (|:| |outmult| (-564)) (|:| |outvect| (-641 (-685 |#2|))))) (-685 |#1|) |#3| (-1 (-418 (-1166 |#1|)) (-1166 |#1|))) 114)) (-1753 (((-1166 |#1|) (-685 |#1|)) 110))) 
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-3778 (-2 (|:| |endPointContinuity| (-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"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1153 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -3894 (-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 (-559)))) (-3393 (*1 *2 *1) (-12 (-5 *2 (-642 (-2 (|:| |var| (-1173)) (|:| |fn| (-316 (-225))) (|:| -3894 (-1091 (-841 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225))))) (-5 *1 (-559)))) (-2175 (*1 *2) (-12 (-5 *2 (-1267)) 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-((-1316 ((|#5| (-1 |#5| |#1| |#5|) |#4| |#5|) 39)) (-4357 (((-3 |#8| "failed") (-1 (-3 |#5| "failed") |#1|) |#4|) 37) ((|#8| (-1 |#5| |#1|) |#4|) 31))) 
-(((-681 |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (-10 -7 (-15 -4357 (|#8| (-1 |#5| |#1|) |#4|)) (-15 -4357 ((-3 |#8| "failed") (-1 (-3 |#5| "failed") |#1|) |#4|)) (-15 -1316 (|#5| (-1 |#5| |#1| |#5|) |#4| |#5|))) (-1045) (-373 |#1|) (-373 |#1|) (-683 |#1| |#2| |#3|) (-1045) (-373 |#5|) (-373 |#5|) (-683 |#5| |#6| |#7|)) (T -681)) 
-((-1316 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1045)) (-4 *2 (-1045)) (-4 *6 (-373 *5)) (-4 *7 (-373 *5)) (-4 *8 (-373 *2)) (-4 *9 (-373 *2)) (-5 *1 (-681 *5 *6 *7 *4 *2 *8 *9 *10)) (-4 *4 (-683 *5 *6 *7)) (-4 *10 (-683 *2 *8 *9)))) (-4357 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 (-3 *8 "failed") *5)) (-4 *5 (-1045)) (-4 *8 (-1045)) (-4 *6 (-373 *5)) (-4 *7 (-373 *5)) (-4 *2 (-683 *8 *9 *10)) (-5 *1 (-681 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-683 *5 *6 *7)) (-4 *9 (-373 *8)) (-4 *10 (-373 *8)))) (-4357 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1045)) (-4 *8 (-1045)) (-4 *6 (-373 *5)) (-4 *7 (-373 *5)) (-4 *2 (-683 *8 *9 *10)) (-5 *1 (-681 *5 *6 *7 *4 *8 *9 *10 *2)) (-4 *4 (-683 *5 *6 *7)) (-4 *9 (-373 *8)) (-4 *10 (-373 *8))))) 
-(-10 -7 (-15 -4357 (|#8| (-1 |#5| |#1|) |#4|)) (-15 -4357 ((-3 |#8| "failed") (-1 (-3 |#5| "failed") |#1|) |#4|)) (-15 -1316 (|#5| (-1 |#5| |#1| |#5|) |#4| |#5|))) 
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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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 (((-790) (-140)) (T -790)) 
 NIL 
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-NIL 
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 NIL 
 (-238 |#1| |#2|) 
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 NIL 
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 NIL 
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 NIL 
 (-266 |#1|) 
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 NIL 
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-NIL 
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-(((-853) (-140)) (T -853)) 
-NIL 
-(-13 (-846) (-1106)) 
-(((-102) . T) ((-611 (-858)) . T) ((-846) . T) ((-1106) . T) ((-1094) . T)) 
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-(((-854) (-13 (-846) (-10 -8 (-15 -2423 ($ (-564))) (-15 -2128 ((-564) $))))) (T -854)) 
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-NIL 
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+((-2755 (($ $ $) 11)) (-1520 (($ $ $) 10)) (-1648 (((-112) $ $) 9)) (-2934 (((-112) $ $) 14)) (-2908 (((-112) $ $) 12)) (-2922 (((-112) $ $) 15))) 
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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 
 (-342 |#1| |#2| |#3|) 
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 NIL 
 (-13 (-612 (-225)) (-612 (-379))) 
 (((-612 (-225)) . T) ((-612 (-379)) . T)) 
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+NIL 
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+NIL 
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 NIL 
 (-266 |#1|) 
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-NIL 
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-NIL 
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+NIL 
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+(((-1099 |#1|) (-425 |#1|) (-1097)) (T -1099)) 
 NIL 
 (-425 |#1|) 
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-(((-102) . T) ((-611 (-858)) . T) ((-616 (-641 $)) . T) ((-616 |#1|) . T) ((-616 |#2|) . T) ((-616 |#3|) . T) ((-616 |#4|) . T) ((-616 |#5|) . T) ((-1094) . T)) 
-((-3009 (((-112) $ $) NIL)) (-2230 (((-112) $) NIL)) (-1341 (((-1170) $) NIL)) (-1598 (((-112) $) NIL)) (-4293 (((-1152) $) NIL)) (-1526 (((-112) $) NIL)) (-1666 (((-112) $) NIL)) (-3801 (((-112) $) NIL)) (-2766 (((-1152) $) NIL)) (-2513 (((-112) $) NIL)) (-1359 (((-564) $) NIL)) (-4052 (((-1114) $) NIL)) (-3234 (((-112) $) NIL)) (-2962 (((-225) $) NIL)) (-3354 (((-858) $) NIL)) (-1606 (((-112) $ $) NIL)) (-4366 (($ $ (-564)) NIL) (($ $ (-641 (-564))) NIL)) (-3765 (((-641 $) $) NIL)) (-1311 (($ (-1152)) NIL) (($ (-1170)) NIL) (($ (-564)) NIL) (($ (-225)) NIL) (($ (-858)) NIL) (($ (-641 $)) NIL)) (-2423 (((-858) $) NIL)) (-2546 (($ $) NIL)) (-2535 (($ $) NIL)) (-1860 (((-112) $ $) NIL)) (-3075 (((-112) $) NIL)) (-2974 (((-112) $ $) NIL)) (-2181 (((-564) $) NIL))) 
-(((-1098) (-1097 (-1152) (-1170) (-564) (-225) (-858))) (T -1098)) 
-NIL 
-(-1097 (-1152) (-1170) (-564) (-225) (-858)) 
-((-3009 (((-112) $ $) NIL)) (-2230 (((-112) $) 45)) (-1341 ((|#2| $) 48)) (-1598 (((-112) $) 20)) (-4293 ((|#1| $) 21)) (-1526 (((-112) $) 42)) (-1666 (((-112) $) 14)) (-3801 (((-112) $) 44)) (-2766 (((-1152) $) NIL)) (-2513 (((-112) $) 46)) (-1359 ((|#3| $) 50)) (-4052 (((-1114) $) NIL)) (-3234 (((-112) $) 47)) (-2962 ((|#4| $) 49)) (-3354 ((|#5| $) 51)) (-1606 (((-112) $ $) 41)) (-4366 (($ $ (-564)) 62) (($ $ (-641 (-564))) 64)) (-3765 (((-641 $) $) 27)) (-1311 (($ |#1|) 53) (($ |#2|) 54) (($ |#3|) 55) (($ |#4|) 56) (($ |#5|) 57) (($ (-641 $)) 52)) (-2423 (((-858) $) 28)) (-2546 (($ $) 26)) (-2535 (($ $) 58)) (-1860 (((-112) $ $) NIL)) (-3075 (((-112) $) 23)) (-2974 (((-112) $ $) 40)) (-2181 (((-564) $) 60))) 
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-NIL 
-(-1097 |#1| |#2| |#3| |#4| |#5|) 
-((-3111 (((-1264) $) 23)) (-2338 (($ (-1170) (-434) |#2|) 11)) (-2423 (((-858) $) 16))) 
-(((-1100 |#1| |#2|) (-13 (-395) (-10 -8 (-15 -2338 ($ (-1170) (-434) |#2|)))) (-1094) (-430 |#1|)) (T -1100)) 
-((-2338 (*1 *1 *2 *3 *4) (-12 (-5 *2 (-1170)) (-5 *3 (-434)) (-4 *5 (-1094)) (-5 *1 (-1100 *5 *4)) (-4 *4 (-430 *5))))) 
-(-13 (-395) (-10 -8 (-15 -2338 ($ (-1170) (-434) |#2|)))) 
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 NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-34) . T) ((-38 |#2|) |has| |#2| (-6 (-4412 "*"))) ((-102) . T) ((-111 |#2| |#2|) . T) ((-131) . T) ((-614 #0=(-407 (-564))) |has| |#2| (-1036 (-407 (-564)))) ((-614 (-564)) . T) ((-614 |#2|) . T) ((-611 (-860)) . T) ((-231 |#2|) . T) ((-233) |has| |#2| (-233)) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((-377 |#2|) . T) ((-411 |#2|) . T) ((-489 |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1097))) ((-644 (-564)) . T) ((-644 |#2|) . T) ((-644 $) . T) ((-646 |#2|) . T) ((-646 $) . T) ((-638 |#2|) -2706 (|has| |#2| (-172)) (|has| |#2| (-6 (-4412 "*")))) ((-637 (-564)) |has| |#2| (-637 (-564))) ((-637 |#2|) . T) ((-715 |#2|) -2706 (|has| |#2| (-172)) (|has| |#2| (-6 (-4412 "*")))) ((-724) . T) ((-898 (-1173)) |has| |#2| (-898 (-1173))) ((-1051 |#1| |#1| |#2| |#3| |#4|) . T) ((-1036 #0#) |has| |#2| (-1036 (-407 (-564)))) ((-1036 (-564)) |has| |#2| (-1036 (-564))) ((-1036 |#2|) . T) ((-1049 |#2|) . T) ((-1054 |#2|) . T) ((-1047) . T) ((-1055) . T) ((-1109) . T) ((-1097) . T) ((-1212) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-((-3836 (((-641 (-1076)) $) 34)) (-1684 (($ $) 31)) (-3810 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-3971 (($ $) 14)) (-3982 ((|#2| $) 12)) (-1568 ((|#3| $) 10))) 
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-NIL 
-(-10 -8 (-15 -3836 ((-641 (-1076)) |#1|)) (-15 -3810 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -3810 (|#1| |#1| (-1076) |#3|)) (-15 -1684 (|#1| |#1|)) (-15 -3810 (|#1| |#2| |#3|)) (-15 -1568 (|#3| |#1|)) (-15 -3971 (|#1| |#1|)) (-15 -3982 (|#2| |#1|))) 
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-(((-1237 |#1| |#2|) (-140) (-1045) (-788)) (T -1237)) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) |has| |#1| (-556)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2807 (|has| |#1| (-556)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) |has| |#1| (-38 (-407 (-564)))) ((-614 (-564)) . T) ((-614 |#1|) |has| |#1| (-172)) ((-614 $) |has| |#1| (-556)) ((-611 (-858)) . T) ((-172) -2807 (|has| |#1| (-556)) (|has| |#1| (-172))) ((-233) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-286 $ $) |has| |#2| (-1106)) ((-290) |has| |#1| (-556)) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-38 (-407 (-564)))) ((-644 |#1|) . T) ((-644 $) . T) ((-713 #0#) |has| |#1| (-38 (-407 (-564)))) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) |has| |#1| (-556)) ((-722) . T) ((-896 (-1170)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-896 (-1170)))) ((-969 |#1| |#2| (-1076)) . T) ((-1051 #0#) |has| |#1| (-38 (-407 (-564)))) ((-1051 |#1|) . T) ((-1051 $) -2807 (|has| |#1| (-556)) (|has| |#1| (-172))) ((-1045) . T) ((-1052) . T) ((-1106) . T) ((-1094) . T)) 
-((-2683 ((|#2| |#2|) 12)) (-2753 (((-418 |#2|) |#2|) 14)) (-4349 (((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-564))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-564)))) 30))) 
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-((-4357 (((-1244 |#2| |#4| |#6|) (-1 |#2| |#1|) (-1244 |#1| |#3| |#5|)) 24))) 
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-NIL 
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-NIL 
-(-13 (-172) (-368) (-612 (-564)) (-1145)) 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
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(NIL) -9 NIL NIL NIL) (-1208 2928390 2928585 2928616 "TYPEAST" 2928621 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2927361 2927563 2927803 "TWOFACT" 2928184 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2926384 2926770 2927005 "TUPLE" 2927161 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2924075 2924594 2925133 "TUBETOOL" 2925867 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2922924 2923129 2923370 "TUBE" 2923868 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2917653 2921896 2922179 "TS" 2922676 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2906293 2910412 2910509 "TSETCAT" 2915778 NIL TSETCAT (NIL T T T T) -9 NIL 2917309 NIL) (-1201 2901025 2902625 2904516 "TSETCAT-" 2904521 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2895664 2896511 2897440 "TRMANIP" 2900161 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2895105 2895168 2895331 "TRIMAT" 2895596 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2892971 2893208 2893565 "TRIGMNIP" 2894854 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2892491 2892604 2892634 "TRIGCAT" 2892847 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2892160 2892239 2892380 "TRIGCAT-" 2892385 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2889005 2891018 2891299 "TREE" 2891914 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2888279 2888807 2888837 "TRANFUN" 2888872 T TRANFUN (NIL) -9 NIL 2888938 NIL) (-1193 2887558 2887749 2888029 "TRANFUN-" 2888034 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2887362 2887394 2887455 "TOPSP" 2887519 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2886710 2886825 2886979 "TOOLSIGN" 2887243 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2885344 2885887 2886126 "TEXTFILE" 2886493 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2883256 2883797 2884226 "TEX" 2884937 T TEX (NIL) -8 NIL NIL NIL) (-1188 2883037 2883068 2883140 "TEX1" 2883219 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2882685 2882748 2882838 "TEMUTL" 2882969 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2880839 2881119 2881444 "TBCMPPK" 2882408 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2872616 2878999 2879055 "TBAGG" 2879455 NIL TBAGG (NIL T T) -9 NIL 2879666 NIL) (-1184 2867686 2869174 2870928 "TBAGG-" 2870933 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2867070 2867177 2867322 "TANEXP" 2867575 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2860460 2866927 2867020 "TABLE" 2867025 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2859872 2859971 2860109 "TABLEAU" 2860357 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2854480 2855700 2856948 "TABLBUMP" 2858658 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2853702 2853849 2854030 "SYSTEM" 2854321 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2850161 2850860 2851643 "SYSSOLP" 2852953 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2849205 2849710 2849829 "SYSNNI" 2850015 NIL SYSNNI (NIL NIL) -8 NIL NIL 2850100) (-1176 2848512 2848971 2849050 "SYSINT" 2849110 NIL SYSINT (NIL NIL) -8 NIL NIL 2849155) (-1175 2844844 2845790 2846500 "SYNTAX" 2847824 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2842002 2842604 2843236 "SYMTAB" 2844234 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2837251 2838153 2839136 "SYMS" 2841041 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2834486 2836709 2836939 "SYMPOLY" 2837056 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2834003 2834078 2834201 "SYMFUNC" 2834398 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2830022 2831315 2832128 "SYMBOL" 2833212 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2823561 2825250 2826970 "SWITCH" 2828324 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2816795 2822382 2822685 "SUTS" 2823316 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2808861 2816042 2816315 "SUPXS" 2816580 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2800621 2808479 2808605 "SUP" 2808770 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2799780 2799907 2800124 "SUPFRACF" 2800489 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2799401 2799460 2799573 "SUP2" 2799715 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2797849 2798123 2798479 "SUMRF" 2799100 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2797184 2797250 2797442 "SUMFS" 2797770 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2781151 2796361 2796612 "SULS" 2796991 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2780753 2780973 2781043 "SUCHTAST" 2781103 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2780048 2780278 2780418 "SUCH" 2780661 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2773914 2774954 2775913 "SUBSPACE" 2779136 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2773344 2773434 2773598 "SUBRESP" 2773802 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2766709 2768009 2769320 "STTF" 2772080 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2760882 2762002 2763149 "STTFNC" 2765609 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2752193 2754064 2755858 "STTAYLOR" 2759123 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2745323 2752057 2752140 "STRTBL" 2752145 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2740687 2745278 2745309 "STRING" 2745314 T STRING (NIL) -8 NIL NIL NIL) (-1151 2735548 2740060 2740090 "STRICAT" 2740149 T STRICAT (NIL) -9 NIL 2740211 NIL) (-1150 2728302 2733167 2733778 "STREAM" 2734972 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2727812 2727889 2728033 "STREAM3" 2728219 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2726794 2726977 2727212 "STREAM2" 2727625 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2726482 2726534 2726627 "STREAM1" 2726736 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2725498 2725679 2725910 "STINPROD" 2726298 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2725050 2725260 2725290 "STEP" 2725370 T STEP (NIL) -9 NIL 2725448 NIL) (-1144 2718482 2724949 2725026 "STBL" 2725031 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2713608 2717703 2717746 "STAGG" 2717899 NIL STAGG (NIL T) -9 NIL 2717988 NIL) (-1142 2711310 2711912 2712784 "STAGG-" 2712789 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2709457 2711080 2711172 "STACK" 2711253 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2702152 2707598 2708054 "SREGSET" 2709087 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2694577 2695946 2697459 "SRDCMPK" 2700758 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2687494 2692017 2692047 "SRAGG" 2693350 T SRAGG (NIL) -9 NIL 2693958 NIL) (-1137 2686511 2686766 2687145 "SRAGG-" 2687150 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2680971 2685458 2685879 "SQMATRIX" 2686137 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2674656 2677689 2678416 "SPLTREE" 2680316 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2670619 2671312 2671958 "SPLNODE" 2674082 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2669666 2669899 2669929 "SPFCAT" 2670373 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2668403 2668613 2668877 "SPECOUT" 2669424 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2660029 2661799 2661829 "SPADXPT" 2666221 T SPADXPT (NIL) -9 NIL 2668255 NIL) (-1130 2659790 2659830 2659899 "SPADPRSR" 2659982 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2657945 2659745 2659776 "SPADAST" 2659781 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2649890 2651663 2651706 "SPACEC" 2656079 NIL SPACEC (NIL T) -9 NIL 2657895 NIL) (-1127 2648020 2649822 2649871 "SPACE3" 2649876 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2646772 2646943 2647234 "SORTPAK" 2647825 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2644864 2645167 2645579 "SOLVETRA" 2646436 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2643914 2644136 2644397 "SOLVESER" 2644637 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2639216 2640106 2641101 "SOLVERAD" 2642966 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2635031 2635640 2636369 "SOLVEFOR" 2638583 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2629301 2634380 2634477 "SNTSCAT" 2634482 NIL SNTSCAT (NIL T T T T) -9 NIL 2634552 NIL) (-1120 2623407 2627624 2628015 "SMTS" 2628991 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2618091 2623295 2623372 "SMP" 2623377 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2616250 2616551 2616949 "SMITH" 2617788 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2609110 2613301 2613404 "SMATCAT" 2614755 NIL SMATCAT (NIL NIL T T T) -9 NIL 2615305 NIL) (-1116 2606050 2606873 2608051 "SMATCAT-" 2608056 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2603716 2605286 2605329 "SKAGG" 2605590 NIL SKAGG (NIL T) -9 NIL 2605725 NIL) (-1114 2600024 2603132 2603327 "SINT" 2603514 T SINT (NIL) -8 NIL NIL 2603687) (-1113 2599796 2599834 2599900 "SIMPAN" 2599980 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2599075 2599331 2599471 "SIG" 2599678 T SIG (NIL) -8 NIL NIL NIL) (-1111 2597913 2598134 2598409 "SIGNRF" 2598834 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2596746 2596897 2597181 "SIGNEF" 2597742 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2596052 2596329 2596453 "SIGAST" 2596644 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2593741 2594196 2594702 "SHP" 2595593 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2587593 2593642 2593718 "SHDP" 2593723 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2587166 2587358 2587388 "SGROUP" 2587481 T SGROUP (NIL) -9 NIL 2587543 NIL) (-1105 2587024 2587050 2587123 "SGROUP-" 2587128 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2583859 2584557 2585280 "SGCF" 2586323 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2578227 2583306 2583403 "SFRTCAT" 2583408 NIL SFRTCAT (NIL T T T T) -9 NIL 2583447 NIL) (-1102 2571648 2572666 2573802 "SFRGCD" 2577210 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2564774 2565847 2567033 "SFQCMPK" 2570581 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2564394 2564483 2564594 "SFORT" 2564715 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2563512 2564234 2564355 "SEXOF" 2564360 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2562619 2563393 2563461 "SEX" 2563466 T SEX (NIL) -8 NIL NIL NIL) (-1097 2558132 2558847 2558942 "SEXCAT" 2561879 NIL SEXCAT (NIL T T T T T) -9 NIL 2562457 NIL) (-1096 2555285 2558066 2558114 "SET" 2558119 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2553509 2553998 2554303 "SETMN" 2555026 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2553005 2553157 2553187 "SETCAT" 2553363 T SETCAT (NIL) -9 NIL 2553473 NIL) (-1093 2552697 2552775 2552905 "SETCAT-" 2552910 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2549058 2551158 2551201 "SETAGG" 2552071 NIL SETAGG (NIL T) -9 NIL 2552411 NIL) (-1091 2548516 2548632 2548869 "SETAGG-" 2548874 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2547959 2548212 2548313 "SEQAST" 2548437 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2547158 2547452 2547513 "SEGXCAT" 2547799 NIL SEGXCAT (NIL T T) -9 NIL 2547919 NIL) (-1088 2546164 2546824 2547006 "SEG" 2547011 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2545143 2545357 2545400 "SEGCAT" 2545922 NIL SEGCAT (NIL T) -9 NIL 2546143 NIL) (-1086 2544144 2544522 2544722 "SEGBIND" 2544978 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2543765 2543824 2543937 "SEGBIND2" 2544079 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2543338 2543566 2543643 "SEGAST" 2543710 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2542557 2542683 2542887 "SEG2" 2543182 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2541967 2542492 2542539 "SDVAR" 2542544 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2534494 2541737 2541867 "SDPOL" 2541872 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2533087 2533353 2533672 "SCPKG" 2534209 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2532251 2532423 2532615 "SCOPE" 2532917 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2531471 2531605 2531784 "SCACHE" 2532106 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2531117 2531303 2531333 "SASTCAT" 2531338 T SASTCAT (NIL) -9 NIL 2531351 NIL) (-1076 2530604 2530952 2531028 "SAOS" 2531063 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2530169 2530204 2530377 "SAERFFC" 2530563 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2524108 2530066 2530146 "SAE" 2530151 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2523701 2523736 2523895 "SAEFACT" 2524067 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2522022 2522336 2522737 "RURPK" 2523367 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2520659 2520965 2521270 "RULESET" 2521856 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2517882 2518412 2518870 "RULE" 2520340 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2517494 2517676 2517759 "RULECOLD" 2517834 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2517284 2517312 2517383 "RTVALUE" 2517445 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2516755 2517001 2517095 "RSTRCAST" 2517212 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2511603 2512398 2513318 "RSETGCD" 2515954 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2500833 2505912 2506009 "RSETCAT" 2510128 NIL RSETCAT (NIL T T T T) -9 NIL 2511225 NIL) (-1064 2498760 2499299 2500123 "RSETCAT-" 2500128 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2491145 2492522 2494042 "RSDCMPK" 2497359 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2489124 2489591 2489665 "RRCC" 2490751 NIL RRCC (NIL T T) -9 NIL 2491095 NIL) (-1061 2488475 2488649 2488928 "RRCC-" 2488933 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2487918 2488171 2488272 "RPTAST" 2488396 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2462189 2471538 2471605 "RPOLCAT" 2482269 NIL RPOLCAT (NIL T T T) -9 NIL 2485428 NIL) (-1058 2453687 2456027 2459149 "RPOLCAT-" 2459154 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2444618 2451898 2452380 "ROUTINE" 2453227 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2441416 2444244 2444384 "ROMAN" 2444500 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2439660 2440276 2440536 "ROIRC" 2441221 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2436018 2438296 2438326 "RNS" 2438630 T RNS (NIL) -9 NIL 2438903 NIL) (-1053 2434527 2434910 2435444 "RNS-" 2435519 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2433950 2434358 2434388 "RNG" 2434393 T RNG (NIL) -9 NIL 2434414 NIL) (-1051 2433316 2433704 2433747 "RMODULE" 2433809 NIL RMODULE (NIL T) -9 NIL 2433851 NIL) (-1050 2432152 2432246 2432582 "RMCAT2" 2433217 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2429002 2431498 2431795 "RMATRIX" 2431914 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2421918 2424178 2424293 "RMATCAT" 2427652 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2428634 NIL) (-1047 2421293 2421440 2421747 "RMATCAT-" 2421752 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2420860 2420935 2421063 "RINTERP" 2421212 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2419953 2420507 2420537 "RING" 2420593 T RING (NIL) -9 NIL 2420685 NIL) (-1044 2419745 2419789 2419886 "RING-" 2419891 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2418586 2418823 2419081 "RIDIST" 2419509 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2409875 2418054 2418260 "RGCHAIN" 2418434 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2409225 2409631 2409672 "RGBCSPC" 2409730 NIL RGBCSPC (NIL T) -9 NIL 2409782 NIL) (-1040 2408383 2408764 2408805 "RGBCMDL" 2409037 NIL RGBCMDL (NIL T) -9 NIL 2409151 NIL) (-1039 2405377 2405991 2406661 "RF" 2407747 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2405023 2405086 2405189 "RFFACTOR" 2405308 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2404748 2404783 2404880 "RFFACT" 2404982 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2402865 2403229 2403611 "RFDIST" 2404388 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2402318 2402410 2402573 "RETSOL" 2402767 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2401954 2402034 2402077 "RETRACT" 2402210 NIL RETRACT (NIL T) -9 NIL 2402297 NIL) (-1033 2401803 2401828 2401915 "RETRACT-" 2401920 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2401405 2401625 2401695 "RETAST" 2401755 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2394143 2401058 2401185 "RESULT" 2401300 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2392734 2393412 2393611 "RESRING" 2394046 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2392370 2392419 2392517 "RESLATC" 2392671 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2392075 2392110 2392217 "REPSQ" 2392329 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2389497 2390077 2390679 "REP" 2391495 T REP (NIL) -7 NIL NIL NIL) (-1026 2389194 2389229 2389340 "REPDB" 2389456 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2383094 2384483 2385706 "REP2" 2388006 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2379471 2380152 2380960 "REP1" 2382321 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2372167 2377612 2378068 "REGSET" 2379101 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2370932 2371315 2371565 "REF" 2371952 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2370309 2370412 2370579 "REDORDER" 2370816 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2366277 2369522 2369749 "RECLOS" 2370137 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2365329 2365510 2365725 "REALSOLV" 2366084 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2365175 2365216 2365246 "REAL" 2365251 T REAL (NIL) -9 NIL 2365286 NIL) (-1017 2361658 2362460 2363344 "REAL0Q" 2364340 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2357259 2358247 2359308 "REAL0" 2360639 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2356730 2356976 2357070 "RDUCEAST" 2357187 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2356135 2356207 2356414 "RDIV" 2356652 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2355203 2355377 2355590 "RDIST" 2355957 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2353800 2354087 2354459 "RDETRS" 2354911 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2351612 2352066 2352604 "RDETR" 2353342 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2350237 2350515 2350912 "RDEEFS" 2351328 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2348746 2349052 2349477 "RDEEF" 2349925 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2342972 2345882 2345912 "RCFIELD" 2347207 T RCFIELD (NIL) -9 NIL 2347937 NIL) (-1007 2341036 2341540 2342236 "RCFIELD-" 2342311 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2337305 2339137 2339180 "RCAGG" 2340264 NIL RCAGG (NIL T) -9 NIL 2340729 NIL) (-1005 2336933 2337027 2337190 "RCAGG-" 2337195 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2336268 2336380 2336545 "RATRET" 2336817 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2335821 2335888 2336009 "RATFACT" 2336196 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2335129 2335249 2335401 "RANDSRC" 2335691 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2334863 2334907 2334980 "RADUTIL" 2335078 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2327979 2333696 2334006 "RADIX" 2334587 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2319600 2327823 2327951 "RADFF" 2327956 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2319252 2319327 2319355 "RADCAT" 2319512 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2319037 2319085 2319182 "RADCAT-" 2319187 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2317140 2318812 2318901 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2280402 "QCMPACK" 2283932 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2275695 2276143 2276571 "QALGSET" 2277801 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2274940 2275114 2275346 "QALGSET2" 2275515 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2273630 2273854 2274171 "PWFFINTB" 2274713 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2271812 2271980 2272334 "PUSHVAR" 2273444 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2267730 2268784 2268825 "PTRANFN" 2270709 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2266132 2266423 2266745 "PTPACK" 2267441 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2265764 2265821 2265930 "PTFUNC2" 2266069 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2260243 2264636 2264677 "PTCAT" 2264973 NIL PTCAT (NIL T) -9 NIL 2265126 NIL) (-975 2259901 2259936 2260060 "PSQFR" 2260202 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2258496 2258794 2259128 "PSEUDLIN" 2259599 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2245259 2247630 2249954 "PSETPK" 2256256 NIL PSETPK 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2213266 "PROPERTY" 2213454 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2207089 2211197 2212017 "PRODUCT" 2212257 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2204367 2206547 2206781 "PR" 2206900 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2204163 2204195 2204254 "PRINT" 2204328 T PRINT (NIL) -7 NIL NIL NIL) (-957 2203503 2203620 2203772 "PRIMES" 2204043 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2201568 2201969 2202435 "PRIMELT" 2203082 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2201297 2201346 2201374 "PRIMCAT" 2201498 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2197412 2201235 2201280 "PRIMARR" 2201285 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2196419 2196597 2196825 "PRIMARR2" 2197230 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2196062 2196118 2196229 "PREASSOC" 2196357 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2195537 2195670 2195698 "PPCURVE" 2195903 T PPCURVE (NIL) -9 NIL 2196039 NIL) (-950 2195132 2195332 2195415 "PORTNUM" 2195474 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2192491 2192890 2193482 "POLYROOT" 2194713 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2186673 2192095 2192255 "POLY" 2192364 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2186056 2186114 2186348 "POLYLIFT" 2186609 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2182331 2182780 2183409 "POLYCATQ" 2185601 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2169463 2174583 2174648 "POLYCAT" 2178162 NIL POLYCAT (NIL T T T) -9 NIL 2180040 NIL) (-944 2162912 2164774 2167158 "POLYCAT-" 2167163 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2162499 2162567 2162687 "POLY2UP" 2162838 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2162131 2162188 2162297 "POLY2" 2162436 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2160816 2161055 2161331 "POLUTIL" 2161905 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2159171 2159448 2159779 "POLTOPOL" 2160538 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2154638 2159107 2159153 "POINT" 2159158 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2152825 2153182 2153557 "PNTHEORY" 2154283 T PNTHEORY 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"PMASS" 2144929 T PMASS (NIL) -7 NIL NIL NIL) (-925 2143530 2143640 2143803 "PMASSFS" 2144144 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2143185 2143253 2143347 "PLOTTOOL" 2143456 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2137792 2138996 2140144 "PLOT" 2142057 T PLOT (NIL) -8 NIL NIL NIL) (-922 2133596 2134640 2135561 "PLOT3D" 2136891 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2132508 2132685 2132920 "PLOT1" 2133400 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2107897 2112574 2117425 "PLEQN" 2127774 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2107215 2107337 2107517 "PINTERP" 2107762 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2106908 2106955 2107058 "PINTERPA" 2107162 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2106129 2106677 2106764 "PI" 2106804 T PI (NIL) -8 NIL NIL 2106871) (-916 2104492 2105467 2105495 "PID" 2105677 T PID (NIL) -9 NIL 2105811 NIL) (-915 2104243 2104280 2104355 "PICOERCE" 2104449 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2103563 2103702 2103878 "PGROEB" 2104099 NIL 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NIL NIL NIL) (-889 2051246 2051869 2052166 "PBWLB" 2052797 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2043719 2045319 2046657 "PATTERN" 2049929 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2043351 2043408 2043517 "PATTERN2" 2043656 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2041108 2041496 2041953 "PATTERN1" 2042940 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2038476 2039057 2039538 "PATRES" 2040673 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2038040 2038107 2038239 "PATRES2" 2038403 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2035923 2036328 2036735 "PATMATCH" 2037707 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2035433 2035642 2035683 "PATMAB" 2035790 NIL PATMAB (NIL T) -9 NIL 2035873 NIL) (-881 2033951 2034287 2034545 "PATLRES" 2035238 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2033497 2033620 2033661 "PATAB" 2033666 NIL PATAB (NIL T) -9 NIL 2033838 NIL) (-879 2030978 2031510 2032083 "PARTPERM" 2032944 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2030599 2030662 2030764 "PARSURF" 2030909 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2030231 2030288 2030397 "PARSU2" 2030536 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2029995 2030035 2030102 "PARSER" 2030184 T PARSER (NIL) -7 NIL NIL NIL) (-875 2029616 2029679 2029781 "PARSCURV" 2029926 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2029248 2029305 2029414 "PARSC2" 2029553 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2028887 2028945 2029042 "PARPCURV" 2029184 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2028519 2028576 2028685 "PARPC2" 2028824 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2028039 2028125 2028244 "PAN2EXPR" 2028420 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2026816 2027160 2027388 "PALETTE" 2027831 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2025209 2025821 2026181 "PAIR" 2026502 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2019079 2024468 2024662 "PADICRC" 2025064 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2012308 2018425 2018609 "PADICRAT" 2018927 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2010623 2012245 2012290 "PADIC" 2012295 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2007799 2009363 2009403 "PADICCT" 2009984 NIL PADICCT (NIL NIL) -9 NIL 2010266 NIL) (-864 2006756 2006956 2007224 "PADEPAC" 2007586 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2005968 2006101 2006307 "PADE" 2006618 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2004355 2005176 2005456 "OWP" 2005772 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2003848 2004061 2004158 "OVERSET" 2004278 T OVERSET (NIL) -8 NIL NIL NIL) (-860 2002894 2003453 2003625 "OVAR" 2003716 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 2002158 2002279 2002440 "OUT" 2002753 T OUT (NIL) -7 NIL NIL NIL) (-858 1991029 1993267 1995467 "OUTFORM" 1999978 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1990365 1990626 1990753 "OUTBFILE" 1990922 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1989672 1989837 1989865 "OUTBCON" 1990183 T OUTBCON (NIL) -9 NIL 1990349 NIL) (-855 1989273 1989385 1989542 "OUTBCON-" 1989547 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1988653 1989002 1989091 "OSI" 1989204 T OSI (NIL) -8 NIL NIL NIL) (-853 1988183 1988521 1988549 "OSGROUP" 1988554 T OSGROUP (NIL) -9 NIL 1988576 NIL) (-852 1986928 1987155 1987440 "ORTHPOL" 1987930 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1984479 1986763 1986884 "OREUP" 1986889 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1981882 1984170 1984297 "ORESUP" 1984421 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1979410 1979910 1980471 "OREPCTO" 1981371 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1973200 1975401 1975442 "OREPCAT" 1977790 NIL OREPCAT (NIL T) -9 NIL 1978894 NIL) (-847 1970347 1971129 1972187 "OREPCAT-" 1972192 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1969498 1969796 1969824 "ORDSET" 1970133 T ORDSET (NIL) -9 NIL 1970297 NIL) (-845 1968929 1969077 1969301 "ORDSET-" 1969306 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1967529 1968320 1968348 "ORDRING" 1968550 T ORDRING (NIL) -9 NIL 1968675 NIL) (-843 1967174 1967268 1967412 "ORDRING-" 1967417 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1966554 1967017 1967045 "ORDMON" 1967050 T ORDMON (NIL) -9 NIL 1967071 NIL) (-841 1965716 1965863 1966058 "ORDFUNS" 1966403 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1965054 1965473 1965501 "ORDFIN" 1965566 T ORDFIN (NIL) -9 NIL 1965640 NIL) (-839 1961613 1963640 1964049 "ORDCOMP" 1964678 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1960879 1961006 1961192 "ORDCOMP2" 1961473 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1957460 1958370 1959184 "OPTPROB" 1960085 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1954262 1954901 1955605 "OPTPACK" 1956776 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1951949 1952715 1952743 "OPTCAT" 1953562 T OPTCAT (NIL) -9 NIL 1954212 NIL) (-834 1951365 1951626 1951731 "OPSIG" 1951864 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1951133 1951172 1951238 "OPQUERY" 1951319 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1948264 1949444 1949948 "OP" 1950662 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1947773 1947970 1948011 "OPERCAT" 1948146 NIL OPERCAT (NIL T) -9 NIL 1948214 NIL) (-830 1947619 1947646 1947732 "OPERCAT-" 1947737 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1944431 1946416 1946785 "ONECOMP" 1947283 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1943736 1943851 1944025 "ONECOMP2" 1944303 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1943155 1943261 1943391 "OMSERVER" 1943626 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1940017 1942595 1942635 "OMSAGG" 1942696 NIL OMSAGG (NIL T) -9 NIL 1942760 NIL) (-825 1938640 1938903 1939185 "OMPKG" 1939755 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1938070 1938173 1938201 "OM" 1938500 T OM (NIL) -9 NIL NIL NIL) (-823 1936617 1937619 1937788 "OMLO" 1937951 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1935577 1935724 1935944 "OMEXPR" 1936443 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1934868 1935123 1935259 "OMERR" 1935461 T OMERR (NIL) -8 NIL NIL NIL) (-820 1934019 1934289 1934449 "OMERRK" 1934728 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1933470 1933696 1933804 "OMENC" 1933931 T OMENC (NIL) -8 NIL NIL NIL) (-818 1927365 1928550 1929721 "OMDEV" 1932319 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1926434 1926605 1926799 "OMCONN" 1927191 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1925021 1925997 1926025 "OINTDOM" 1926030 T OINTDOM (NIL) -9 NIL 1926051 NIL) (-815 1920800 1922011 1922727 "OFMONOID" 1924337 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1920211 1920737 1920782 "ODVAR" 1920787 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1917634 1919956 1920111 "ODR" 1920116 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1910215 1917410 1917536 "ODPOL" 1917541 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1904037 1910087 1910192 "ODP" 1910197 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1902803 1903018 1903293 "ODETOOLS" 1903811 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1899770 1900428 1901144 "ODESYS" 1902136 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1894652 1895560 1896585 "ODERTRIC" 1898845 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1894078 1894160 1894354 "ODERED" 1894564 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1890966 1891514 1892191 "ODERAT" 1893501 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1887923 1888390 1888987 "ODEPRRIC" 1890495 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1885866 1886462 1886948 "ODEPROB" 1887457 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1882386 1882871 1883518 "ODEPRIM" 1885345 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1881635 1881737 1881997 "ODEPAL" 1882278 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1877797 1878588 1879452 "ODEPACK" 1880791 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1876858 1876965 1877187 "ODEINT" 1877686 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1870959 1872384 1873831 "ODEIFTBL" 1875431 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1866357 1867143 1868095 "ODEEF" 1870118 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1865706 1865795 1866018 "ODECONST" 1866262 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1863831 1864492 1864520 "ODECAT" 1865125 T ODECAT (NIL) -9 NIL 1865656 NIL) (-795 1860703 1863543 1863662 "OCT" 1863744 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1860341 1860384 1860511 "OCTCT2" 1860654 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1855081 1857515 1857555 "OC" 1858652 NIL OC (NIL T) -9 NIL 1859510 NIL) (-792 1852308 1853056 1854046 "OC-" 1854140 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1851660 1852128 1852156 "OCAMON" 1852161 T OCAMON (NIL) -9 NIL 1852182 NIL) (-790 1851191 1851532 1851560 "OASGP" 1851565 T OASGP (NIL) -9 NIL 1851585 NIL) (-789 1850452 1850941 1850969 "OAMONS" 1851009 T OAMONS (NIL) -9 NIL 1851052 NIL) (-788 1849866 1850299 1850327 "OAMON" 1850332 T OAMON (NIL) -9 NIL 1850352 NIL) (-787 1849144 1849662 1849690 "OAGROUP" 1849695 T OAGROUP (NIL) -9 NIL 1849715 NIL) (-786 1848834 1848884 1848972 "NUMTUBE" 1849088 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1842407 1843925 1845461 "NUMQUAD" 1847318 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1838163 1839151 1840176 "NUMODE" 1841402 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1835518 1836398 1836426 "NUMINT" 1837349 T NUMINT (NIL) -9 NIL 1838113 NIL) (-782 1834466 1834663 1834881 "NUMFMT" 1835320 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1820825 1823770 1826302 "NUMERIC" 1831973 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1815195 1820274 1820369 "NTSCAT" 1820374 NIL NTSCAT (NIL T T T T) -9 NIL 1820413 NIL) (-779 1814389 1814554 1814747 "NTPOLFN" 1815034 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1802466 1811214 1812026 "NSUP" 1813610 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1802098 1802155 1802264 "NSUP2" 1802403 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1792326 1801872 1802005 "NSMP" 1802010 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1790758 1791059 1791416 "NREP" 1792014 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1789349 1789601 1789959 "NPCOEF" 1790501 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1788415 1788530 1788746 "NORMRETR" 1789230 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1786456 1786746 1787155 "NORMPK" 1788123 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1786141 1786169 1786293 "NORMMA" 1786422 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1785941 1786098 1786127 "NONE" 1786132 T NONE (NIL) -8 NIL NIL NIL) (-769 1785730 1785759 1785828 "NONE1" 1785905 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1785227 1785289 1785468 "NODE1" 1785662 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1783507 1784358 1784613 "NNI" 1784960 T NNI (NIL) -8 NIL NIL 1785195) (-766 1781927 1782240 1782604 "NLINSOL" 1783175 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1778168 1779163 1780062 "NIPROB" 1781048 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1776925 1777159 1777461 "NFINTBAS" 1777930 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1776099 1776575 1776616 "NETCLT" 1776788 NIL NETCLT (NIL T) -9 NIL 1776870 NIL) (-762 1774807 1775038 1775319 "NCODIV" 1775867 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1774569 1774606 1774681 "NCNTFRAC" 1774764 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1772749 1773113 1773533 "NCEP" 1774194 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1771620 1772393 1772421 "NASRING" 1772531 T NASRING (NIL) -9 NIL 1772611 NIL) (-758 1771415 1771459 1771553 "NASRING-" 1771558 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1770542 1771067 1771095 "NARNG" 1771212 T NARNG (NIL) -9 NIL 1771303 NIL) (-756 1770234 1770301 1770435 "NARNG-" 1770440 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1769113 1769320 1769555 "NAGSP" 1770019 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1760385 1762069 1763742 "NAGS" 1767460 T NAGS (NIL) -7 NIL NIL NIL) (-753 1758933 1759241 1759572 "NAGF07" 1760074 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1753471 1754762 1756069 "NAGF04" 1757646 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1746439 1748053 1749686 "NAGF02" 1751858 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1741663 1742763 1743880 "NAGF01" 1745342 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1735291 1736857 1738442 "NAGE04" 1740098 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1726460 1728581 1730711 "NAGE02" 1733181 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1722413 1723360 1724324 "NAGE01" 1725516 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1720208 1720742 1721300 "NAGD03" 1721875 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1711958 1713886 1715840 "NAGD02" 1718274 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1705769 1707194 1708634 "NAGD01" 1710538 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1701978 1702800 1703637 "NAGC06" 1704952 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1700443 1700775 1701131 "NAGC05" 1701642 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1699819 1699938 1700082 "NAGC02" 1700319 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1698853 1699436 1699476 "NAALG" 1699555 NIL NAALG (NIL T) -9 NIL 1699616 NIL) (-739 1698688 1698717 1698807 "NAALG-" 1698812 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1692638 1693746 1694933 "MULTSQFR" 1697584 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1691957 1692032 1692216 "MULTFACT" 1692550 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1685015 1688920 1688973 "MTSCAT" 1690043 NIL MTSCAT (NIL T T) -9 NIL 1690557 NIL) (-735 1684727 1684781 1684873 "MTHING" 1684955 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1684519 1684552 1684612 "MSYSCMD" 1684687 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1680601 1683274 1683594 "MSET" 1684232 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1677670 1680162 1680203 "MSETAGG" 1680208 NIL MSETAGG (NIL T) -9 NIL 1680242 NIL) (-731 1673511 1675049 1675794 "MRING" 1676970 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1673077 1673144 1673275 "MRF2" 1673438 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1672695 1672730 1672874 "MRATFAC" 1673036 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1670307 1670602 1671033 "MPRFF" 1672400 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1664604 1670161 1670258 "MPOLY" 1670263 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1664094 1664129 1664337 "MPCPF" 1664563 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1663608 1663651 1663835 "MPC3" 1664045 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1662803 1662884 1663105 "MPC2" 1663523 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1661104 1661441 1661831 "MONOTOOL" 1662463 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1660329 1660646 1660674 "MONOID" 1660893 T MONOID (NIL) -9 NIL 1661040 NIL) (-721 1659875 1659994 1660175 "MONOID-" 1660180 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1650699 1656642 1656701 "MONOGEN" 1657375 NIL MONOGEN (NIL T T) -9 NIL 1657831 NIL) (-719 1647917 1648652 1649652 "MONOGEN-" 1649771 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1646750 1647196 1647224 "MONADWU" 1647616 T MONADWU (NIL) -9 NIL 1647854 NIL) (-717 1646122 1646281 1646529 "MONADWU-" 1646534 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1645481 1645725 1645753 "MONAD" 1645960 T MONAD (NIL) -9 NIL 1646072 NIL) (-715 1645166 1645244 1645376 "MONAD-" 1645381 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1643455 1644079 1644358 "MOEBIUS" 1644919 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1642821 1643225 1643265 "MODULE" 1643270 NIL MODULE (NIL T) -9 NIL 1643296 NIL) (-712 1642389 1642485 1642675 "MODULE-" 1642680 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1640069 1640753 1641080 "MODRING" 1642213 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1637013 1638174 1638695 "MODOP" 1639598 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1635601 1636080 1636357 "MODMONOM" 1636876 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1625642 1633892 1634306 "MODMON" 1635238 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1622798 1624486 1624762 "MODFIELD" 1625517 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1621775 1622079 1622269 "MMLFORM" 1622628 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1621301 1621344 1621523 "MMAP" 1621726 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1619484 1620251 1620292 "MLO" 1620715 NIL MLO (NIL T) -9 NIL 1620957 NIL) (-703 1616850 1617366 1617968 "MLIFT" 1618965 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1616241 1616325 1616479 "MKUCFUNC" 1616761 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1615840 1615910 1616033 "MKRECORD" 1616164 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1614887 1615049 1615277 "MKFUNC" 1615651 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1614275 1614379 1614535 "MKFLCFN" 1614770 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1613552 1613654 1613839 "MKBCFUNC" 1614168 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1610259 1613106 1613242 "MINT" 1613436 T MINT (NIL) -8 NIL NIL NIL) (-696 1609071 1609314 1609591 "MHROWRED" 1610014 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1604451 1607606 1608011 "MFLOAT" 1608686 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1603808 1603884 1604055 "MFINFACT" 1604363 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1600123 1600971 1601855 "MESH" 1602944 T MESH (NIL) -7 NIL NIL NIL) (-692 1598513 1598825 1599178 "MDDFACT" 1599810 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1595308 1597672 1597713 "MDAGG" 1597968 NIL MDAGG (NIL T) -9 NIL 1598111 NIL) (-690 1585051 1594601 1594808 "MCMPLX" 1595121 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1584192 1584338 1584538 "MCDEN" 1584900 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1582082 1582352 1582732 "MCALCFN" 1583922 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1581007 1581247 1581480 "MAYBE" 1581888 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1578619 1579142 1579704 "MATSTOR" 1580478 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1574576 1577991 1578239 "MATRIX" 1578404 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1570340 1571049 1571785 "MATLIN" 1573933 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1560446 1563632 1563709 "MATCAT" 1568589 NIL MATCAT (NIL T T T) -9 NIL 1570006 NIL) (-682 1556802 1557823 1559179 "MATCAT-" 1559184 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1555396 1555549 1555882 "MATCAT2" 1556637 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1553508 1553832 1554216 "MAPPKG3" 1555071 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1552489 1552662 1552884 "MAPPKG2" 1553332 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1550988 1551272 1551599 "MAPPKG1" 1552195 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1550067 1550394 1550571 "MAPPAST" 1550831 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1549678 1549736 1549859 "MAPHACK3" 1550003 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1549270 1549331 1549445 "MAPHACK2" 1549610 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1548707 1548811 1548953 "MAPHACK1" 1549161 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1546786 1547407 1547711 "MAGMA" 1548435 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1546265 1546510 1546601 "MACROAST" 1546715 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1542683 1544504 1544965 "M3D" 1545837 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1536789 1541052 1541093 "LZSTAGG" 1541875 NIL LZSTAGG (NIL T) -9 NIL 1542170 NIL) (-669 1532746 1533920 1535377 "LZSTAGG-" 1535382 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1529833 1530637 1531124 "LWORD" 1532291 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1529409 1529637 1529712 "LSTAST" 1529778 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1522575 1529180 1529314 "LSQM" 1529319 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1521799 1521938 1522166 "LSPP" 1522430 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1519611 1519912 1520368 "LSMP" 1521488 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1516390 1517064 1517794 "LSMP1" 1518913 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1510267 1515557 1515598 "LSAGG" 1515660 NIL LSAGG (NIL T) -9 NIL 1515738 NIL) (-661 1506962 1507886 1509099 "LSAGG-" 1509104 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1504561 1506106 1506355 "LPOLY" 1506757 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1504143 1504228 1504351 "LPEFRAC" 1504470 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1502464 1503237 1503490 "LO" 1503975 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1502116 1502228 1502256 "LOGIC" 1502367 T LOGIC (NIL) -9 NIL 1502448 NIL) (-656 1501978 1502001 1502072 "LOGIC-" 1502077 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1501171 1501311 1501504 "LODOOPS" 1501834 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1498594 1501087 1501153 "LODO" 1501158 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1497132 1497367 1497720 "LODOF" 1498341 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1493454 1495885 1495926 "LODOCAT" 1496364 NIL LODOCAT (NIL T) -9 NIL 1496575 NIL) (-651 1493187 1493245 1493372 "LODOCAT-" 1493377 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1490507 1493028 1493146 "LODO2" 1493151 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1487942 1490444 1490489 "LODO1" 1490494 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1486823 1486988 1487293 "LODEEF" 1487765 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1482062 1484953 1484994 "LNAGG" 1485941 NIL LNAGG (NIL T) -9 NIL 1486385 NIL) (-646 1481209 1481423 1481765 "LNAGG-" 1481770 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1477345 1478134 1478773 "LMOPS" 1480624 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1476714 1477102 1477143 "LMODULE" 1477204 NIL LMODULE (NIL T) -9 NIL 1477246 NIL) (-643 1473912 1476359 1476482 "LMDICT" 1476624 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1473611 1473820 1473880 "LITERAL" 1473885 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1466794 1472557 1472855 "LIST" 1473346 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1466319 1466393 1466532 "LIST3" 1466714 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1465326 1465504 1465732 "LIST2" 1466137 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1463460 1463772 1464171 "LIST2MAP" 1464973 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1462156 1462826 1462867 "LINEXP" 1463122 NIL LINEXP (NIL T) -9 NIL 1463271 NIL) (-636 1460803 1461063 1461360 "LINDEP" 1461908 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1457570 1458289 1459066 "LIMITRF" 1460058 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1455873 1456169 1456578 "LIMITPS" 1457265 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1450301 1455384 1455612 "LIE" 1455694 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1449324 1449793 1449833 "LIECAT" 1449973 NIL LIECAT (NIL T) -9 NIL 1450124 NIL) (-631 1449165 1449192 1449280 "LIECAT-" 1449285 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1441661 1448614 1448779 "LIB" 1449020 T LIB (NIL) -8 NIL NIL NIL) (-629 1437296 1438179 1439114 "LGROBP" 1440778 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1435305 1435579 1435928 "LF" 1437017 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1434145 1434837 1434865 "LFCAT" 1435072 T LFCAT (NIL) -9 NIL 1435211 NIL) (-626 1431047 1431677 1432365 "LEXTRIPK" 1433509 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1427791 1428617 1429120 "LEXP" 1430627 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1427267 1427512 1427604 "LETAST" 1427719 T LETAST (NIL) -8 NIL NIL NIL) (-623 1425665 1425978 1426379 "LEADCDET" 1426949 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1424855 1424929 1425158 "LAZM3PK" 1425586 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1419772 1422932 1423470 "LAUPOL" 1424367 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1419351 1419395 1419556 "LAPLACE" 1419722 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1417290 1418452 1418703 "LA" 1419184 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1416337 1416921 1416962 "LALG" 1417024 NIL LALG (NIL T) -9 NIL 1417083 NIL) (-617 1416051 1416110 1416246 "LALG-" 1416251 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1415886 1415910 1415951 "KVTFROM" 1416013 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1414809 1415253 1415438 "KTVLOGIC" 1415721 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1414644 1414668 1414709 "KRCFROM" 1414771 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1413548 1413735 1414034 "KOVACIC" 1414444 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1413383 1413407 1413448 "KONVERT" 1413510 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1413218 1413242 1413283 "KOERCE" 1413345 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1410900 1411688 1412089 "KERNEL" 1412850 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1410396 1410477 1410609 "KERNEL2" 1410814 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1404166 1408935 1408989 "KDAGG" 1409366 NIL KDAGG (NIL T T) -9 NIL 1409572 NIL) (-607 1403695 1403819 1404024 "KDAGG-" 1404029 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1396843 1403356 1403511 "KAFILE" 1403573 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1391271 1396354 1396582 "JORDAN" 1396664 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1390650 1390920 1391041 "JOINAST" 1391170 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1390496 1390555 1390610 "JAVACODE" 1390615 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1386748 1388701 1388755 "IXAGG" 1389684 NIL IXAGG (NIL T T) -9 NIL 1390143 NIL) (-601 1385667 1385973 1386392 "IXAGG-" 1386397 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1381199 1385589 1385648 "IVECTOR" 1385653 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1379965 1380202 1380468 "ITUPLE" 1380966 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1378479 1378656 1378949 "ITRIGMNP" 1379787 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1377224 1377428 1377711 "ITFUN3" 1378255 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1376856 1376913 1377022 "ITFUN2" 1377161 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1374658 1375718 1376017 "ITAYLOR" 1376590 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1363603 1368795 1369958 "ISUPS" 1373528 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1362707 1362847 1363083 "ISUMP" 1363450 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1357921 1362508 1362587 "ISTRING" 1362660 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1357397 1357642 1357734 "ISAST" 1357849 T ISAST (NIL) -8 NIL NIL NIL) (-590 1356606 1356688 1356904 "IRURPK" 1357311 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1355542 1355743 1355983 "IRSN" 1356386 T IRSN (NIL) -7 NIL NIL NIL) (-588 1353613 1353968 1354397 "IRRF2F" 1355180 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1353360 1353398 1353474 "IRREDFFX" 1353569 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1351975 1352234 1352533 "IROOT" 1353093 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1348579 1349659 1350351 "IR" 1351315 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1346192 1346687 1347253 "IR2" 1348057 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1345292 1345405 1345619 "IR2F" 1346075 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1345083 1345117 1345177 "IPRNTPK" 1345252 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1341663 1344972 1345041 "IPF" 1345046 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1339990 1341588 1341645 "IPADIC" 1341650 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1339302 1339550 1339680 "IP4ADDR" 1339880 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1338775 1339006 1339116 "IOMODE" 1339212 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1337848 1338372 1338499 "IOBFILE" 1338668 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1337336 1337752 1337780 "IOBCON" 1337785 T IOBCON (NIL) -9 NIL 1337806 NIL) (-575 1336847 1336905 1337088 "INVLAPLA" 1337272 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1326495 1328849 1331235 "INTTR" 1334511 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1322830 1323572 1324437 "INTTOOLS" 1325680 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1322416 1322507 1322624 "INTSLPE" 1322733 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1320370 1322339 1322398 "INTRVL" 1322403 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1317972 1318484 1319059 "INTRF" 1319855 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1317383 1317480 1317622 "INTRET" 1317870 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1315380 1315769 1316239 "INTRAT" 1316991 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1312643 1313226 1313845 "INTPM" 1314865 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1309387 1309987 1310725 "INTPAF" 1312029 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1304566 1305528 1306579 "INTPACK" 1308356 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1301443 1304295 1304422 "INT" 1304459 T INT (NIL) -8 NIL NIL NIL) (-563 1300695 1300847 1301055 "INTHERTR" 1301285 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1300134 1300214 1300402 "INTHERAL" 1300609 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1297980 1298423 1298880 "INTHEORY" 1299697 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1289386 1291007 1292779 "INTG0" 1296332 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1269959 1274749 1279559 "INTFTBL" 1284596 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1269208 1269346 1269519 "INTFACT" 1269818 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1266635 1267081 1267638 "INTEF" 1268762 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1265068 1265807 1265835 "INTDOM" 1266136 T INTDOM (NIL) -9 NIL 1266343 NIL) (-555 1264437 1264611 1264853 "INTDOM-" 1264858 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1260897 1262821 1262875 "INTCAT" 1263674 NIL INTCAT (NIL T) -9 NIL 1263994 NIL) (-553 1260369 1260472 1260600 "INTBIT" 1260789 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1259068 1259222 1259529 "INTALG" 1260214 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1258551 1258641 1258798 "INTAF" 1258972 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1251894 1258361 1258501 "INTABL" 1258506 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1251235 1251701 1251766 "INT8" 1251800 T INT8 (NIL) -8 NIL NIL 1251845) (-548 1250575 1251041 1251106 "INT64" 1251140 T INT64 (NIL) -8 NIL NIL 1251185) (-547 1249915 1250381 1250446 "INT32" 1250480 T INT32 (NIL) -8 NIL NIL 1250525) (-546 1249255 1249721 1249786 "INT16" 1249820 T INT16 (NIL) -8 NIL NIL 1249865) (-545 1244235 1246944 1246972 "INS" 1247906 T INS (NIL) -9 NIL 1248571 NIL) (-544 1241475 1242246 1243220 "INS-" 1243293 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1240250 1240477 1240775 "INPSIGN" 1241228 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1239368 1239485 1239682 "INPRODPF" 1240130 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1238262 1238379 1238616 "INPRODFF" 1239248 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1237262 1237414 1237674 "INNMFACT" 1238098 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1236459 1236556 1236744 "INMODGCD" 1237161 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1234967 1235212 1235536 "INFSP" 1236204 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1234151 1234268 1234451 "INFPROD0" 1234847 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1231006 1232216 1232731 "INFORM" 1233644 T INFORM (NIL) -8 NIL NIL NIL) (-535 1230616 1230676 1230774 "INFORM1" 1230941 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1230139 1230228 1230342 "INFINITY" 1230522 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1229315 1229859 1229960 "INETCLTS" 1230058 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1227931 1228181 1228502 "INEP" 1229063 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1227180 1227828 1227893 "INDE" 1227898 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1226744 1226812 1226929 "INCRMAPS" 1227107 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1225562 1226013 1226219 "INBFILE" 1226558 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1220862 1221798 1222742 "INBFF" 1224650 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1219770 1220039 1220067 "INBCON" 1220580 T INBCON (NIL) -9 NIL 1220846 NIL) (-526 1219022 1219245 1219521 "INBCON-" 1219526 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1218501 1218746 1218837 "INAST" 1218951 T INAST (NIL) -8 NIL NIL NIL) (-524 1217928 1218180 1218286 "IMPTAST" 1218415 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1214374 1217772 1217876 "IMATRIX" 1217881 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1213086 1213209 1213524 "IMATQF" 1214230 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1211306 1211533 1211870 "IMATLIN" 1212842 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1205884 1211230 1211288 "ILIST" 1211293 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1203789 1205744 1205857 "IIARRAY2" 1205862 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1199187 1203700 1203764 "IFF" 1203769 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1198534 1198804 1198920 "IFAST" 1199091 T IFAST (NIL) -8 NIL NIL NIL) (-516 1193529 1197826 1198014 "IFARRAY" 1198391 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1192709 1193433 1193506 "IFAMON" 1193511 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1192293 1192358 1192412 "IEVALAB" 1192619 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1191968 1192036 1192196 "IEVALAB-" 1192201 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1191599 1191882 1191945 "IDPO" 1191950 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1190849 1191488 1191563 "IDPOAMS" 1191568 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1190156 1190738 1190813 "IDPOAM" 1190818 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1189215 1189491 1189544 "IDPC" 1189957 NIL IDPC (NIL T T) -9 NIL 1190106 NIL) (-508 1188684 1189107 1189180 "IDPAM" 1189185 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1188060 1188576 1188649 "IDPAG" 1188654 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1187705 1187896 1187971 "IDENT" 1188005 T IDENT (NIL) -8 NIL NIL NIL) (-505 1183960 1184808 1185703 "IDECOMP" 1186862 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1176796 1177883 1178930 "IDEAL" 1182996 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1175960 1176072 1176271 "ICDEN" 1176680 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1175031 1175440 1175587 "ICARD" 1175833 T ICARD (NIL) -8 NIL NIL NIL) (-501 1173091 1173404 1173809 "IBPTOOLS" 1174708 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1168698 1172711 1172824 "IBITS" 1173010 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1165421 1165997 1166692 "IBATOOL" 1168115 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1163200 1163662 1164195 "IBACHIN" 1164956 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1161029 1163046 1163149 "IARRAY2" 1163154 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1157135 1160955 1161012 "IARRAY1" 1161017 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1151244 1155547 1156028 "IAN" 1156674 T IAN (NIL) -8 NIL NIL NIL) (-494 1150755 1150812 1150985 "IALGFACT" 1151181 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1150283 1150396 1150424 "HYPCAT" 1150631 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1149821 1149938 1150124 "HYPCAT-" 1150129 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1149416 1149616 1149699 "HOSTNAME" 1149758 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1149261 1149298 1149339 "HOMOTOP" 1149344 NIL HOMOTOP (NIL T) -9 NIL 1149377 NIL) (-489 1145893 1147271 1147312 "HOAGG" 1148293 NIL HOAGG (NIL T) -9 NIL 1148972 NIL) (-488 1144487 1144886 1145412 "HOAGG-" 1145417 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1138491 1144082 1144231 "HEXADEC" 1144358 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1137239 1137461 1137724 "HEUGCD" 1138268 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1136315 1137076 1137206 "HELLFDIV" 1137211 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1134494 1136092 1136180 "HEAP" 1136259 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1133757 1134046 1134180 "HEADAST" 1134380 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1127623 1133672 1133734 "HDP" 1133739 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1121611 1127258 1127410 "HDMP" 1127524 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1120935 1121075 1121239 "HB" 1121467 T HB (NIL) -7 NIL NIL NIL) (-479 1114321 1120781 1120885 "HASHTBL" 1120890 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1113797 1114042 1114134 "HASAST" 1114249 T HASAST (NIL) -8 NIL NIL NIL) (-477 1111575 1113419 1113601 "HACKPI" 1113635 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1107243 1111428 1111541 "GTSET" 1111546 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1100658 1107121 1107219 "GSTBL" 1107224 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092936 1099689 1099954 "GSERIES" 1100449 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1092077 1092494 1092522 "GROUP" 1092725 T GROUP (NIL) -9 NIL 1092859 NIL) (-472 1091443 1091602 1091853 "GROUP-" 1091858 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089810 1090131 1090518 "GROEBSOL" 1091120 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088724 1089012 1089063 "GRMOD" 1089592 NIL GRMOD (NIL T T) -9 NIL 1089760 NIL) (-469 1088492 1088528 1088656 "GRMOD-" 1088661 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083782 1084846 1085846 "GRIMAGE" 1087512 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1082248 1082509 1082833 "GRDEF" 1083478 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081692 1081808 1081949 "GRAY" 1082127 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080879 1081285 1081336 "GRALG" 1081489 NIL GRALG (NIL T T) -9 NIL 1081582 NIL) (-464 1080540 1080613 1080776 "GRALG-" 1080781 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1077317 1080125 1080303 "GPOLSET" 1080447 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076671 1076728 1076986 "GOSPER" 1077254 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1072403 1073109 1073635 "GMODPOL" 1076370 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1071408 1071592 1071830 "GHENSEL" 1072215 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1065564 1066407 1067427 "GENUPS" 1070492 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1065261 1065312 1065401 "GENUFACT" 1065507 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064673 1064750 1064915 "GENPGCD" 1065179 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1064147 1064182 1064395 "GENMFACT" 1064632 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062713 1062970 1063277 "GENEEZ" 1063890 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1056858 1062324 1062486 "GDMP" 1062636 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1046200 1050629 1051735 "GCNAALG" 1055841 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1044593 1045455 1045483 "GCDDOM" 1045738 T GCDDOM (NIL) -9 NIL 1045895 NIL) (-451 1044063 1044190 1044405 "GCDDOM-" 1044410 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1042735 1042920 1043224 "GB" 1043842 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1031351 1033681 1036073 "GBINTERN" 1040426 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1029188 1029480 1029901 "GBF" 1031026 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027969 1028134 1028401 "GBEUCLID" 1029004 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1027318 1027443 1027592 "GAUSSFAC" 1027840 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1025685 1025987 1026301 "GALUTIL" 1027037 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023993 1024267 1024591 "GALPOLYU" 1025412 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1021358 1021648 1022055 "GALFACTU" 1023690 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1013163 1014663 1016271 "GALFACT" 1019790 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1010551 1011209 1011237 "FVFUN" 1012393 T FVFUN (NIL) -9 NIL 1013113 NIL) (-440 1009817 1009999 1010027 "FVC" 1010318 T FVC (NIL) -9 NIL 1010501 NIL) (-439 1009460 1009642 1009710 "FUNDESC" 1009769 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1009075 1009257 1009338 "FUNCTION" 1009412 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006819 1007397 1007863 "FT" 1008629 T FT (NIL) -8 NIL NIL NIL) (-436 1005610 1006120 1006323 "FTEM" 1006636 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003901 1004190 1004587 "FSUPFACT" 1005301 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1002298 1002587 1002919 "FST" 1003589 T FST (NIL) -8 NIL NIL NIL) (-433 1001497 1001603 1001791 "FSRED" 1002180 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1000196 1000452 1000799 "FSPRMELT" 1001212 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 997502 997940 998426 "FSPECF" 999759 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 979657 987981 988022 "FS" 991906 NIL FS (NIL T) -9 NIL 994195 NIL) (-429 968300 971293 975350 "FS-" 975650 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 967828 967882 968052 "FSINT" 968241 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 966120 966821 967124 "FSERIES" 967607 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 965162 965278 965502 "FSCINT" 966000 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 961370 964106 964147 "FSAGG" 964517 NIL FSAGG (NIL T) -9 NIL 964776 NIL) (-424 959132 959733 960529 "FSAGG-" 960624 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 958174 958317 958544 "FSAGG2" 958985 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 955856 956136 956683 "FS2UPS" 957892 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 955490 955533 955662 "FS2" 955807 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 954368 954539 954841 "FS2EXPXP" 955315 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 953794 953909 954061 "FRUTIL" 954248 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 945207 949289 950647 "FR" 952468 NIL FR (NIL T) -8 NIL NIL NIL) (-417 940255 942925 942965 "FRNAALG" 944361 NIL FRNAALG (NIL T) -9 NIL 944968 NIL) (-416 935928 937004 938279 "FRNAALG-" 939029 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 935566 935609 935736 "FRNAAF2" 935879 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 933946 934420 934715 "FRMOD" 935378 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 931697 932329 932646 "FRIDEAL" 933737 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 930892 930979 931268 "FRIDEAL2" 931604 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 930025 930439 930480 "FRETRCT" 930485 NIL FRETRCT (NIL T) -9 NIL 930661 NIL) (-410 929137 929368 929719 "FRETRCT-" 929724 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 926315 927525 927584 "FRAMALG" 928466 NIL FRAMALG (NIL T T) -9 NIL 928758 NIL) (-408 924449 924904 925534 "FRAMALG-" 925757 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 918370 923924 924200 "FRAC" 924205 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 918006 918063 918170 "FRAC2" 918307 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 917642 917699 917806 "FR2" 917943 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 912280 915167 915195 "FPS" 916314 T FPS (NIL) -9 NIL 916871 NIL) (-403 911729 911838 912002 "FPS-" 912148 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 909149 910818 910846 "FPC" 911071 T FPC (NIL) -9 NIL 911213 NIL) (-401 908942 908982 909079 "FPC-" 909084 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 907732 908430 908471 "FPATMAB" 908476 NIL FPATMAB (NIL T) -9 NIL 908628 NIL) (-399 905405 905908 906334 "FPARFRAC" 907369 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 900798 901297 901979 "FORTRAN" 904837 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 898514 899014 899553 "FORT" 900279 T FORT (NIL) -7 NIL NIL NIL) (-396 896190 896752 896780 "FORTFN" 897840 T FORTFN (NIL) -9 NIL 898464 NIL) (-395 895954 896004 896032 "FORTCAT" 896091 T FORTCAT (NIL) -9 NIL 896153 NIL) (-394 894060 894570 894960 "FORMULA" 895584 T FORMULA (NIL) -8 NIL NIL NIL) (-393 893848 893878 893947 "FORMULA1" 894024 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 893371 893423 893596 "FORDER" 893790 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 892467 892631 892824 "FOP" 893198 T FOP (NIL) -7 NIL NIL NIL) (-390 891048 891747 891921 "FNLA" 892349 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 889777 890192 890220 "FNCAT" 890680 T FNCAT (NIL) -9 NIL 890940 NIL) (-388 889316 889736 889764 "FNAME" 889769 T FNAME (NIL) -8 NIL NIL NIL) (-387 887945 888908 888936 "FMTC" 888941 T FMTC (NIL) -9 NIL 888977 NIL) (-386 884278 885468 886097 "FMONOID" 887349 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 883470 884020 884169 "FM" 884174 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880894 881540 881568 "FMFUN" 882712 T FMFUN (NIL) -9 NIL 883420 NIL) (-383 880163 880344 880372 "FMC" 880662 T FMC (NIL) -9 NIL 880844 NIL) (-382 877331 878191 878245 "FMCAT" 879440 NIL FMCAT (NIL T T) -9 NIL 879935 NIL) (-381 876197 877097 877197 "FM1" 877276 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873971 874387 874881 "FLOATRP" 875748 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 867545 871700 872321 "FLOAT" 873370 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864983 865483 866061 "FLOATCP" 867012 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863758 864596 864637 "FLINEXP" 864642 NIL FLINEXP (NIL T) -9 NIL 864735 NIL) (-376 862912 863147 863475 "FLINEXP-" 863480 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861988 862132 862356 "FLASORT" 862764 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 859179 860047 860099 "FLALG" 861326 NIL FLALG (NIL T T) -9 NIL 861793 NIL) (-373 852915 856665 856706 "FLAGG" 857968 NIL FLAGG (NIL T) -9 NIL 858620 NIL) (-372 851641 851980 852470 "FLAGG-" 852475 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850683 850826 851053 "FLAGG2" 851494 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847624 848632 848691 "FINRALG" 849819 NIL FINRALG (NIL T T) -9 NIL 850327 NIL) (-369 846784 847013 847352 "FINRALG-" 847357 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 846164 846403 846431 "FINITE" 846627 T FINITE (NIL) -9 NIL 846734 NIL) (-367 838596 840783 840823 "FINAALG" 844490 NIL FINAALG (NIL T) -9 NIL 845943 NIL) (-366 833928 834978 836122 "FINAALG-" 837501 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 833296 833683 833786 "FILE" 833858 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831954 832292 832346 "FILECAT" 833030 NIL FILECAT (NIL T T) -9 NIL 833246 NIL) (-363 829788 831316 831344 "FIELD" 831384 T FIELD (NIL) -9 NIL 831464 NIL) (-362 828408 828793 829304 "FIELD-" 829309 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 826258 827043 827390 "FGROUP" 828094 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825348 825512 825732 "FGLMICPK" 826090 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 821180 825273 825330 "FFX" 825335 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820781 820842 820977 "FFSLPE" 821113 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816770 817553 818349 "FFPOLY" 820017 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 816274 816310 816519 "FFPOLY2" 816728 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 812117 816193 816256 "FFP" 816261 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807515 812028 812092 "FF" 812097 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802641 806858 807048 "FFNBX" 807369 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797570 801776 802034 "FFNBP" 802495 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792203 796854 797065 "FFNB" 797403 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 791035 791233 791548 "FFINTBAS" 792000 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787228 789442 789470 "FFIELDC" 790090 T FFIELDC (NIL) -9 NIL 790466 NIL) (-348 785890 786261 786758 "FFIELDC-" 786763 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785459 785505 785629 "FFHOM" 785832 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783154 783641 784158 "FFF" 784974 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778772 782896 782997 "FFCGX" 783097 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774393 778504 778611 "FFCGP" 778715 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769576 774120 774228 "FFCG" 774329 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751374 760447 760533 "FFCAT" 765698 NIL FFCAT (NIL T T T) -9 NIL 767149 NIL) (-341 746572 747619 748933 "FFCAT-" 750163 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745983 746026 746261 "FFCAT2" 746523 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735304 738955 740175 "FEXPR" 744835 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734304 734739 734780 "FEVALAB" 734864 NIL FEVALAB (NIL T) -9 NIL 735125 NIL) (-337 733463 733673 734011 "FEVALAB-" 734016 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 732029 732846 733049 "FDIV" 733362 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 729069 729810 729925 "FDIVCAT" 731493 NIL FDIVCAT (NIL T T T T) -9 NIL 731930 NIL) (-334 728831 728858 729028 "FDIVCAT-" 729033 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 728051 728138 728415 "FDIV2" 728738 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726737 726996 727285 "FCPAK1" 727782 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725836 726237 726378 "FCOMP" 726628 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709538 712986 716524 "FC" 722318 T FC (NIL) -8 NIL NIL NIL) (-329 702082 706102 706142 "FAXF" 707944 NIL FAXF (NIL T) -9 NIL 708636 NIL) (-328 699358 700016 700841 "FAXF-" 701306 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694410 698734 698910 "FARRAY" 699215 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689629 691695 691748 "FAMR" 692771 NIL FAMR (NIL T T) -9 NIL 693231 NIL) (-325 688519 688821 689256 "FAMR-" 689261 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687688 688441 688494 "FAMONOID" 688499 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685474 686184 686237 "FAMONC" 687178 NIL FAMONC (NIL T T) -9 NIL 687564 NIL) (-322 684139 685228 685365 "FAGROUP" 685370 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681934 682253 682656 "FACUTIL" 683820 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681033 681218 681440 "FACTFUNC" 681744 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673455 680336 680535 "EXPUPXS" 680889 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670938 671478 672064 "EXPRTUBE" 672889 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667209 667801 668531 "EXPRODE" 670277 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652694 665858 666287 "EXPR" 666813 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647248 647835 648641 "EXPR2UPS" 651992 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646880 646937 647046 "EXPR2" 647185 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638271 646033 646323 "EXPEXPAN" 646717 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 638071 638228 638257 "EXIT" 638262 T EXIT (NIL) -8 NIL NIL NIL) (-311 637551 637795 637886 "EXITAST" 638000 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637178 637240 637353 "EVALCYC" 637483 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636719 636837 636878 "EVALAB" 637048 NIL EVALAB (NIL T) -9 NIL 637152 NIL) (-308 636200 636322 636543 "EVALAB-" 636548 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633634 634936 634964 "EUCDOM" 635519 T EUCDOM (NIL) -9 NIL 635869 NIL) (-306 632039 632481 633071 "EUCDOM-" 633076 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619577 622337 625087 "ESTOOLS" 629309 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619209 619266 619375 "ESTOOLS2" 619514 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618960 619002 619082 "ESTOOLS1" 619161 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612997 614605 614633 "ES" 617401 T ES (NIL) -9 NIL 618811 NIL) (-301 607944 609231 611048 "ES-" 611212 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604318 605079 605859 "ESCONT" 607184 T ESCONT (NIL) -7 NIL NIL NIL) (-299 604063 604095 604177 "ESCONT1" 604280 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603738 603788 603888 "ES2" 604007 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603368 603426 603535 "ES1" 603674 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602584 602713 602889 "ERROR" 603212 T ERROR (NIL) -7 NIL NIL NIL) (-295 595976 602443 602534 "EQTBL" 602539 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588479 591290 592739 "EQ" 594560 NIL -2035 (NIL T) -8 NIL NIL NIL) (-293 588111 588168 588277 "EQ2" 588416 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583400 584449 585542 "EP" 587050 NIL EP (NIL T) -7 NIL NIL NIL) (-291 582000 582291 582597 "ENV" 583114 T ENV (NIL) -8 NIL NIL NIL) (-290 581145 581699 581727 "ENTIRER" 581732 T ENTIRER (NIL) -9 NIL 581778 NIL) (-289 577612 579100 579470 "EMR" 580944 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576756 576941 576995 "ELTAGG" 577375 NIL ELTAGG (NIL T T) -9 NIL 577586 NIL) (-287 576475 576537 576678 "ELTAGG-" 576683 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576264 576293 576347 "ELTAB" 576431 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575390 575536 575735 "ELFUTS" 576115 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575132 575188 575216 "ELEMFUN" 575321 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 575002 575023 575091 "ELEMFUN-" 575096 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569846 573102 573143 "ELAGG" 574083 NIL ELAGG (NIL T) -9 NIL 574546 NIL) (-281 568131 568565 569228 "ELAGG-" 569233 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566796 567074 567367 "ELABEXPR" 567858 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559660 561463 562290 "EFUPXS" 566072 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553110 554911 555721 "EFULS" 558936 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550595 550953 551425 "EFSTRUC" 552742 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 540446 542012 543559 "EF" 549110 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 539520 539931 540080 "EAB" 540317 T EAB (NIL) -8 NIL NIL NIL) (-274 538702 539479 539507 "E04UCFA" 539512 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537884 538661 538689 "E04NAFA" 538694 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 537066 537843 537871 "E04MBFA" 537876 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 536248 537025 537053 "E04JAFA" 537058 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 535432 536207 536235 "E04GCFA" 536240 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 534616 535391 535419 "E04FDFA" 535424 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533798 534575 534603 "E04DGFA" 534608 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527971 529323 530687 "E04AGNT" 532454 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526651 527157 527197 "DVARCAT" 527672 NIL DVARCAT (NIL T) -9 NIL 527871 NIL) (-265 525855 526067 526381 "DVARCAT-" 526386 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518992 525654 525783 "DSMP" 525788 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 513774 514937 516005 "DROPT" 517944 T DROPT (NIL) -8 NIL NIL NIL) (-262 513439 513498 513596 "DROPT1" 513709 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 508554 509680 510817 "DROPT0" 512322 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506899 507224 507610 "DRAWPT" 508188 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 501486 502409 503488 "DRAW" 505873 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 501119 501172 501290 "DRAWHACK" 501427 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499850 500119 500410 "DRAWCX" 500848 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 499365 499434 499585 "DRAWCURV" 499776 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 489833 491795 493910 "DRAWCFUN" 497270 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 486599 488528 488569 "DQAGG" 489198 NIL DQAGG (NIL T) -9 NIL 489471 NIL) (-253 475143 481604 481687 "DPOLCAT" 483539 NIL DPOLCAT (NIL T T T T) -9 NIL 484084 NIL) (-252 469979 471328 473286 "DPOLCAT-" 473291 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 463101 469840 469938 "DPMO" 469943 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 456126 462881 463048 "DPMM" 463053 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 455731 456045 456093 "DOMCTOR" 456098 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454999 455253 455390 "DOMAIN" 455614 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 448987 454634 454786 "DMP" 454900 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 448587 448643 448787 "DLP" 448925 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 442409 447914 448104 "DLIST" 448429 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 439206 441262 441303 "DLAGG" 441853 NIL DLAGG (NIL T) -9 NIL 442083 NIL) (-243 437985 438649 438677 "DIVRING" 438769 T DIVRING (NIL) -9 NIL 438852 NIL) (-242 437222 437412 437712 "DIVRING-" 437717 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 435324 435681 436087 "DISPLAY" 436836 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 429212 435238 435301 "DIRPROD" 435306 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 428060 428263 428528 "DIRPROD2" 429005 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 417269 423275 423328 "DIRPCAT" 423738 NIL DIRPCAT (NIL NIL T) -9 NIL 424578 NIL) (-237 414595 415237 416118 "DIRPCAT-" 416455 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 413882 414042 414228 "DIOSP" 414429 T DIOSP (NIL) -7 NIL NIL NIL) (-235 410537 412794 412835 "DIOPS" 413269 NIL DIOPS (NIL T) -9 NIL 413498 NIL) (-234 410086 410200 410391 "DIOPS-" 410396 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408944 409572 409600 "DIFRING" 409787 T DIFRING (NIL) -9 NIL 409897 NIL) (-232 408590 408667 408819 "DIFRING-" 408824 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 406361 407633 407674 "DIFEXT" 408037 NIL DIFEXT (NIL T) -9 NIL 408331 NIL) (-230 404646 405074 405740 "DIFEXT-" 405745 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401921 404178 404219 "DIAGG" 404224 NIL DIAGG (NIL T) -9 NIL 404244 NIL) (-228 401305 401462 401714 "DIAGG-" 401719 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 396722 400264 400541 "DHMATRIX" 401074 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 392334 393243 394253 "DFSFUN" 395732 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 387412 391265 391577 "DFLOAT" 392042 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 385675 385956 386345 "DFINTTLS" 387120 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 382704 383696 384096 "DERHAM" 385341 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 380505 382479 382568 "DEQUEUE" 382648 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 379759 379892 380075 "DEGRED" 380367 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 376189 376934 377780 "DEFINTRF" 378987 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 373744 374213 374805 "DEFINTEF" 375708 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373094 373364 373479 "DEFAST" 373649 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367098 372689 372838 "DECIMAL" 372965 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 364609 365068 365574 "DDFACT" 366642 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 364205 364248 364399 "DBLRESP" 364560 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362077 362438 362798 "DBASE" 363972 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 361319 361557 361703 "DATAARY" 361976 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 360425 361278 361306 "D03FAFA" 361311 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 359532 360384 360412 "D03EEFA" 360417 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 357482 357948 358437 "D03AGNT" 359063 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356771 357441 357469 "D02EJFA" 357474 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356060 356730 356758 "D02CJFA" 356763 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 355349 356019 356047 "D02BHFA" 356052 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354638 355308 355336 "D02BBFA" 355341 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347835 349424 351030 "D02AGNT" 353052 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345603 346126 346672 "D01WGTS" 347309 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344670 345562 345590 "D01TRNS" 345595 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343738 344629 344657 "D01GBFA" 344662 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342806 343697 343725 "D01FCFA" 343730 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341874 342765 342793 "D01ASFA" 342798 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340942 341833 341861 "D01AQFA" 341866 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340010 340901 340929 "D01APFA" 340934 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339078 339969 339997 "D01ANFA" 340002 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 338146 339037 339065 "D01AMFA" 339070 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 337214 338105 338133 "D01ALFA" 338138 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 336282 337173 337201 "D01AKFA" 337206 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335350 336241 336269 "D01AJFA" 336274 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328645 330198 331759 "D01AGNT" 333809 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327982 328110 328262 "CYCLOTOM" 328513 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324717 325430 326157 "CYCLES" 327275 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324029 324163 324334 "CVMP" 324578 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321870 322128 322497 "CTRIGMNP" 323757 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321338 321664 321737 "CTOR" 321817 T CTOR (NIL) -8 NIL NIL NIL) (-186 320847 321069 321170 "CTORKIND" 321257 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320169 320454 320482 "CTORCAT" 320664 T CTORCAT (NIL) -9 NIL 320777 NIL) (-184 319767 319878 320037 "CTORCAT-" 320042 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319256 319470 319568 "CTORCALL" 319689 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318630 318729 318882 "CSTTOOLS" 319153 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314429 315086 315844 "CRFP" 317942 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313904 314150 314242 "CRCEAST" 314357 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312951 313136 313364 "CRAPACK" 313708 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312335 312436 312640 "CPMATCH" 312827 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312060 312088 312194 "CPIMA" 312301 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308424 309096 309814 "COORDSYS" 311395 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307836 307957 308099 "CONTOUR" 308302 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303727 305839 306331 "CONTFRAC" 307376 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303607 303628 303656 "CONDUIT" 303693 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302746 303300 303328 "COMRING" 303333 T COMRING (NIL) -9 NIL 303385 NIL) (-171 301800 302104 302288 "COMPPROP" 302582 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301461 301496 301624 "COMPLPAT" 301759 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291755 301270 301379 "COMPLEX" 301384 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291391 291448 291555 "COMPLEX2" 291692 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291109 291144 291242 "COMPFACT" 291350 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275585 285568 285608 "COMPCAT" 286612 NIL COMPCAT (NIL T) -9 NIL 287958 NIL) (-165 265095 268024 271651 "COMPCAT-" 272007 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264824 264852 264955 "COMMUPC" 265061 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264618 264652 264711 "COMMONOP" 264785 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264174 264369 264456 "COMM" 264551 T COMM (NIL) -8 NIL NIL NIL) (-161 263750 263978 264053 "COMMAAST" 264119 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262999 263193 263221 "COMBOPC" 263559 T COMBOPC (NIL) -9 NIL 263734 NIL) (-159 261895 262105 262347 "COMBINAT" 262789 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258352 258926 259553 "COMBF" 261317 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257110 257468 257703 "COLOR" 258137 T COLOR (NIL) -8 NIL NIL NIL) (-156 256586 256831 256923 "COLONAST" 257038 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256226 256273 256398 "CMPLXRT" 256533 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255674 255926 256025 "CLLCTAST" 256147 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251174 252204 253284 "CLIP" 254614 T CLIP (NIL) -7 NIL NIL NIL) (-152 249520 250280 250519 "CLIF" 251001 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245695 247666 247707 "CLAGG" 248636 NIL CLAGG (NIL T) -9 NIL 249172 NIL) (-150 244117 244574 245157 "CLAGG-" 245162 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243661 243746 243886 "CINTSLPE" 244026 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241162 241633 242181 "CHVAR" 243189 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240371 240925 240953 "CHARZ" 240958 T CHARZ (NIL) -9 NIL 240973 NIL) (-146 240125 240165 240243 "CHARPOL" 240325 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239218 239805 239833 "CHARNZ" 239880 T CHARNZ (NIL) -9 NIL 239936 NIL) (-144 237180 237908 238243 "CHAR" 238903 T CHAR (NIL) -8 NIL NIL NIL) (-143 236906 236967 236995 "CFCAT" 237106 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236151 236262 236444 "CDEN" 236790 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232116 235304 235584 "CCLASS" 235891 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231423 231566 231729 "CATEGORY" 231973 T -10 (NIL) -8 NIL NIL NIL) (-139 231028 231342 231390 "CATCTOR" 231395 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230479 230731 230829 "CATAST" 230950 T CATAST (NIL) -8 NIL NIL NIL) (-137 229955 230200 230292 "CASEAST" 230407 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224964 225984 226737 "CARTEN" 229258 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224072 224220 224441 "CARTEN2" 224811 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222387 223222 223479 "CARD" 223835 T CARD (NIL) -8 NIL NIL NIL) (-133 221963 222191 222266 "CAPSLAST" 222332 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221467 221675 221703 "CACHSET" 221835 T CACHSET (NIL) -9 NIL 221913 NIL) (-131 220937 221259 221287 "CABMON" 221337 T CABMON (NIL) -9 NIL 221393 NIL) (-130 220410 220641 220751 "BYTEORD" 220847 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219386 219944 220086 "BYTE" 220249 T BYTE (NIL) -8 NIL NIL 220371) (-128 214736 218891 219063 "BYTEBUF" 219234 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212245 214428 214535 "BTREE" 214662 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209694 211893 212015 "BTOURN" 212155 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207064 209164 209205 "BTCAT" 209273 NIL BTCAT (NIL T) -9 NIL 209350 NIL) (-124 206731 206811 206960 "BTCAT-" 206965 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201996 205874 205902 "BTAGG" 206124 T BTAGG (NIL) -9 NIL 206285 NIL) (-122 201486 201611 201817 "BTAGG-" 201822 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198481 200764 200979 "BSTREE" 201303 NIL BSTREE (NIL T) -8 NIL NIL 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NIL NIL NIL) (-107 162085 163560 163601 "BGAGG" 163861 NIL BGAGG (NIL T) -9 NIL 163998 NIL) (-106 161916 161948 162039 "BGAGG-" 162044 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160987 161300 161505 "BFUNCT" 161731 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159677 159855 160143 "BEZOUT" 160811 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156146 158529 158859 "BBTREE" 159380 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155880 155933 155961 "BASTYPE" 156080 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155732 155761 155834 "BASTYPE-" 155839 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155166 155242 155394 "BALFACT" 155643 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154022 154581 154767 "AUTOMOR" 155011 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153748 153753 153779 "ATTREG" 153784 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152000 152445 152797 "ATTRBUT" 153414 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151608 151828 151894 "ATTRAST" 151952 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151144 151257 151283 "ATRIG" 151484 T ATRIG 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3167741 "WEIER" 3168520 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1269 3165898 3166348 3166390 "VSPACE" 3166526 NIL VSPACE (NIL T) -9 NIL 3166600 NIL) (-1268 3165736 3165763 3165854 "VSPACE-" 3165859 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1267 3165544 3165587 3165655 "VOID" 3165690 T VOID (NIL) -8 NIL NIL NIL) (-1266 3163680 3164039 3164445 "VIEW" 3165160 T VIEW (NIL) -7 NIL NIL NIL) (-1265 3160104 3160743 3161480 "VIEWDEF" 3162965 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1264 3149408 3151652 3153825 "VIEW3D" 3157953 T VIEW3D (NIL) -8 NIL NIL NIL) (-1263 3141659 3143319 3144898 "VIEW2D" 3147851 T VIEW2D (NIL) -8 NIL NIL NIL) (-1262 3137011 3141429 3141521 "VECTOR" 3141602 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1261 3135588 3135847 3136165 "VECTOR2" 3136741 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1260 3129062 3133369 3133412 "VECTCAT" 3134407 NIL VECTCAT (NIL T) -9 NIL 3134994 NIL) (-1259 3128076 3128330 3128720 "VECTCAT-" 3128725 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1258 3127530 3127727 3127847 "VARIABLE" 3127991 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1257 3127463 3127468 3127498 "UTYPE" 3127503 T UTYPE (NIL) -9 NIL NIL NIL) (-1256 3126293 3126447 3126709 "UTSODETL" 3127289 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1255 3123733 3124193 3124717 "UTSODE" 3125834 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1254 3115570 3121359 3121848 "UTS" 3123302 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1253 3106444 3111811 3111854 "UTSCAT" 3112966 NIL UTSCAT (NIL T) -9 NIL 3113724 NIL) (-1252 3103791 3104514 3105503 "UTSCAT-" 3105508 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1251 3103418 3103461 3103594 "UTS2" 3103742 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1250 3097644 3100256 3100299 "URAGG" 3102369 NIL URAGG (NIL T) -9 NIL 3103092 NIL) (-1249 3094583 3095446 3096569 "URAGG-" 3096574 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1248 3090293 3093218 3093683 "UPXSSING" 3094247 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1247 3082359 3089540 3089813 "UPXS" 3090078 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1246 3075432 3082263 3082335 "UPXSCONS" 3082340 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1245 3065177 3071970 3072032 "UPXSCCA" 3072606 NIL UPXSCCA (NIL T T) -9 NIL 3072839 NIL) (-1244 3064815 3064900 3065074 "UPXSCCA-" 3065079 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1243 3054412 3060978 3061021 "UPXSCAT" 3061669 NIL UPXSCAT (NIL T) -9 NIL 3062278 NIL) (-1242 3053842 3053921 3054100 "UPXS2" 3054327 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1241 3052496 3052749 3053100 "UPSQFREE" 3053585 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1240 3045917 3048974 3049029 "UPSCAT" 3050190 NIL UPSCAT (NIL T T) -9 NIL 3050964 NIL) (-1239 3045121 3045328 3045655 "UPSCAT-" 3045660 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1238 3030776 3038544 3038587 "UPOLYC" 3040688 NIL UPOLYC (NIL T) -9 NIL 3041909 NIL) (-1237 3022104 3024530 3027677 "UPOLYC-" 3027682 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1236 3021731 3021774 3021907 "UPOLYC2" 3022055 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1235 3013542 3021414 3021543 "UP" 3021650 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1234 3012881 3012988 3013152 "UPMP" 3013431 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1233 3012434 3012515 3012654 "UPDIVP" 3012794 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1232 3011002 3011251 3011567 "UPDECOMP" 3012183 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1231 3010237 3010349 3010534 "UPCDEN" 3010886 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1230 3009756 3009825 3009974 "UP2" 3010162 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1229 3008223 3008960 3009237 "UNISEG" 3009514 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1228 3007438 3007565 3007770 "UNISEG2" 3008066 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1227 3006498 3006678 3006904 "UNIFACT" 3007254 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1226 2990430 3005675 3005926 "ULS" 3006305 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1225 2978429 2990334 2990406 "ULSCONS" 2990411 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1224 2960448 2972433 2972495 "ULSCCAT" 2973133 NIL ULSCCAT (NIL T T) -9 NIL 2973421 NIL) (-1223 2959498 2959743 2960131 "ULSCCAT-" 2960136 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1222 2948872 2955352 2955395 "ULSCAT" 2956258 NIL ULSCAT (NIL T) -9 NIL 2956989 NIL) (-1221 2948302 2948381 2948560 "ULS2" 2948787 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1220 2947429 2947939 2948046 "UINT8" 2948157 T UINT8 (NIL) -8 NIL NIL 2948242) (-1219 2946555 2947065 2947172 "UINT64" 2947283 T UINT64 (NIL) -8 NIL NIL 2947368) (-1218 2945681 2946191 2946298 "UINT32" 2946409 T UINT32 (NIL) -8 NIL NIL 2946494) (-1217 2944807 2945317 2945424 "UINT16" 2945535 T UINT16 (NIL) -8 NIL NIL 2945620) (-1216 2943110 2944067 2944097 "UFD" 2944309 T UFD (NIL) -9 NIL 2944423 NIL) (-1215 2942904 2942950 2943045 "UFD-" 2943050 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1214 2941986 2942169 2942385 "UDVO" 2942710 T UDVO (NIL) -7 NIL NIL NIL) (-1213 2939802 2940211 2940682 "UDPO" 2941550 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1212 2939735 2939740 2939770 "TYPE" 2939775 T TYPE (NIL) -9 NIL NIL NIL) (-1211 2939495 2939690 2939721 "TYPEAST" 2939726 T TYPEAST (NIL) -8 NIL NIL NIL) (-1210 2938466 2938668 2938908 "TWOFACT" 2939289 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1209 2937489 2937875 2938110 "TUPLE" 2938266 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1208 2935180 2935699 2936238 "TUBETOOL" 2936972 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1207 2934029 2934234 2934475 "TUBE" 2934973 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1206 2928758 2933001 2933284 "TS" 2933781 NIL TS (NIL T) -8 NIL NIL NIL) (-1205 2917398 2921517 2921614 "TSETCAT" 2926883 NIL TSETCAT (NIL T T T T) -9 NIL 2928414 NIL) (-1204 2912130 2913730 2915621 "TSETCAT-" 2915626 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1203 2906769 2907616 2908545 "TRMANIP" 2911266 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1202 2906210 2906273 2906436 "TRIMAT" 2906701 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1201 2904076 2904313 2904670 "TRIGMNIP" 2905959 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1200 2903596 2903709 2903739 "TRIGCAT" 2903952 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1199 2903265 2903344 2903485 "TRIGCAT-" 2903490 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1198 2900110 2902123 2902404 "TREE" 2903019 NIL TREE (NIL T) -8 NIL NIL NIL) (-1197 2899384 2899912 2899942 "TRANFUN" 2899977 T TRANFUN (NIL) -9 NIL 2900043 NIL) (-1196 2898663 2898854 2899134 "TRANFUN-" 2899139 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1195 2898467 2898499 2898560 "TOPSP" 2898624 T TOPSP (NIL) -7 NIL NIL NIL) (-1194 2897815 2897930 2898084 "TOOLSIGN" 2898348 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1193 2896449 2896992 2897231 "TEXTFILE" 2897598 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1192 2894361 2894902 2895331 "TEX" 2896042 T TEX (NIL) -8 NIL NIL NIL) (-1191 2894142 2894173 2894245 "TEX1" 2894324 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1190 2893790 2893853 2893943 "TEMUTL" 2894074 T TEMUTL (NIL) -7 NIL NIL NIL) (-1189 2891944 2892224 2892549 "TBCMPPK" 2893513 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1188 2883721 2890104 2890160 "TBAGG" 2890560 NIL TBAGG (NIL T T) -9 NIL 2890771 NIL) (-1187 2878791 2880279 2882033 "TBAGG-" 2882038 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1186 2878175 2878282 2878427 "TANEXP" 2878680 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1185 2871565 2878032 2878125 "TABLE" 2878130 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1184 2870977 2871076 2871214 "TABLEAU" 2871462 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1183 2865585 2866805 2868053 "TABLBUMP" 2869763 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1182 2864807 2864954 2865135 "SYSTEM" 2865426 T SYSTEM (NIL) -8 NIL NIL NIL) (-1181 2861266 2861965 2862748 "SYSSOLP" 2864058 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1180 2860310 2860815 2860934 "SYSNNI" 2861120 NIL SYSNNI (NIL NIL) -8 NIL NIL 2861205) (-1179 2859617 2860076 2860155 "SYSINT" 2860215 NIL SYSINT (NIL NIL) -8 NIL NIL 2860260) (-1178 2855949 2856895 2857605 "SYNTAX" 2858929 T SYNTAX (NIL) -8 NIL NIL NIL) (-1177 2853107 2853709 2854341 "SYMTAB" 2855339 T SYMTAB (NIL) -8 NIL NIL NIL) (-1176 2848356 2849258 2850241 "SYMS" 2852146 T SYMS (NIL) -8 NIL NIL NIL) (-1175 2845591 2847814 2848044 "SYMPOLY" 2848161 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1174 2845108 2845183 2845306 "SYMFUNC" 2845503 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1173 2841127 2842420 2843233 "SYMBOL" 2844317 T SYMBOL (NIL) -8 NIL NIL NIL) (-1172 2834666 2836355 2838075 "SWITCH" 2839429 T SWITCH (NIL) -8 NIL NIL NIL) (-1171 2827900 2833487 2833790 "SUTS" 2834421 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1170 2819966 2827147 2827420 "SUPXS" 2827685 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2811726 2819584 2819710 "SUP" 2819875 NIL SUP (NIL T) -8 NIL NIL NIL) (-1168 2810885 2811012 2811229 "SUPFRACF" 2811594 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1167 2810506 2810565 2810678 "SUP2" 2810820 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1166 2808954 2809228 2809584 "SUMRF" 2810205 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1165 2808289 2808355 2808547 "SUMFS" 2808875 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1164 2792256 2807466 2807717 "SULS" 2808096 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1163 2791858 2792078 2792148 "SUCHTAST" 2792208 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1162 2791153 2791383 2791523 "SUCH" 2791766 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1161 2785019 2786059 2787018 "SUBSPACE" 2790241 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1160 2784449 2784539 2784703 "SUBRESP" 2784907 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1159 2777814 2779114 2780425 "STTF" 2783185 NIL STTF (NIL T) -7 NIL NIL NIL) (-1158 2771987 2773107 2774254 "STTFNC" 2776714 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1157 2763298 2765169 2766963 "STTAYLOR" 2770228 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1156 2756428 2763162 2763245 "STRTBL" 2763250 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1155 2751792 2756383 2756414 "STRING" 2756419 T STRING (NIL) -8 NIL NIL NIL) (-1154 2746653 2751165 2751195 "STRICAT" 2751254 T STRICAT (NIL) -9 NIL 2751316 NIL) (-1153 2739407 2744272 2744883 "STREAM" 2746077 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1152 2738917 2738994 2739138 "STREAM3" 2739324 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1151 2737899 2738082 2738317 "STREAM2" 2738730 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1150 2737587 2737639 2737732 "STREAM1" 2737841 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1149 2736603 2736784 2737015 "STINPROD" 2737403 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1148 2736155 2736365 2736395 "STEP" 2736475 T STEP (NIL) -9 NIL 2736553 NIL) (-1147 2729587 2736054 2736131 "STBL" 2736136 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1146 2724713 2728808 2728851 "STAGG" 2729004 NIL STAGG (NIL T) -9 NIL 2729093 NIL) (-1145 2722415 2723017 2723889 "STAGG-" 2723894 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1144 2720562 2722185 2722277 "STACK" 2722358 NIL STACK (NIL T) -8 NIL NIL NIL) (-1143 2713257 2718703 2719159 "SREGSET" 2720192 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1142 2705682 2707051 2708564 "SRDCMPK" 2711863 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1141 2698599 2703122 2703152 "SRAGG" 2704455 T SRAGG (NIL) -9 NIL 2705063 NIL) (-1140 2697616 2697871 2698250 "SRAGG-" 2698255 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1139 2692076 2696563 2696984 "SQMATRIX" 2697242 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1138 2685761 2688794 2689521 "SPLTREE" 2691421 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1137 2681724 2682417 2683063 "SPLNODE" 2685187 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1136 2680771 2681004 2681034 "SPFCAT" 2681478 T SPFCAT (NIL) -9 NIL NIL NIL) (-1135 2679508 2679718 2679982 "SPECOUT" 2680529 T SPECOUT (NIL) -7 NIL NIL NIL) (-1134 2671134 2672904 2672934 "SPADXPT" 2677326 T SPADXPT (NIL) -9 NIL 2679360 NIL) (-1133 2670895 2670935 2671004 "SPADPRSR" 2671087 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1132 2669050 2670850 2670881 "SPADAST" 2670886 T SPADAST (NIL) -8 NIL NIL NIL) (-1131 2660995 2662768 2662811 "SPACEC" 2667184 NIL SPACEC (NIL T) -9 NIL 2669000 NIL) (-1130 2659125 2660927 2660976 "SPACE3" 2660981 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1129 2657877 2658048 2658339 "SORTPAK" 2658930 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1128 2655969 2656272 2656684 "SOLVETRA" 2657541 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1127 2655019 2655241 2655502 "SOLVESER" 2655742 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1126 2650321 2651211 2652206 "SOLVERAD" 2654071 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1125 2646136 2646745 2647474 "SOLVEFOR" 2649688 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1124 2640406 2645485 2645582 "SNTSCAT" 2645587 NIL SNTSCAT (NIL T T T T) -9 NIL 2645657 NIL) (-1123 2634512 2638729 2639120 "SMTS" 2640096 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1122 2629196 2634400 2634477 "SMP" 2634482 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1121 2627355 2627656 2628054 "SMITH" 2628893 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1120 2620068 2624264 2624367 "SMATCAT" 2625718 NIL SMATCAT (NIL NIL T T T) -9 NIL 2626268 NIL) (-1119 2617008 2617831 2619009 "SMATCAT-" 2619014 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1118 2614674 2616244 2616287 "SKAGG" 2616548 NIL SKAGG (NIL T) -9 NIL 2616683 NIL) (-1117 2610982 2614090 2614285 "SINT" 2614472 T SINT (NIL) -8 NIL NIL 2614645) (-1116 2610754 2610792 2610858 "SIMPAN" 2610938 T SIMPAN (NIL) -7 NIL NIL NIL) (-1115 2610033 2610289 2610429 "SIG" 2610636 T SIG (NIL) -8 NIL NIL NIL) (-1114 2608871 2609092 2609367 "SIGNRF" 2609792 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1113 2607704 2607855 2608139 "SIGNEF" 2608700 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1112 2607010 2607287 2607411 "SIGAST" 2607602 T SIGAST (NIL) -8 NIL NIL NIL) (-1111 2604699 2605154 2605660 "SHP" 2606551 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1110 2598551 2604600 2604676 "SHDP" 2604681 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1109 2598124 2598316 2598346 "SGROUP" 2598439 T SGROUP (NIL) -9 NIL 2598501 NIL) (-1108 2597982 2598008 2598081 "SGROUP-" 2598086 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1107 2594817 2595515 2596238 "SGCF" 2597281 T SGCF (NIL) -7 NIL NIL NIL) (-1106 2589185 2594264 2594361 "SFRTCAT" 2594366 NIL SFRTCAT (NIL T T T T) -9 NIL 2594405 NIL) (-1105 2582606 2583624 2584760 "SFRGCD" 2588168 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1104 2575732 2576805 2577991 "SFQCMPK" 2581539 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1103 2575352 2575441 2575552 "SFORT" 2575673 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1102 2574470 2575192 2575313 "SEXOF" 2575318 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1101 2573577 2574351 2574419 "SEX" 2574424 T SEX (NIL) -8 NIL NIL NIL) (-1100 2569090 2569805 2569900 "SEXCAT" 2572837 NIL SEXCAT (NIL T T T T T) -9 NIL 2573415 NIL) (-1099 2566243 2569024 2569072 "SET" 2569077 NIL SET (NIL T) -8 NIL NIL NIL) (-1098 2564467 2564956 2565261 "SETMN" 2565984 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1097 2563963 2564115 2564145 "SETCAT" 2564321 T SETCAT (NIL) -9 NIL 2564431 NIL) (-1096 2563655 2563733 2563863 "SETCAT-" 2563868 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1095 2560016 2562116 2562159 "SETAGG" 2563029 NIL SETAGG (NIL T) -9 NIL 2563369 NIL) (-1094 2559474 2559590 2559827 "SETAGG-" 2559832 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1093 2558917 2559170 2559271 "SEQAST" 2559395 T SEQAST (NIL) -8 NIL NIL NIL) (-1092 2558116 2558410 2558471 "SEGXCAT" 2558757 NIL SEGXCAT (NIL T T) -9 NIL 2558877 NIL) (-1091 2557122 2557782 2557964 "SEG" 2557969 NIL SEG (NIL T) -8 NIL NIL NIL) (-1090 2556101 2556315 2556358 "SEGCAT" 2556880 NIL SEGCAT (NIL T) -9 NIL 2557101 NIL) (-1089 2555102 2555480 2555680 "SEGBIND" 2555936 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1088 2554723 2554782 2554895 "SEGBIND2" 2555037 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1087 2554296 2554524 2554601 "SEGAST" 2554668 T SEGAST (NIL) -8 NIL NIL NIL) (-1086 2553515 2553641 2553845 "SEG2" 2554140 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1085 2552925 2553450 2553497 "SDVAR" 2553502 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1084 2545452 2552695 2552825 "SDPOL" 2552830 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1083 2544045 2544311 2544630 "SCPKG" 2545167 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1082 2543209 2543381 2543573 "SCOPE" 2543875 T SCOPE (NIL) -8 NIL NIL NIL) (-1081 2542429 2542563 2542742 "SCACHE" 2543064 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1080 2542075 2542261 2542291 "SASTCAT" 2542296 T SASTCAT (NIL) -9 NIL 2542309 NIL) (-1079 2541562 2541910 2541986 "SAOS" 2542021 T SAOS (NIL) -8 NIL NIL NIL) (-1078 2541127 2541162 2541335 "SAERFFC" 2541521 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1077 2535066 2541024 2541104 "SAE" 2541109 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1076 2534659 2534694 2534853 "SAEFACT" 2535025 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1075 2532980 2533294 2533695 "RURPK" 2534325 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1074 2531617 2531923 2532228 "RULESET" 2532814 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1073 2528840 2529370 2529828 "RULE" 2531298 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1072 2528452 2528634 2528717 "RULECOLD" 2528792 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1071 2528242 2528270 2528341 "RTVALUE" 2528403 T RTVALUE (NIL) -8 NIL NIL NIL) (-1070 2527713 2527959 2528053 "RSTRCAST" 2528170 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1069 2522561 2523356 2524276 "RSETGCD" 2526912 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1068 2511791 2516870 2516967 "RSETCAT" 2521086 NIL RSETCAT (NIL T T T T) -9 NIL 2522183 NIL) (-1067 2509718 2510257 2511081 "RSETCAT-" 2511086 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1066 2502103 2503480 2505000 "RSDCMPK" 2508317 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1065 2500082 2500549 2500623 "RRCC" 2501709 NIL RRCC (NIL T T) -9 NIL 2502053 NIL) (-1064 2499433 2499607 2499886 "RRCC-" 2499891 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1063 2498876 2499129 2499230 "RPTAST" 2499354 T RPTAST (NIL) -8 NIL NIL NIL) (-1062 2472727 2482084 2482151 "RPOLCAT" 2492815 NIL RPOLCAT (NIL T T T) -9 NIL 2495974 NIL) (-1061 2464225 2466565 2469687 "RPOLCAT-" 2469692 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1060 2455156 2462436 2462918 "ROUTINE" 2463765 T ROUTINE (NIL) -8 NIL NIL NIL) (-1059 2451954 2454782 2454922 "ROMAN" 2455038 T ROMAN (NIL) -8 NIL NIL NIL) (-1058 2450198 2450814 2451074 "ROIRC" 2451759 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1057 2446430 2448714 2448744 "RNS" 2449048 T RNS (NIL) -9 NIL 2449322 NIL) (-1056 2444939 2445322 2445856 "RNS-" 2445931 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1055 2444342 2444750 2444780 "RNG" 2444785 T RNG (NIL) -9 NIL 2444806 NIL) (-1054 2443741 2444129 2444172 "RMODULE" 2444177 NIL RMODULE (NIL T) -9 NIL 2444204 NIL) (-1053 2442577 2442671 2443007 "RMCAT2" 2443642 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1052 2439427 2441923 2442220 "RMATRIX" 2442339 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1051 2432254 2434514 2434629 "RMATCAT" 2437988 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2438970 NIL) (-1050 2431629 2431776 2432083 "RMATCAT-" 2432088 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1049 2431030 2431251 2431294 "RLINSET" 2431488 NIL RLINSET (NIL T) -9 NIL 2431579 NIL) (-1048 2430597 2430672 2430800 "RINTERP" 2430949 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1047 2429655 2430209 2430239 "RING" 2430295 T RING (NIL) -9 NIL 2430387 NIL) (-1046 2429447 2429491 2429588 "RING-" 2429593 NIL RING- (NIL T) -8 NIL NIL NIL) (-1045 2428288 2428525 2428783 "RIDIST" 2429211 T RIDIST (NIL) -7 NIL NIL NIL) (-1044 2419577 2427756 2427962 "RGCHAIN" 2428136 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1043 2418927 2419333 2419374 "RGBCSPC" 2419432 NIL RGBCSPC (NIL T) -9 NIL 2419484 NIL) (-1042 2418085 2418466 2418507 "RGBCMDL" 2418739 NIL RGBCMDL (NIL T) -9 NIL 2418853 NIL) (-1041 2415079 2415693 2416363 "RF" 2417449 NIL RF (NIL T) -7 NIL NIL NIL) (-1040 2414725 2414788 2414891 "RFFACTOR" 2415010 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1039 2414450 2414485 2414582 "RFFACT" 2414684 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1038 2412567 2412931 2413313 "RFDIST" 2414090 T RFDIST (NIL) -7 NIL NIL NIL) (-1037 2412020 2412112 2412275 "RETSOL" 2412469 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1036 2411656 2411736 2411779 "RETRACT" 2411912 NIL RETRACT (NIL T) -9 NIL 2411999 NIL) (-1035 2411505 2411530 2411617 "RETRACT-" 2411622 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1034 2411107 2411327 2411397 "RETAST" 2411457 T RETAST (NIL) -8 NIL NIL NIL) (-1033 2403845 2410760 2410887 "RESULT" 2411002 T RESULT (NIL) -8 NIL NIL NIL) (-1032 2402436 2403114 2403313 "RESRING" 2403748 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1031 2402072 2402121 2402219 "RESLATC" 2402373 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1030 2401777 2401812 2401919 "REPSQ" 2402031 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1029 2399199 2399779 2400381 "REP" 2401197 T REP (NIL) -7 NIL NIL NIL) (-1028 2398896 2398931 2399042 "REPDB" 2399158 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1027 2392796 2394185 2395408 "REP2" 2397708 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1026 2389173 2389854 2390662 "REP1" 2392023 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1025 2381869 2387314 2387770 "REGSET" 2388803 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1024 2380634 2381017 2381267 "REF" 2381654 NIL REF (NIL T) -8 NIL NIL NIL) (-1023 2380011 2380114 2380281 "REDORDER" 2380518 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1022 2375979 2379224 2379451 "RECLOS" 2379839 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1021 2375031 2375212 2375427 "REALSOLV" 2375786 T REALSOLV (NIL) -7 NIL NIL NIL) (-1020 2374877 2374918 2374948 "REAL" 2374953 T REAL (NIL) -9 NIL 2374988 NIL) (-1019 2371360 2372162 2373046 "REAL0Q" 2374042 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1018 2366961 2367949 2369010 "REAL0" 2370341 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1017 2366432 2366678 2366772 "RDUCEAST" 2366889 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1016 2365837 2365909 2366116 "RDIV" 2366354 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1015 2364905 2365079 2365292 "RDIST" 2365659 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1014 2363502 2363789 2364161 "RDETRS" 2364613 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1013 2361314 2361768 2362306 "RDETR" 2363044 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1012 2359939 2360217 2360614 "RDEEFS" 2361030 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1011 2358448 2358754 2359179 "RDEEF" 2359627 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1010 2352509 2355429 2355459 "RCFIELD" 2356754 T RCFIELD (NIL) -9 NIL 2357485 NIL) (-1009 2350573 2351077 2351773 "RCFIELD-" 2351848 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1008 2346842 2348674 2348717 "RCAGG" 2349801 NIL RCAGG (NIL T) -9 NIL 2350266 NIL) (-1007 2346470 2346564 2346727 "RCAGG-" 2346732 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1006 2345805 2345917 2346082 "RATRET" 2346354 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1005 2345358 2345425 2345546 "RATFACT" 2345733 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1004 2344666 2344786 2344938 "RANDSRC" 2345228 T RANDSRC (NIL) -7 NIL NIL NIL) (-1003 2344400 2344444 2344517 "RADUTIL" 2344615 T RADUTIL (NIL) -7 NIL NIL NIL) (-1002 2337516 2343233 2343543 "RADIX" 2344124 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1001 2329135 2337358 2337488 "RADFF" 2337493 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1000 2328782 2328857 2328887 "RADCAT" 2329047 T RADCAT (NIL) -9 NIL NIL NIL) (-999 2328566 2328614 2328712 "RADCAT-" 2328717 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-998 2326669 2328341 2328430 "QUEUE" 2328510 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-997 2323210 2326606 2326651 "QUAT" 2326656 NIL QUAT (NIL T) -8 NIL NIL NIL) (-996 2322848 2322891 2323018 "QUATCT2" 2323161 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-995 2316310 2319655 2319695 "QUATCAT" 2320475 NIL QUATCAT (NIL T) -9 NIL 2321241 NIL) (-994 2312454 2313491 2314878 "QUATCAT-" 2314972 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-993 2309927 2311538 2311579 "QUAGG" 2311954 NIL QUAGG (NIL T) -9 NIL 2312129 NIL) (-992 2309532 2309752 2309820 "QQUTAST" 2309879 T QQUTAST (NIL) -8 NIL NIL NIL) (-991 2308430 2308930 2309102 "QFORM" 2309404 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-990 2299435 2304674 2304714 "QFCAT" 2305372 NIL QFCAT (NIL T) -9 NIL 2306373 NIL) (-989 2295007 2296208 2297799 "QFCAT-" 2297893 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-988 2294645 2294688 2294815 "QFCAT2" 2294958 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2294105 2294215 2294345 "QEQUAT" 2294535 T QEQUAT (NIL) -8 NIL NIL NIL) (-986 2287252 2288324 2289508 "QCMPACK" 2293038 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-985 2284801 2285249 2285677 "QALGSET" 2286907 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-984 2284046 2284220 2284452 "QALGSET2" 2284621 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-983 2282736 2282960 2283277 "PWFFINTB" 2283819 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-982 2280918 2281086 2281440 "PUSHVAR" 2282550 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-981 2276836 2277890 2277931 "PTRANFN" 2279815 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-980 2275238 2275529 2275851 "PTPACK" 2276547 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-979 2274870 2274927 2275036 "PTFUNC2" 2275175 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-978 2269347 2273742 2273783 "PTCAT" 2274079 NIL PTCAT (NIL T) -9 NIL 2274232 NIL) (-977 2269005 2269040 2269164 "PSQFR" 2269306 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-976 2267600 2267898 2268232 "PSEUDLIN" 2268703 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-975 2254363 2256734 2259058 "PSETPK" 2265360 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-974 2247381 2250121 2250217 "PSETCAT" 2253238 NIL PSETCAT (NIL T T T T) -9 NIL 2254052 NIL) (-973 2245217 2245851 2246672 "PSETCAT-" 2246677 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-972 2244566 2244731 2244759 "PSCURVE" 2245027 T PSCURVE (NIL) -9 NIL 2245194 NIL) (-971 2240564 2242080 2242145 "PSCAT" 2242989 NIL PSCAT (NIL T T T) -9 NIL 2243229 NIL) (-970 2239627 2239843 2240243 "PSCAT-" 2240248 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-969 2238332 2238992 2239197 "PRTITION" 2239442 T PRTITION (NIL) -8 NIL NIL NIL) (-968 2237807 2238053 2238145 "PRTDAST" 2238260 T PRTDAST (NIL) -8 NIL NIL NIL) (-967 2226897 2229111 2231299 "PRS" 2235669 NIL PRS (NIL T T) -7 NIL NIL NIL) (-966 2224708 2226247 2226287 "PRQAGG" 2226470 NIL PRQAGG (NIL T) -9 NIL 2226572 NIL) (-965 2223912 2224217 2224245 "PROPLOG" 2224492 T PROPLOG (NIL) -9 NIL 2224658 NIL) (-964 2222342 2222863 2223120 "PROPFRML" 2223688 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-963 2221811 2221918 2222046 "PROPERTY" 2222234 T PROPERTY (NIL) -8 NIL NIL NIL) (-962 2215869 2219977 2220797 "PRODUCT" 2221037 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-961 2213147 2215327 2215561 "PR" 2215680 NIL PR (NIL T T) -8 NIL NIL NIL) (-960 2212943 2212975 2213034 "PRINT" 2213108 T PRINT (NIL) -7 NIL NIL NIL) (-959 2212283 2212400 2212552 "PRIMES" 2212823 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-958 2210348 2210749 2211215 "PRIMELT" 2211862 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-957 2210077 2210126 2210154 "PRIMCAT" 2210278 T PRIMCAT (NIL) -9 NIL NIL NIL) (-956 2206192 2210015 2210060 "PRIMARR" 2210065 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-955 2205199 2205377 2205605 "PRIMARR2" 2206010 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-954 2204842 2204898 2205009 "PREASSOC" 2205137 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-953 2204317 2204450 2204478 "PPCURVE" 2204683 T PPCURVE (NIL) -9 NIL 2204819 NIL) (-952 2203912 2204112 2204195 "PORTNUM" 2204254 T PORTNUM (NIL) -8 NIL NIL NIL) (-951 2201271 2201670 2202262 "POLYROOT" 2203493 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-950 2195453 2200875 2201035 "POLY" 2201144 NIL POLY (NIL T) -8 NIL NIL NIL) (-949 2194836 2194894 2195128 "POLYLIFT" 2195389 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-948 2191111 2191560 2192189 "POLYCATQ" 2194381 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-947 2177823 2182951 2183016 "POLYCAT" 2186530 NIL POLYCAT (NIL T T T) -9 NIL 2188408 NIL) (-946 2171272 2173134 2175518 "POLYCAT-" 2175523 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-945 2170859 2170927 2171047 "POLY2UP" 2171198 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-944 2170491 2170548 2170657 "POLY2" 2170796 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-943 2169176 2169415 2169691 "POLUTIL" 2170265 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-942 2167531 2167808 2168139 "POLTOPOL" 2168898 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-941 2162996 2167467 2167513 "POINT" 2167518 NIL POINT (NIL T) -8 NIL NIL NIL) (-940 2161183 2161540 2161915 "PNTHEORY" 2162641 T PNTHEORY (NIL) -7 NIL NIL NIL) (-939 2159641 2159938 2160337 "PMTOOLS" 2160881 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-938 2159234 2159312 2159429 "PMSYM" 2159557 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-937 2158744 2158813 2158987 "PMQFCAT" 2159159 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-936 2158099 2158209 2158365 "PMPRED" 2158621 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-935 2157492 2157578 2157740 "PMPREDFS" 2158000 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-934 2156156 2156364 2156742 "PMPLCAT" 2157254 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-933 2155688 2155767 2155919 "PMLSAGG" 2156071 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-932 2155161 2155237 2155419 "PMKERNEL" 2155606 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-931 2154778 2154853 2154966 "PMINS" 2155080 NIL PMINS (NIL T) -7 NIL NIL NIL) (-930 2154220 2154289 2154498 "PMFS" 2154703 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-929 2153448 2153566 2153771 "PMDOWN" 2154097 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-928 2152615 2152773 2152954 "PMASS" 2153287 T PMASS (NIL) -7 NIL NIL NIL) (-927 2151888 2151998 2152161 "PMASSFS" 2152502 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-926 2151543 2151611 2151705 "PLOTTOOL" 2151814 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-925 2146150 2147354 2148502 "PLOT" 2150415 T PLOT (NIL) -8 NIL NIL NIL) (-924 2141954 2142998 2143919 "PLOT3D" 2145249 T PLOT3D (NIL) -8 NIL NIL NIL) (-923 2140866 2141043 2141278 "PLOT1" 2141758 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-922 2116255 2120932 2125783 "PLEQN" 2136132 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-921 2115573 2115695 2115875 "PINTERP" 2116120 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-920 2115266 2115313 2115416 "PINTERPA" 2115520 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-919 2114487 2115035 2115122 "PI" 2115162 T PI (NIL) -8 NIL NIL 2115229) (-918 2112784 2113759 2113787 "PID" 2113969 T PID (NIL) -9 NIL 2114103 NIL) (-917 2112535 2112572 2112647 "PICOERCE" 2112741 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-916 2111855 2111994 2112170 "PGROEB" 2112391 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-915 2107442 2108256 2109161 "PGE" 2110970 T PGE (NIL) -7 NIL NIL NIL) (-914 2105565 2105812 2106178 "PGCD" 2107159 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-913 2104903 2105006 2105167 "PFRPAC" 2105449 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-912 2101544 2103451 2103804 "PFR" 2104582 NIL PFR (NIL T) -8 NIL NIL NIL) (-911 2099933 2100177 2100502 "PFOTOOLS" 2101291 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-910 2098466 2098705 2099056 "PFOQ" 2099690 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-909 2096967 2097179 2097535 "PFO" 2098250 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-908 2093520 2096856 2096925 "PF" 2096930 NIL PF (NIL NIL) -8 NIL NIL NIL) (-907 2090854 2092125 2092153 "PFECAT" 2092738 T PFECAT (NIL) -9 NIL 2093122 NIL) (-906 2090299 2090453 2090667 "PFECAT-" 2090672 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-905 2088902 2089154 2089455 "PFBRU" 2090048 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-904 2086767 2087120 2087552 "PFBR" 2088553 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-903 2082649 2084143 2084819 "PERM" 2086124 NIL PERM (NIL T) -8 NIL NIL NIL) (-902 2077883 2078856 2079726 "PERMGRP" 2081812 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-901 2075989 2076946 2076987 "PERMCAT" 2077433 NIL PERMCAT (NIL T) -9 NIL 2077738 NIL) (-900 2075642 2075683 2075807 "PERMAN" 2075942 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-899 2073130 2075307 2075429 "PENDTREE" 2075553 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-898 2071154 2071922 2071963 "PDRING" 2072620 NIL PDRING (NIL T) -9 NIL 2072906 NIL) (-897 2070257 2070475 2070837 "PDRING-" 2070842 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-896 2067472 2068250 2068918 "PDEPROB" 2069609 T PDEPROB (NIL) -8 NIL NIL NIL) (-895 2065017 2065521 2066076 "PDEPACK" 2066937 T PDEPACK (NIL) -7 NIL NIL NIL) (-894 2063929 2064119 2064370 "PDECOMP" 2064816 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-893 2061508 2062351 2062379 "PDECAT" 2063166 T PDECAT (NIL) -9 NIL 2063879 NIL) (-892 2061259 2061292 2061382 "PCOMP" 2061469 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-891 2059437 2060060 2060357 "PBWLB" 2060988 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-890 2051910 2053510 2054848 "PATTERN" 2058120 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-889 2051542 2051599 2051708 "PATTERN2" 2051847 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-888 2049299 2049687 2050144 "PATTERN1" 2051131 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-887 2046667 2047248 2047729 "PATRES" 2048864 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-886 2046231 2046298 2046430 "PATRES2" 2046594 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-885 2044114 2044519 2044926 "PATMATCH" 2045898 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-884 2043624 2043833 2043874 "PATMAB" 2043981 NIL PATMAB (NIL T) -9 NIL 2044064 NIL) (-883 2042142 2042478 2042736 "PATLRES" 2043429 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-882 2041688 2041811 2041852 "PATAB" 2041857 NIL PATAB (NIL T) -9 NIL 2042029 NIL) (-881 2039169 2039701 2040274 "PARTPERM" 2041135 T PARTPERM (NIL) -7 NIL NIL NIL) (-880 2038790 2038853 2038955 "PARSURF" 2039100 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-879 2038422 2038479 2038588 "PARSU2" 2038727 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-878 2038186 2038226 2038293 "PARSER" 2038375 T PARSER (NIL) -7 NIL NIL NIL) (-877 2037807 2037870 2037972 "PARSCURV" 2038117 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-876 2037439 2037496 2037605 "PARSC2" 2037744 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-875 2037078 2037136 2037233 "PARPCURV" 2037375 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-874 2036710 2036767 2036876 "PARPC2" 2037015 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-873 2036230 2036316 2036435 "PAN2EXPR" 2036611 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-872 2035007 2035351 2035579 "PALETTE" 2036022 T PALETTE (NIL) -8 NIL NIL NIL) (-871 2033400 2034012 2034372 "PAIR" 2034693 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-870 2027270 2032659 2032853 "PADICRC" 2033255 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-869 2020499 2026616 2026800 "PADICRAT" 2027118 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-868 2018814 2020436 2020481 "PADIC" 2020486 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-867 2015924 2017488 2017528 "PADICCT" 2018109 NIL PADICCT (NIL NIL) -9 NIL 2018391 NIL) (-866 2014881 2015081 2015349 "PADEPAC" 2015711 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-865 2014093 2014226 2014432 "PADE" 2014743 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-864 2012480 2013301 2013581 "OWP" 2013897 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-863 2011973 2012186 2012283 "OVERSET" 2012403 T OVERSET (NIL) -8 NIL NIL NIL) (-862 2011019 2011578 2011750 "OVAR" 2011841 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-861 2010283 2010404 2010565 "OUT" 2010878 T OUT (NIL) -7 NIL NIL NIL) (-860 1999154 2001392 2003592 "OUTFORM" 2008103 T OUTFORM (NIL) -8 NIL NIL NIL) (-859 1998490 1998751 1998878 "OUTBFILE" 1999047 T OUTBFILE (NIL) -8 NIL NIL NIL) (-858 1997797 1997962 1997990 "OUTBCON" 1998308 T OUTBCON (NIL) -9 NIL 1998474 NIL) (-857 1997398 1997510 1997667 "OUTBCON-" 1997672 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-856 1996778 1997127 1997216 "OSI" 1997329 T OSI (NIL) -8 NIL NIL NIL) (-855 1996308 1996646 1996674 "OSGROUP" 1996679 T OSGROUP (NIL) -9 NIL 1996701 NIL) (-854 1995053 1995280 1995565 "ORTHPOL" 1996055 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-853 1992604 1994888 1995009 "OREUP" 1995014 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-852 1990007 1992295 1992422 "ORESUP" 1992546 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-851 1987535 1988035 1988596 "OREPCTO" 1989496 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-850 1981221 1983422 1983463 "OREPCAT" 1985811 NIL OREPCAT (NIL T) -9 NIL 1986915 NIL) (-849 1978368 1979150 1980208 "OREPCAT-" 1980213 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-848 1977519 1977817 1977845 "ORDSET" 1978154 T ORDSET (NIL) -9 NIL 1978318 NIL) (-847 1976950 1977098 1977322 "ORDSET-" 1977327 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-846 1975515 1976306 1976334 "ORDRING" 1976536 T ORDRING (NIL) -9 NIL 1976661 NIL) (-845 1975160 1975254 1975398 "ORDRING-" 1975403 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-844 1974540 1975003 1975031 "ORDMON" 1975036 T ORDMON (NIL) -9 NIL 1975057 NIL) (-843 1973702 1973849 1974044 "ORDFUNS" 1974389 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-842 1973040 1973459 1973487 "ORDFIN" 1973552 T ORDFIN (NIL) -9 NIL 1973626 NIL) (-841 1969599 1971626 1972035 "ORDCOMP" 1972664 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-840 1968865 1968992 1969178 "ORDCOMP2" 1969459 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-839 1965446 1966356 1967170 "OPTPROB" 1968071 T OPTPROB (NIL) -8 NIL NIL NIL) (-838 1962248 1962887 1963591 "OPTPACK" 1964762 T OPTPACK (NIL) -7 NIL NIL NIL) (-837 1959935 1960701 1960729 "OPTCAT" 1961548 T OPTCAT (NIL) -9 NIL 1962198 NIL) (-836 1959319 1959612 1959717 "OPSIG" 1959850 T OPSIG (NIL) -8 NIL NIL NIL) (-835 1959087 1959126 1959192 "OPQUERY" 1959273 T OPQUERY (NIL) -7 NIL NIL NIL) (-834 1956218 1957398 1957902 "OP" 1958616 NIL OP (NIL T) -8 NIL NIL NIL) (-833 1955592 1955818 1955859 "OPERCAT" 1956071 NIL OPERCAT (NIL T) -9 NIL 1956168 NIL) (-832 1955347 1955403 1955520 "OPERCAT-" 1955525 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-831 1952160 1954144 1954513 "ONECOMP" 1955011 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-830 1951465 1951580 1951754 "ONECOMP2" 1952032 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-829 1950884 1950990 1951120 "OMSERVER" 1951355 T OMSERVER (NIL) -7 NIL NIL NIL) (-828 1947746 1950324 1950364 "OMSAGG" 1950425 NIL OMSAGG (NIL T) -9 NIL 1950489 NIL) (-827 1946369 1946632 1946914 "OMPKG" 1947484 T OMPKG (NIL) -7 NIL NIL NIL) (-826 1945799 1945902 1945930 "OM" 1946229 T OM (NIL) -9 NIL NIL NIL) (-825 1944346 1945348 1945517 "OMLO" 1945680 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-824 1943306 1943453 1943673 "OMEXPR" 1944172 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-823 1942597 1942852 1942988 "OMERR" 1943190 T OMERR (NIL) -8 NIL NIL NIL) (-822 1941748 1942018 1942178 "OMERRK" 1942457 T OMERRK (NIL) -8 NIL NIL NIL) (-821 1941199 1941425 1941533 "OMENC" 1941660 T OMENC (NIL) -8 NIL NIL NIL) (-820 1935094 1936279 1937450 "OMDEV" 1940048 T OMDEV (NIL) -8 NIL NIL NIL) (-819 1934163 1934334 1934528 "OMCONN" 1934920 T OMCONN (NIL) -8 NIL NIL NIL) (-818 1932684 1933660 1933688 "OINTDOM" 1933693 T OINTDOM (NIL) -9 NIL 1933714 NIL) (-817 1928463 1929674 1930390 "OFMONOID" 1932000 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-816 1927874 1928400 1928445 "ODVAR" 1928450 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-815 1925297 1927619 1927774 "ODR" 1927779 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-814 1917878 1925073 1925199 "ODPOL" 1925204 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-813 1911700 1917750 1917855 "ODP" 1917860 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-812 1910466 1910681 1910956 "ODETOOLS" 1911474 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-811 1907433 1908091 1908807 "ODESYS" 1909799 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-810 1902315 1903223 1904248 "ODERTRIC" 1906508 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-809 1901741 1901823 1902017 "ODERED" 1902227 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-808 1898629 1899177 1899854 "ODERAT" 1901164 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-807 1895586 1896053 1896650 "ODEPRRIC" 1898158 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-806 1893529 1894125 1894611 "ODEPROB" 1895120 T ODEPROB (NIL) -8 NIL NIL NIL) (-805 1890049 1890534 1891181 "ODEPRIM" 1893008 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-804 1889298 1889400 1889660 "ODEPAL" 1889941 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-803 1885460 1886251 1887115 "ODEPACK" 1888454 T ODEPACK (NIL) -7 NIL NIL NIL) (-802 1884521 1884628 1884850 "ODEINT" 1885349 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-801 1878622 1880047 1881494 "ODEIFTBL" 1883094 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-800 1874020 1874806 1875758 "ODEEF" 1877781 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-799 1873369 1873458 1873681 "ODECONST" 1873925 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-798 1871494 1872155 1872183 "ODECAT" 1872788 T ODECAT (NIL) -9 NIL 1873319 NIL) (-797 1868366 1871206 1871325 "OCT" 1871407 NIL OCT (NIL T) -8 NIL NIL NIL) (-796 1868004 1868047 1868174 "OCTCT2" 1868317 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-795 1862653 1865088 1865128 "OC" 1866225 NIL OC (NIL T) -9 NIL 1867083 NIL) (-794 1859880 1860628 1861618 "OC-" 1861712 NIL OC- (NIL T T) -8 NIL NIL NIL) (-793 1859232 1859700 1859728 "OCAMON" 1859733 T OCAMON (NIL) -9 NIL 1859754 NIL) (-792 1858763 1859104 1859132 "OASGP" 1859137 T OASGP (NIL) -9 NIL 1859157 NIL) (-791 1858024 1858513 1858541 "OAMONS" 1858581 T OAMONS (NIL) -9 NIL 1858624 NIL) (-790 1857438 1857871 1857899 "OAMON" 1857904 T OAMON (NIL) -9 NIL 1857924 NIL) (-789 1856696 1857214 1857242 "OAGROUP" 1857247 T OAGROUP (NIL) -9 NIL 1857267 NIL) (-788 1856386 1856436 1856524 "NUMTUBE" 1856640 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-787 1849959 1851477 1853013 "NUMQUAD" 1854870 T NUMQUAD (NIL) -7 NIL NIL NIL) (-786 1845715 1846703 1847728 "NUMODE" 1848954 T NUMODE (NIL) -7 NIL NIL NIL) (-785 1843070 1843950 1843978 "NUMINT" 1844901 T NUMINT (NIL) -9 NIL 1845665 NIL) (-784 1842018 1842215 1842433 "NUMFMT" 1842872 T NUMFMT (NIL) -7 NIL NIL NIL) (-783 1828377 1831322 1833854 "NUMERIC" 1839525 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-782 1822747 1827826 1827921 "NTSCAT" 1827926 NIL NTSCAT (NIL T T T T) -9 NIL 1827965 NIL) (-781 1821941 1822106 1822299 "NTPOLFN" 1822586 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-780 1810018 1818766 1819578 "NSUP" 1821162 NIL NSUP (NIL T) -8 NIL NIL NIL) (-779 1809650 1809707 1809816 "NSUP2" 1809955 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-778 1799878 1809424 1809557 "NSMP" 1809562 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-777 1798310 1798611 1798968 "NREP" 1799566 NIL NREP (NIL T) -7 NIL NIL NIL) (-776 1796901 1797153 1797511 "NPCOEF" 1798053 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-775 1795967 1796082 1796298 "NORMRETR" 1796782 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-774 1794008 1794298 1794707 "NORMPK" 1795675 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-773 1793693 1793721 1793845 "NORMMA" 1793974 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-772 1793493 1793650 1793679 "NONE" 1793684 T NONE (NIL) -8 NIL NIL NIL) (-771 1793282 1793311 1793380 "NONE1" 1793457 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-770 1792779 1792841 1793020 "NODE1" 1793214 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-769 1791059 1791910 1792165 "NNI" 1792512 T NNI (NIL) -8 NIL NIL 1792747) (-768 1789479 1789792 1790156 "NLINSOL" 1790727 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-767 1785720 1786715 1787614 "NIPROB" 1788600 T NIPROB (NIL) -8 NIL NIL NIL) (-766 1784477 1784711 1785013 "NFINTBAS" 1785482 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-765 1783651 1784127 1784168 "NETCLT" 1784340 NIL NETCLT (NIL T) -9 NIL 1784422 NIL) (-764 1782359 1782590 1782871 "NCODIV" 1783419 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-763 1782121 1782158 1782233 "NCNTFRAC" 1782316 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-762 1780301 1780665 1781085 "NCEP" 1781746 NIL NCEP (NIL T) -7 NIL NIL NIL) (-761 1779152 1779925 1779953 "NASRING" 1780063 T NASRING (NIL) -9 NIL 1780143 NIL) (-760 1778947 1778991 1779085 "NASRING-" 1779090 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-759 1778054 1778579 1778607 "NARNG" 1778724 T NARNG (NIL) -9 NIL 1778815 NIL) (-758 1777746 1777813 1777947 "NARNG-" 1777952 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-757 1776625 1776832 1777067 "NAGSP" 1777531 T NAGSP (NIL) -7 NIL NIL NIL) (-756 1767897 1769581 1771254 "NAGS" 1774972 T NAGS (NIL) -7 NIL NIL NIL) (-755 1766445 1766753 1767084 "NAGF07" 1767586 T NAGF07 (NIL) -7 NIL NIL NIL) (-754 1760983 1762274 1763581 "NAGF04" 1765158 T NAGF04 (NIL) -7 NIL NIL NIL) (-753 1753951 1755565 1757198 "NAGF02" 1759370 T NAGF02 (NIL) -7 NIL NIL NIL) (-752 1749175 1750275 1751392 "NAGF01" 1752854 T NAGF01 (NIL) -7 NIL NIL NIL) (-751 1742803 1744369 1745954 "NAGE04" 1747610 T NAGE04 (NIL) -7 NIL NIL NIL) (-750 1733972 1736093 1738223 "NAGE02" 1740693 T NAGE02 (NIL) -7 NIL NIL NIL) (-749 1729925 1730872 1731836 "NAGE01" 1733028 T NAGE01 (NIL) -7 NIL NIL NIL) (-748 1727720 1728254 1728812 "NAGD03" 1729387 T NAGD03 (NIL) -7 NIL NIL NIL) (-747 1719470 1721398 1723352 "NAGD02" 1725786 T NAGD02 (NIL) -7 NIL NIL NIL) (-746 1713281 1714706 1716146 "NAGD01" 1718050 T NAGD01 (NIL) -7 NIL NIL NIL) (-745 1709490 1710312 1711149 "NAGC06" 1712464 T NAGC06 (NIL) -7 NIL NIL NIL) (-744 1707955 1708287 1708643 "NAGC05" 1709154 T NAGC05 (NIL) -7 NIL NIL NIL) (-743 1707331 1707450 1707594 "NAGC02" 1707831 T NAGC02 (NIL) -7 NIL NIL NIL) (-742 1706290 1706873 1706913 "NAALG" 1706992 NIL NAALG (NIL T) -9 NIL 1707053 NIL) (-741 1706125 1706154 1706244 "NAALG-" 1706249 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-740 1700075 1701183 1702370 "MULTSQFR" 1705021 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-739 1699394 1699469 1699653 "MULTFACT" 1699987 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-738 1692118 1696031 1696084 "MTSCAT" 1697154 NIL MTSCAT (NIL T T) -9 NIL 1697669 NIL) (-737 1691830 1691884 1691976 "MTHING" 1692058 NIL MTHING (NIL T) -7 NIL NIL NIL) (-736 1691622 1691655 1691715 "MSYSCMD" 1691790 T MSYSCMD (NIL) -7 NIL NIL NIL) (-735 1687704 1690377 1690697 "MSET" 1691335 NIL MSET (NIL T) -8 NIL NIL NIL) (-734 1684773 1687265 1687306 "MSETAGG" 1687311 NIL MSETAGG (NIL T) -9 NIL 1687345 NIL) (-733 1680614 1682152 1682897 "MRING" 1684073 NIL MRING (NIL T T) -8 NIL NIL NIL) (-732 1680180 1680247 1680378 "MRF2" 1680541 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-731 1679798 1679833 1679977 "MRATFAC" 1680139 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-730 1677410 1677705 1678136 "MPRFF" 1679503 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-729 1671707 1677264 1677361 "MPOLY" 1677366 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-728 1671197 1671232 1671440 "MPCPF" 1671666 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-727 1670711 1670754 1670938 "MPC3" 1671148 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-726 1669906 1669987 1670208 "MPC2" 1670626 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1668207 1668544 1668934 "MONOTOOL" 1669566 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-724 1667432 1667749 1667777 "MONOID" 1667996 T MONOID (NIL) -9 NIL 1668143 NIL) (-723 1666978 1667097 1667278 "MONOID-" 1667283 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-722 1657453 1663404 1663463 "MONOGEN" 1664137 NIL MONOGEN (NIL T T) -9 NIL 1664593 NIL) (-721 1654671 1655406 1656406 "MONOGEN-" 1656525 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-720 1653504 1653950 1653978 "MONADWU" 1654370 T MONADWU (NIL) -9 NIL 1654608 NIL) (-719 1652876 1653035 1653283 "MONADWU-" 1653288 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-718 1652235 1652479 1652507 "MONAD" 1652714 T MONAD (NIL) -9 NIL 1652826 NIL) (-717 1651920 1651998 1652130 "MONAD-" 1652135 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-716 1650209 1650833 1651112 "MOEBIUS" 1651673 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-715 1649487 1649891 1649931 "MODULE" 1649936 NIL MODULE (NIL T) -9 NIL 1649975 NIL) (-714 1649055 1649151 1649341 "MODULE-" 1649346 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-713 1646735 1647419 1647746 "MODRING" 1648879 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-712 1643679 1644840 1645361 "MODOP" 1646264 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-711 1642267 1642746 1643023 "MODMONOM" 1643542 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-710 1632308 1640558 1640972 "MODMON" 1641904 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-709 1629464 1631152 1631428 "MODFIELD" 1632183 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-708 1628441 1628745 1628935 "MMLFORM" 1629294 T MMLFORM (NIL) -8 NIL NIL NIL) (-707 1627967 1628010 1628189 "MMAP" 1628392 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-706 1626046 1626813 1626854 "MLO" 1627277 NIL MLO (NIL T) -9 NIL 1627519 NIL) (-705 1623412 1623928 1624530 "MLIFT" 1625527 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-704 1622803 1622887 1623041 "MKUCFUNC" 1623323 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-703 1622402 1622472 1622595 "MKRECORD" 1622726 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-702 1621449 1621611 1621839 "MKFUNC" 1622213 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-701 1620837 1620941 1621097 "MKFLCFN" 1621332 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-700 1620114 1620216 1620401 "MKBCFUNC" 1620730 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-699 1616821 1619668 1619804 "MINT" 1619998 T MINT (NIL) -8 NIL NIL NIL) (-698 1615633 1615876 1616153 "MHROWRED" 1616576 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-697 1611013 1614168 1614573 "MFLOAT" 1615248 T MFLOAT (NIL) -8 NIL NIL NIL) (-696 1610370 1610446 1610617 "MFINFACT" 1610925 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-695 1606685 1607533 1608417 "MESH" 1609506 T MESH (NIL) -7 NIL NIL NIL) (-694 1605075 1605387 1605740 "MDDFACT" 1606372 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-693 1601870 1604234 1604275 "MDAGG" 1604530 NIL MDAGG (NIL T) -9 NIL 1604673 NIL) (-692 1591610 1601163 1601370 "MCMPLX" 1601683 T MCMPLX (NIL) -8 NIL NIL NIL) (-691 1590751 1590897 1591097 "MCDEN" 1591459 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-690 1588641 1588911 1589291 "MCALCFN" 1590481 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-689 1587566 1587806 1588039 "MAYBE" 1588447 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-688 1585178 1585701 1586263 "MATSTOR" 1587037 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-687 1581135 1584550 1584798 "MATRIX" 1584963 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-686 1576899 1577608 1578344 "MATLIN" 1580492 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-685 1567005 1570191 1570268 "MATCAT" 1575148 NIL MATCAT (NIL T T T) -9 NIL 1576565 NIL) (-684 1563361 1564382 1565738 "MATCAT-" 1565743 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-683 1561955 1562108 1562441 "MATCAT2" 1563196 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-682 1560067 1560391 1560775 "MAPPKG3" 1561630 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-681 1559048 1559221 1559443 "MAPPKG2" 1559891 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-680 1557547 1557831 1558158 "MAPPKG1" 1558754 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-679 1556626 1556953 1557130 "MAPPAST" 1557390 T MAPPAST (NIL) -8 NIL NIL NIL) (-678 1556237 1556295 1556418 "MAPHACK3" 1556562 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-677 1555829 1555890 1556004 "MAPHACK2" 1556169 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-676 1555266 1555370 1555512 "MAPHACK1" 1555720 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-675 1553345 1553966 1554270 "MAGMA" 1554994 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-674 1552824 1553069 1553160 "MACROAST" 1553274 T MACROAST (NIL) -8 NIL NIL NIL) (-673 1549242 1551063 1551524 "M3D" 1552396 NIL M3D (NIL T) -8 NIL NIL NIL) (-672 1543348 1547611 1547652 "LZSTAGG" 1548434 NIL LZSTAGG (NIL T) -9 NIL 1548729 NIL) (-671 1539305 1540479 1541936 "LZSTAGG-" 1541941 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-670 1536392 1537196 1537683 "LWORD" 1538850 NIL LWORD (NIL T) -8 NIL NIL NIL) (-669 1535968 1536196 1536271 "LSTAST" 1536337 T LSTAST (NIL) -8 NIL NIL NIL) (-668 1529134 1535739 1535873 "LSQM" 1535878 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-667 1528358 1528497 1528725 "LSPP" 1528989 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-666 1526170 1526471 1526927 "LSMP" 1528047 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-665 1522949 1523623 1524353 "LSMP1" 1525472 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-664 1516826 1522116 1522157 "LSAGG" 1522219 NIL LSAGG (NIL T) -9 NIL 1522297 NIL) (-663 1513521 1514445 1515658 "LSAGG-" 1515663 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-662 1511120 1512665 1512914 "LPOLY" 1513316 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-661 1510702 1510787 1510910 "LPEFRAC" 1511029 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-660 1509023 1509796 1510049 "LO" 1510534 NIL LO (NIL T T T) -8 NIL NIL NIL) (-659 1508675 1508787 1508815 "LOGIC" 1508926 T LOGIC (NIL) -9 NIL 1509007 NIL) (-658 1508537 1508560 1508631 "LOGIC-" 1508636 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-657 1507730 1507870 1508063 "LODOOPS" 1508393 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-656 1505153 1507646 1507712 "LODO" 1507717 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-655 1503691 1503926 1504279 "LODOF" 1504900 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-654 1499909 1502340 1502381 "LODOCAT" 1502819 NIL LODOCAT (NIL T) -9 NIL 1503030 NIL) (-653 1499642 1499700 1499827 "LODOCAT-" 1499832 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-652 1496962 1499483 1499601 "LODO2" 1499606 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-651 1494397 1496899 1496944 "LODO1" 1496949 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-650 1493278 1493443 1493748 "LODEEF" 1494220 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-649 1488517 1491408 1491449 "LNAGG" 1492396 NIL LNAGG (NIL T) -9 NIL 1492840 NIL) (-648 1487664 1487878 1488220 "LNAGG-" 1488225 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-647 1483800 1484589 1485228 "LMOPS" 1487079 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-646 1483203 1483591 1483632 "LMODULE" 1483637 NIL LMODULE (NIL T) -9 NIL 1483663 NIL) (-645 1480401 1482848 1482971 "LMDICT" 1483113 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-644 1479807 1480028 1480069 "LLINSET" 1480260 NIL LLINSET (NIL T) -9 NIL 1480351 NIL) (-643 1479506 1479715 1479775 "LITERAL" 1479780 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-642 1472689 1478452 1478750 "LIST" 1479241 NIL LIST (NIL T) -8 NIL NIL NIL) (-641 1472214 1472288 1472427 "LIST3" 1472609 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-640 1471221 1471399 1471627 "LIST2" 1472032 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-639 1469355 1469667 1470066 "LIST2MAP" 1470868 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-638 1468951 1469188 1469229 "LINSET" 1469234 NIL LINSET (NIL T) -9 NIL 1469268 NIL) (-637 1467612 1468282 1468323 "LINEXP" 1468578 NIL LINEXP (NIL T) -9 NIL 1468727 NIL) (-636 1466259 1466519 1466816 "LINDEP" 1467364 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1463026 1463745 1464522 "LIMITRF" 1465514 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1461329 1461625 1462034 "LIMITPS" 1462721 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1455757 1460840 1461068 "LIE" 1461150 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1454705 1455174 1455214 "LIECAT" 1455354 NIL LIECAT (NIL T) -9 NIL 1455505 NIL) (-631 1454546 1454573 1454661 "LIECAT-" 1454666 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1447042 1453995 1454160 "LIB" 1454401 T LIB (NIL) -8 NIL NIL NIL) (-629 1442677 1443560 1444495 "LGROBP" 1446159 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1440675 1440949 1441299 "LF" 1442398 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1439515 1440207 1440235 "LFCAT" 1440442 T LFCAT (NIL) -9 NIL 1440581 NIL) (-626 1436417 1437047 1437735 "LEXTRIPK" 1438879 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1433161 1433987 1434490 "LEXP" 1435997 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1432637 1432882 1432974 "LETAST" 1433089 T LETAST (NIL) -8 NIL NIL NIL) (-623 1431035 1431348 1431749 "LEADCDET" 1432319 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1430225 1430299 1430528 "LAZM3PK" 1430956 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1425142 1428302 1428840 "LAUPOL" 1429737 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1424721 1424765 1424926 "LAPLACE" 1425092 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1422660 1423822 1424073 "LA" 1424554 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1421654 1422238 1422279 "LALG" 1422341 NIL LALG (NIL T) -9 NIL 1422400 NIL) (-617 1421368 1421427 1421563 "LALG-" 1421568 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1421203 1421227 1421268 "KVTFROM" 1421330 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1420126 1420570 1420755 "KTVLOGIC" 1421038 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1419961 1419985 1420026 "KRCFROM" 1420088 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1418865 1419052 1419351 "KOVACIC" 1419761 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1418700 1418724 1418765 "KONVERT" 1418827 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1418535 1418559 1418600 "KOERCE" 1418662 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1416217 1417005 1417406 "KERNEL" 1418167 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1415713 1415794 1415926 "KERNEL2" 1416131 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1409483 1414252 1414306 "KDAGG" 1414683 NIL KDAGG (NIL T T) -9 NIL 1414889 NIL) (-607 1409012 1409136 1409341 "KDAGG-" 1409346 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1402160 1408673 1408828 "KAFILE" 1408890 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1396588 1401671 1401899 "JORDAN" 1401981 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1395967 1396237 1396358 "JOINAST" 1396487 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1395813 1395872 1395927 "JAVACODE" 1395932 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1392065 1394018 1394072 "IXAGG" 1395001 NIL IXAGG (NIL T T) -9 NIL 1395460 NIL) (-601 1390984 1391290 1391709 "IXAGG-" 1391714 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386514 1390906 1390965 "IVECTOR" 1390970 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1385280 1385517 1385783 "ITUPLE" 1386281 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1383782 1383959 1384254 "ITRIGMNP" 1385102 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1382527 1382731 1383014 "ITFUN3" 1383558 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1382159 1382216 1382325 "ITFUN2" 1382464 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1379961 1381021 1381320 "ITAYLOR" 1381893 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1368906 1374098 1375261 "ISUPS" 1378831 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1368010 1368150 1368386 "ISUMP" 1368753 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1363224 1367811 1367890 "ISTRING" 1367963 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1362700 1362945 1363037 "ISAST" 1363152 T ISAST (NIL) -8 NIL NIL NIL) (-590 1361909 1361991 1362207 "IRURPK" 1362614 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1360845 1361046 1361286 "IRSN" 1361689 T IRSN (NIL) -7 NIL NIL NIL) (-588 1358916 1359271 1359700 "IRRF2F" 1360483 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1358663 1358701 1358777 "IRREDFFX" 1358872 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1357278 1357537 1357836 "IROOT" 1358396 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1353882 1354962 1355654 "IR" 1356618 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1351495 1351990 1352556 "IR2" 1353360 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1350595 1350708 1350922 "IR2F" 1351378 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1350386 1350420 1350480 "IPRNTPK" 1350555 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1346966 1350275 1350344 "IPF" 1350349 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1345293 1346891 1346948 "IPADIC" 1346953 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1344605 1344853 1344983 "IP4ADDR" 1345183 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1344078 1344309 1344419 "IOMODE" 1344515 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1343151 1343675 1343802 "IOBFILE" 1343971 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1342639 1343055 1343083 "IOBCON" 1343088 T IOBCON (NIL) -9 NIL 1343109 NIL) (-575 1342150 1342208 1342391 "INVLAPLA" 1342575 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1331798 1334152 1336538 "INTTR" 1339814 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1328133 1328875 1329740 "INTTOOLS" 1330983 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1327719 1327810 1327927 "INTSLPE" 1328036 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1325673 1327642 1327701 "INTRVL" 1327706 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1323275 1323787 1324362 "INTRF" 1325158 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1322686 1322783 1322925 "INTRET" 1323173 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1320683 1321072 1321542 "INTRAT" 1322294 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1317946 1318529 1319148 "INTPM" 1320168 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1314690 1315290 1316028 "INTPAF" 1317332 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1309869 1310831 1311882 "INTPACK" 1313659 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1306746 1309598 1309725 "INT" 1309762 T INT (NIL) -8 NIL NIL NIL) (-563 1305998 1306150 1306358 "INTHERTR" 1306588 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1305437 1305517 1305705 "INTHERAL" 1305912 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1303283 1303726 1304183 "INTHEORY" 1305000 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1294689 1296310 1298082 "INTG0" 1301635 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1275262 1280052 1284862 "INTFTBL" 1289899 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1274511 1274649 1274822 "INTFACT" 1275121 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1271938 1272384 1272941 "INTEF" 1274065 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1270305 1271044 1271072 "INTDOM" 1271373 T INTDOM (NIL) -9 NIL 1271580 NIL) (-555 1269674 1269848 1270090 "INTDOM-" 1270095 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1266062 1267990 1268044 "INTCAT" 1268843 NIL INTCAT (NIL T) -9 NIL 1269164 NIL) (-553 1265534 1265637 1265765 "INTBIT" 1265954 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1264233 1264387 1264694 "INTALG" 1265379 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1263716 1263806 1263963 "INTAF" 1264137 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1257059 1263526 1263666 "INTABL" 1263671 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1256400 1256866 1256931 "INT8" 1256965 T INT8 (NIL) -8 NIL NIL 1257010) (-548 1255740 1256206 1256271 "INT64" 1256305 T INT64 (NIL) -8 NIL NIL 1256350) (-547 1255080 1255546 1255611 "INT32" 1255645 T INT32 (NIL) -8 NIL NIL 1255690) (-546 1254420 1254886 1254951 "INT16" 1254985 T INT16 (NIL) -8 NIL NIL 1255030) (-545 1249330 1252043 1252071 "INS" 1253005 T INS (NIL) -9 NIL 1253670 NIL) (-544 1246570 1247341 1248315 "INS-" 1248388 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1245345 1245572 1245870 "INPSIGN" 1246323 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1244463 1244580 1244777 "INPRODPF" 1245225 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1243357 1243474 1243711 "INPRODFF" 1244343 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1242357 1242509 1242769 "INNMFACT" 1243193 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1241554 1241651 1241839 "INMODGCD" 1242256 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1240062 1240307 1240631 "INFSP" 1241299 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1239246 1239363 1239546 "INFPROD0" 1239942 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1236101 1237311 1237826 "INFORM" 1238739 T INFORM (NIL) -8 NIL NIL NIL) (-535 1235711 1235771 1235869 "INFORM1" 1236036 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1235234 1235323 1235437 "INFINITY" 1235617 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1234410 1234954 1235055 "INETCLTS" 1235153 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1233026 1233276 1233597 "INEP" 1234158 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1232275 1232923 1232988 "INDE" 1232993 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1231839 1231907 1232024 "INCRMAPS" 1232202 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1230657 1231108 1231314 "INBFILE" 1231653 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1225957 1226893 1227837 "INBFF" 1229745 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1224865 1225134 1225162 "INBCON" 1225675 T INBCON (NIL) -9 NIL 1225941 NIL) (-526 1224117 1224340 1224616 "INBCON-" 1224621 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1223596 1223841 1223932 "INAST" 1224046 T INAST (NIL) -8 NIL NIL NIL) (-524 1223023 1223275 1223381 "IMPTAST" 1223510 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1219469 1222867 1222971 "IMATRIX" 1222976 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1218181 1218304 1218619 "IMATQF" 1219325 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1216401 1216628 1216965 "IMATLIN" 1217937 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1210979 1216325 1216383 "ILIST" 1216388 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1208884 1210839 1210952 "IIARRAY2" 1210957 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1204282 1208795 1208859 "IFF" 1208864 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1203629 1203899 1204015 "IFAST" 1204186 T IFAST (NIL) -8 NIL NIL NIL) (-516 1198624 1202921 1203109 "IFARRAY" 1203486 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1197804 1198528 1198601 "IFAMON" 1198606 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1197388 1197453 1197507 "IEVALAB" 1197714 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1197063 1197131 1197291 "IEVALAB-" 1197296 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1196694 1196977 1197040 "IDPO" 1197045 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1195944 1196583 1196658 "IDPOAMS" 1196663 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1195251 1195833 1195908 "IDPOAM" 1195913 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1194310 1194586 1194639 "IDPC" 1195052 NIL IDPC (NIL T T) -9 NIL 1195201 NIL) (-508 1193779 1194202 1194275 "IDPAM" 1194280 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1193155 1193671 1193744 "IDPAG" 1193749 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1192800 1192991 1193066 "IDENT" 1193100 T IDENT (NIL) -8 NIL NIL NIL) (-505 1189055 1189903 1190798 "IDECOMP" 1191957 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1181891 1182978 1184025 "IDEAL" 1188091 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1181055 1181167 1181366 "ICDEN" 1181775 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1180126 1180535 1180682 "ICARD" 1180928 T ICARD (NIL) -8 NIL NIL NIL) (-501 1178186 1178499 1178904 "IBPTOOLS" 1179803 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1173793 1177806 1177919 "IBITS" 1178105 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1170516 1171092 1171787 "IBATOOL" 1173210 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1168295 1168757 1169290 "IBACHIN" 1170051 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1166124 1168141 1168244 "IARRAY2" 1168249 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1162230 1166050 1166107 "IARRAY1" 1166112 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1156339 1160642 1161123 "IAN" 1161769 T IAN (NIL) -8 NIL NIL NIL) (-494 1155850 1155907 1156080 "IALGFACT" 1156276 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1155378 1155491 1155519 "HYPCAT" 1155726 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1154916 1155033 1155219 "HYPCAT-" 1155224 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1154511 1154711 1154794 "HOSTNAME" 1154853 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1154356 1154393 1154434 "HOMOTOP" 1154439 NIL HOMOTOP (NIL T) -9 NIL 1154472 NIL) (-489 1150988 1152366 1152407 "HOAGG" 1153388 NIL HOAGG (NIL T) -9 NIL 1154067 NIL) (-488 1149582 1149981 1150507 "HOAGG-" 1150512 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1143586 1149177 1149326 "HEXADEC" 1149453 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1142334 1142556 1142819 "HEUGCD" 1143363 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1141410 1142171 1142301 "HELLFDIV" 1142306 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1139589 1141187 1141275 "HEAP" 1141354 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1138852 1139141 1139275 "HEADAST" 1139475 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1132718 1138767 1138829 "HDP" 1138834 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1126706 1132353 1132505 "HDMP" 1132619 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1126030 1126170 1126334 "HB" 1126562 T HB (NIL) -7 NIL NIL NIL) (-479 1119416 1125876 1125980 "HASHTBL" 1125985 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1118892 1119137 1119229 "HASAST" 1119344 T HASAST (NIL) -8 NIL NIL NIL) (-477 1116670 1118514 1118696 "HACKPI" 1118730 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1112338 1116523 1116636 "GTSET" 1116641 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1105753 1112216 1112314 "GSTBL" 1112319 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1098031 1104784 1105049 "GSERIES" 1105544 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1097172 1097589 1097617 "GROUP" 1097820 T GROUP (NIL) -9 NIL 1097954 NIL) (-472 1096538 1096697 1096948 "GROUP-" 1096953 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1094905 1095226 1095613 "GROEBSOL" 1096215 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1093819 1094107 1094158 "GRMOD" 1094687 NIL GRMOD (NIL T T) -9 NIL 1094855 NIL) (-469 1093587 1093623 1093751 "GRMOD-" 1093756 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1088877 1089941 1090941 "GRIMAGE" 1092607 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1087343 1087604 1087928 "GRDEF" 1088573 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1086787 1086903 1087044 "GRAY" 1087222 T GRAY (NIL) -7 NIL NIL NIL) (-465 1085974 1086380 1086431 "GRALG" 1086584 NIL GRALG (NIL T T) -9 NIL 1086677 NIL) (-464 1085635 1085708 1085871 "GRALG-" 1085876 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1082412 1085220 1085398 "GPOLSET" 1085542 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1081766 1081823 1082081 "GOSPER" 1082349 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1077498 1078204 1078730 "GMODPOL" 1081465 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1076503 1076687 1076925 "GHENSEL" 1077310 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1070659 1071502 1072522 "GENUPS" 1075587 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1070356 1070407 1070496 "GENUFACT" 1070602 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1069768 1069845 1070010 "GENPGCD" 1070274 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1069242 1069277 1069490 "GENMFACT" 1069727 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1067808 1068065 1068372 "GENEEZ" 1068985 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1061953 1067419 1067581 "GDMP" 1067731 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1051295 1055724 1056830 "GCNAALG" 1060936 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1049622 1050484 1050512 "GCDDOM" 1050767 T GCDDOM (NIL) -9 NIL 1050924 NIL) (-451 1049092 1049219 1049434 "GCDDOM-" 1049439 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1047764 1047949 1048253 "GB" 1048871 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1036380 1038710 1041102 "GBINTERN" 1045455 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1034217 1034509 1034930 "GBF" 1036055 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1032998 1033163 1033430 "GBEUCLID" 1034033 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1032347 1032472 1032621 "GAUSSFAC" 1032869 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1030714 1031016 1031330 "GALUTIL" 1032066 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1029022 1029296 1029620 "GALPOLYU" 1030441 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1026387 1026677 1027084 "GALFACTU" 1028719 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1018192 1019692 1021300 "GALFACT" 1024819 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1015580 1016238 1016266 "FVFUN" 1017422 T FVFUN (NIL) -9 NIL 1018142 NIL) (-440 1014846 1015028 1015056 "FVC" 1015347 T FVC (NIL) -9 NIL 1015530 NIL) (-439 1014489 1014671 1014739 "FUNDESC" 1014798 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1014104 1014286 1014367 "FUNCTION" 1014441 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1011848 1012426 1012892 "FT" 1013658 T FT (NIL) -8 NIL NIL NIL) (-436 1010639 1011149 1011352 "FTEM" 1011665 T FTEM (NIL) -8 NIL NIL NIL) (-435 1008930 1009219 1009616 "FSUPFACT" 1010330 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1007327 1007616 1007948 "FST" 1008618 T FST (NIL) -8 NIL NIL NIL) (-433 1006526 1006632 1006820 "FSRED" 1007209 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 1005225 1005481 1005828 "FSPRMELT" 1006241 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 1002531 1002969 1003455 "FSPECF" 1004788 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 984169 992500 992541 "FS" 996425 NIL FS (NIL T) -9 NIL 998714 NIL) (-429 972812 975805 979862 "FS-" 980162 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 972340 972394 972564 "FSINT" 972753 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 970632 971333 971636 "FSERIES" 972119 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 969674 969790 970014 "FSCINT" 970512 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 965882 968618 968659 "FSAGG" 969029 NIL FSAGG (NIL T) -9 NIL 969288 NIL) (-424 963644 964245 965041 "FSAGG-" 965136 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 962686 962829 963056 "FSAGG2" 963497 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 960368 960648 961195 "FS2UPS" 962404 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 960002 960045 960174 "FS2" 960319 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 958880 959051 959353 "FS2EXPXP" 959827 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 958306 958421 958573 "FRUTIL" 958760 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 949719 953801 955159 "FR" 956980 NIL FR (NIL T) -8 NIL NIL NIL) (-417 944688 947362 947402 "FRNAALG" 948798 NIL FRNAALG (NIL T) -9 NIL 949405 NIL) (-416 940361 941437 942712 "FRNAALG-" 943462 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 939999 940042 940169 "FRNAAF2" 940312 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 938379 938853 939148 "FRMOD" 939811 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 936130 936762 937079 "FRIDEAL" 938170 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 935325 935412 935701 "FRIDEAL2" 936037 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 934458 934872 934913 "FRETRCT" 934918 NIL FRETRCT (NIL T) -9 NIL 935094 NIL) (-410 933570 933801 934152 "FRETRCT-" 934157 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 930658 931868 931927 "FRAMALG" 932809 NIL FRAMALG (NIL T T) -9 NIL 933101 NIL) (-408 928792 929247 929877 "FRAMALG-" 930100 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 922713 928267 928543 "FRAC" 928548 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 922349 922406 922513 "FRAC2" 922650 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 921985 922042 922149 "FR2" 922286 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 916498 919391 919419 "FPS" 920538 T FPS (NIL) -9 NIL 921095 NIL) (-403 915947 916056 916220 "FPS-" 916366 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 913249 914918 914946 "FPC" 915171 T FPC (NIL) -9 NIL 915313 NIL) (-401 913042 913082 913179 "FPC-" 913184 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 911832 912530 912571 "FPATMAB" 912576 NIL FPATMAB (NIL T) -9 NIL 912728 NIL) (-399 909505 910008 910434 "FPARFRAC" 911469 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 904898 905397 906079 "FORTRAN" 908937 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 902614 903114 903653 "FORT" 904379 T FORT (NIL) -7 NIL NIL NIL) (-396 900290 900852 900880 "FORTFN" 901940 T FORTFN (NIL) -9 NIL 902564 NIL) (-395 900054 900104 900132 "FORTCAT" 900191 T FORTCAT (NIL) -9 NIL 900253 NIL) (-394 898160 898670 899060 "FORMULA" 899684 T FORMULA (NIL) -8 NIL NIL NIL) (-393 897948 897978 898047 "FORMULA1" 898124 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 897471 897523 897696 "FORDER" 897890 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 896567 896731 896924 "FOP" 897298 T FOP (NIL) -7 NIL NIL NIL) (-390 895148 895847 896021 "FNLA" 896449 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 893877 894292 894320 "FNCAT" 894780 T FNCAT (NIL) -9 NIL 895040 NIL) (-388 893416 893836 893864 "FNAME" 893869 T FNAME (NIL) -8 NIL NIL NIL) (-387 891979 892942 892970 "FMTC" 892975 T FMTC (NIL) -9 NIL 893011 NIL) (-386 888312 889502 890131 "FMONOID" 891383 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 887504 888054 888203 "FM" 888208 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 884928 885574 885602 "FMFUN" 886746 T FMFUN (NIL) -9 NIL 887454 NIL) (-383 884197 884378 884406 "FMC" 884696 T FMC (NIL) -9 NIL 884878 NIL) (-382 881276 882136 882190 "FMCAT" 883385 NIL FMCAT (NIL T T) -9 NIL 883880 NIL) (-381 880142 881042 881142 "FM1" 881221 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 877916 878332 878826 "FLOATRP" 879693 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 871490 875645 876266 "FLOAT" 877315 T FLOAT (NIL) -8 NIL NIL NIL) (-378 868928 869428 870006 "FLOATCP" 870957 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 867668 868506 868547 "FLINEXP" 868552 NIL FLINEXP (NIL T) -9 NIL 868645 NIL) (-376 866822 867057 867385 "FLINEXP-" 867390 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 865898 866042 866266 "FLASORT" 866674 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 863014 863882 863934 "FLALG" 865161 NIL FLALG (NIL T T) -9 NIL 865628 NIL) (-373 856750 860500 860541 "FLAGG" 861803 NIL FLAGG (NIL T) -9 NIL 862455 NIL) (-372 855476 855815 856305 "FLAGG-" 856310 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 854518 854661 854888 "FLAGG2" 855329 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 851369 852377 852436 "FINRALG" 853564 NIL FINRALG (NIL T T) -9 NIL 854072 NIL) (-369 850529 850758 851097 "FINRALG-" 851102 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 849909 850148 850176 "FINITE" 850372 T FINITE (NIL) -9 NIL 850479 NIL) (-367 842266 844453 844493 "FINAALG" 848160 NIL FINAALG (NIL T) -9 NIL 849613 NIL) (-366 837598 838648 839792 "FINAALG-" 841171 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 836966 837353 837456 "FILE" 837528 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 835624 835962 836016 "FILECAT" 836700 NIL FILECAT (NIL T T) -9 NIL 836916 NIL) (-363 833340 834868 834896 "FIELD" 834936 T FIELD (NIL) -9 NIL 835016 NIL) (-362 831960 832345 832856 "FIELD-" 832861 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 829810 830595 830942 "FGROUP" 831646 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 828900 829064 829284 "FGLMICPK" 829642 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 824732 828825 828882 "FFX" 828887 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 824333 824394 824529 "FFSLPE" 824665 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 820322 821105 821901 "FFPOLY" 823569 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 819826 819862 820071 "FFPOLY2" 820280 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 815669 819745 819808 "FFP" 819813 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 811067 815580 815644 "FF" 815649 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 806193 810410 810600 "FFNBX" 810921 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 801122 805328 805586 "FFNBP" 806047 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 795755 800406 800617 "FFNB" 800955 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 794587 794785 795100 "FFINTBAS" 795552 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 790656 792876 792904 "FFIELDC" 793524 T FFIELDC (NIL) -9 NIL 793900 NIL) (-348 789318 789689 790186 "FFIELDC-" 790191 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 788887 788933 789057 "FFHOM" 789260 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 786582 787069 787586 "FFF" 788402 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 782200 786324 786425 "FFCGX" 786525 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 777821 781932 782039 "FFCGP" 782143 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 773004 777548 777656 "FFCG" 777757 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 754400 763481 763567 "FFCAT" 768732 NIL FFCAT (NIL T T T) -9 NIL 770183 NIL) (-341 749598 750645 751959 "FFCAT-" 753189 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 749009 749052 749287 "FFCAT2" 749549 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 738330 741981 743201 "FEXPR" 747861 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 737330 737765 737806 "FEVALAB" 737890 NIL FEVALAB (NIL T) -9 NIL 738151 NIL) (-337 736489 736699 737037 "FEVALAB-" 737042 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 735055 735872 736075 "FDIV" 736388 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 732075 732816 732931 "FDIVCAT" 734499 NIL FDIVCAT (NIL T T T T) -9 NIL 734936 NIL) (-334 731837 731864 732034 "FDIVCAT-" 732039 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 731057 731144 731421 "FDIV2" 731744 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 729743 730002 730291 "FCPAK1" 730788 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 728842 729243 729384 "FCOMP" 729634 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 712544 715992 719530 "FC" 725324 T FC (NIL) -8 NIL NIL NIL) (-329 704907 708935 708975 "FAXF" 710777 NIL FAXF (NIL T) -9 NIL 711469 NIL) (-328 702183 702841 703666 "FAXF-" 704131 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 697235 701559 701735 "FARRAY" 702040 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 692129 694196 694249 "FAMR" 695272 NIL FAMR (NIL T T) -9 NIL 695732 NIL) (-325 691019 691321 691756 "FAMR-" 691761 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 690188 690941 690994 "FAMONOID" 690999 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 687974 688684 688737 "FAMONC" 689678 NIL FAMONC (NIL T T) -9 NIL 690064 NIL) (-322 686639 687728 687865 "FAGROUP" 687870 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 684434 684753 685156 "FACUTIL" 686320 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 683533 683718 683940 "FACTFUNC" 684244 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 675955 682836 683035 "EXPUPXS" 683389 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 673438 673978 674564 "EXPRTUBE" 675389 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 669709 670301 671031 "EXPRODE" 672777 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 655194 668358 668787 "EXPR" 669313 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 649748 650335 651141 "EXPR2UPS" 654492 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 649380 649437 649546 "EXPR2" 649685 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 640771 648533 648823 "EXPEXPAN" 649217 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 640571 640728 640757 "EXIT" 640762 T EXIT (NIL) -8 NIL NIL NIL) (-311 640051 640295 640386 "EXITAST" 640500 T EXITAST (NIL) -8 NIL NIL NIL) (-310 639678 639740 639853 "EVALCYC" 639983 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 639219 639337 639378 "EVALAB" 639548 NIL EVALAB (NIL T) -9 NIL 639652 NIL) (-308 638700 638822 639043 "EVALAB-" 639048 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 636068 637370 637398 "EUCDOM" 637953 T EUCDOM (NIL) -9 NIL 638303 NIL) (-306 634473 634915 635505 "EUCDOM-" 635510 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 622011 624771 627521 "ESTOOLS" 631743 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 621643 621700 621809 "ESTOOLS2" 621948 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 621394 621436 621516 "ESTOOLS1" 621595 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 615431 617039 617067 "ES" 619835 T ES (NIL) -9 NIL 621245 NIL) (-301 610378 611665 613482 "ES-" 613646 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 606752 607513 608293 "ESCONT" 609618 T ESCONT (NIL) -7 NIL NIL NIL) (-299 606497 606529 606611 "ESCONT1" 606714 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 606172 606222 606322 "ES2" 606441 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 605802 605860 605969 "ES1" 606108 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 605018 605147 605323 "ERROR" 605646 T ERROR (NIL) -7 NIL NIL NIL) (-295 598410 604877 604968 "EQTBL" 604973 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 590913 593724 595173 "EQ" 596994 NIL -2010 (NIL T) -8 NIL NIL NIL) (-293 590545 590602 590711 "EQ2" 590850 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 585834 586883 587976 "EP" 589484 NIL EP (NIL T) -7 NIL NIL NIL) (-291 584434 584725 585031 "ENV" 585548 T ENV (NIL) -8 NIL NIL NIL) (-290 583528 584082 584110 "ENTIRER" 584115 T ENTIRER (NIL) -9 NIL 584161 NIL) (-289 579995 581483 581853 "EMR" 583327 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 579139 579324 579378 "ELTAGG" 579758 NIL ELTAGG (NIL T T) -9 NIL 579969 NIL) (-287 578858 578920 579061 "ELTAGG-" 579066 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 578647 578676 578730 "ELTAB" 578814 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 577773 577919 578118 "ELFUTS" 578498 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 577515 577571 577599 "ELEMFUN" 577704 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 577385 577406 577474 "ELEMFUN-" 577479 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 572229 575485 575526 "ELAGG" 576466 NIL ELAGG (NIL T) -9 NIL 576929 NIL) (-281 570514 570948 571611 "ELAGG-" 571616 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 569179 569457 569750 "ELABEXPR" 570241 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 562043 563846 564673 "EFUPXS" 568455 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 555493 557294 558104 "EFULS" 561319 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 552978 553336 553808 "EFSTRUC" 555125 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 542769 544335 545883 "EF" 551493 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 541843 542254 542403 "EAB" 542640 T EAB (NIL) -8 NIL NIL NIL) (-274 541025 541802 541830 "E04UCFA" 541835 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 540207 540984 541012 "E04NAFA" 541017 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 539389 540166 540194 "E04MBFA" 540199 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 538571 539348 539376 "E04JAFA" 539381 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 537755 538530 538558 "E04GCFA" 538563 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 536939 537714 537742 "E04FDFA" 537747 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 536121 536898 536926 "E04DGFA" 536931 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 530294 531646 533010 "E04AGNT" 534777 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 528974 529480 529520 "DVARCAT" 529995 NIL DVARCAT (NIL T) -9 NIL 530194 NIL) (-265 528178 528390 528704 "DVARCAT-" 528709 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 521315 527977 528106 "DSMP" 528111 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 516097 517260 518328 "DROPT" 520267 T DROPT (NIL) -8 NIL NIL NIL) (-262 515762 515821 515919 "DROPT1" 516032 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 510877 512003 513140 "DROPT0" 514645 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 509222 509547 509933 "DRAWPT" 510511 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 503809 504732 505811 "DRAW" 508196 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 503442 503495 503613 "DRAWHACK" 503750 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 502173 502442 502733 "DRAWCX" 503171 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 501688 501757 501908 "DRAWCURV" 502099 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 492156 494118 496233 "DRAWCFUN" 499593 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 488922 490851 490892 "DQAGG" 491521 NIL DQAGG (NIL T) -9 NIL 491794 NIL) (-253 477046 483515 483598 "DPOLCAT" 485450 NIL DPOLCAT (NIL T T T T) -9 NIL 485995 NIL) (-252 471882 473231 475189 "DPOLCAT-" 475194 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 465004 471743 471841 "DPMO" 471846 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 458029 464784 464951 "DPMM" 464956 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 457602 457948 457996 "DOMCTOR" 458001 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456870 457124 457261 "DOMAIN" 457485 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450858 456505 456657 "DMP" 456771 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450458 450514 450658 "DLP" 450796 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 444280 449785 449975 "DLIST" 450300 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 441077 443133 443174 "DLAGG" 443724 NIL DLAGG (NIL T) -9 NIL 443954 NIL) (-243 439753 440417 440445 "DIVRING" 440537 T DIVRING (NIL) -9 NIL 440620 NIL) (-242 438990 439180 439480 "DIVRING-" 439485 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 437092 437449 437855 "DISPLAY" 438604 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430980 437006 437069 "DIRPROD" 437074 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429828 430031 430296 "DIRPROD2" 430773 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418603 424609 424662 "DIRPCAT" 425072 NIL DIRPCAT (NIL NIL T) -9 NIL 425912 NIL) (-237 415929 416571 417452 "DIRPCAT-" 417789 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 415216 415376 415562 "DIOSP" 415763 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411871 414128 414169 "DIOPS" 414603 NIL DIOPS (NIL T) -9 NIL 414832 NIL) (-234 411420 411534 411725 "DIOPS-" 411730 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 410243 410871 410899 "DIFRING" 411086 T DIFRING (NIL) -9 NIL 411196 NIL) (-232 409889 409966 410118 "DIFRING-" 410123 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407625 408897 408938 "DIFEXT" 409301 NIL DIFEXT (NIL T) -9 NIL 409595 NIL) (-230 405910 406338 407004 "DIFEXT-" 407009 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 403185 405442 405483 "DIAGG" 405488 NIL DIAGG (NIL T) -9 NIL 405508 NIL) (-228 402569 402726 402978 "DIAGG-" 402983 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397986 401528 401805 "DHMATRIX" 402338 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393598 394507 395517 "DFSFUN" 396996 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388676 392529 392841 "DFLOAT" 393306 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386939 387220 387609 "DFINTTLS" 388384 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383968 384960 385360 "DERHAM" 386605 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381769 383743 383832 "DEQUEUE" 383912 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 381023 381156 381339 "DEGRED" 381631 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377453 378198 379044 "DEFINTRF" 380251 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 375008 375477 376069 "DEFINTEF" 376972 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 374358 374628 374743 "DEFAST" 374913 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368362 373953 374102 "DECIMAL" 374229 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365873 366332 366838 "DDFACT" 367906 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365469 365512 365663 "DBLRESP" 365824 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 363341 363702 364062 "DBASE" 365236 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362583 362821 362967 "DATAARY" 363240 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361689 362542 362570 "D03FAFA" 362575 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360796 361648 361676 "D03EEFA" 361681 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358746 359212 359701 "D03AGNT" 360327 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 358035 358705 358733 "D02EJFA" 358738 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 357324 357994 358022 "D02CJFA" 358027 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356613 357283 357311 "D02BHFA" 357316 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355902 356572 356600 "D02BBFA" 356605 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 349099 350688 352294 "D02AGNT" 354316 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346867 347390 347936 "D01WGTS" 348573 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345934 346826 346854 "D01TRNS" 346859 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 345002 345893 345921 "D01GBFA" 345926 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 344070 344961 344989 "D01FCFA" 344994 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 343138 344029 344057 "D01ASFA" 344062 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 342206 343097 343125 "D01AQFA" 343130 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 341274 342165 342193 "D01APFA" 342198 T D01APFA (NIL) -8 NIL NIL NIL) (-197 340342 341233 341261 "D01ANFA" 341266 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339410 340301 340329 "D01AMFA" 340334 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338478 339369 339397 "D01ALFA" 339402 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337546 338437 338465 "D01AKFA" 338470 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336614 337505 337533 "D01AJFA" 337538 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329909 331462 333023 "D01AGNT" 335073 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 329246 329374 329526 "CYCLOTOM" 329777 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325981 326694 327421 "CYCLES" 328539 T CYCLES (NIL) -7 NIL NIL NIL) (-189 325293 325427 325598 "CVMP" 325842 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 323134 323392 323761 "CTRIGMNP" 325021 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322570 322928 323001 "CTOR" 323081 T CTOR (NIL) -8 NIL NIL NIL) (-186 322079 322301 322402 "CTORKIND" 322489 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321370 321686 321714 "CTORCAT" 321896 T CTORCAT (NIL) -9 NIL 322009 NIL) (-184 320968 321079 321238 "CTORCAT-" 321243 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320457 320671 320769 "CTORCALL" 320890 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 319831 319930 320083 "CSTTOOLS" 320354 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315630 316287 317045 "CRFP" 319143 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 315105 315351 315443 "CRCEAST" 315558 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 314152 314337 314565 "CRAPACK" 314909 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313536 313637 313841 "CPMATCH" 314028 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 313261 313289 313395 "CPIMA" 313502 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309609 310281 311000 "COORDSYS" 312596 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 309021 309142 309284 "CONTOUR" 309487 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304912 307024 307516 "CONTFRAC" 308561 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304792 304813 304841 "CONDUIT" 304878 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303880 304434 304462 "COMRING" 304467 T COMRING (NIL) -9 NIL 304519 NIL) (-171 302934 303238 303422 "COMPPROP" 303716 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302595 302630 302758 "COMPLPAT" 302893 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292886 302404 302513 "COMPLEX" 302518 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292522 292579 292686 "COMPLEX2" 292823 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 292240 292275 292373 "COMPFACT" 292481 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 276320 286314 286354 "COMPCAT" 287358 NIL COMPCAT (NIL T) -9 NIL 288706 NIL) (-165 265830 268759 272386 "COMPCAT-" 272742 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265559 265587 265690 "COMMUPC" 265796 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 265353 265387 265446 "COMMONOP" 265520 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264909 265104 265191 "COMM" 265286 T COMM (NIL) -8 NIL NIL NIL) (-161 264485 264713 264788 "COMMAAST" 264854 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263734 263928 263956 "COMBOPC" 264294 T COMBOPC (NIL) -9 NIL 264469 NIL) (-159 262630 262840 263082 "COMBINAT" 263524 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 259087 259661 260288 "COMBF" 262052 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257845 258203 258438 "COLOR" 258872 T COLOR (NIL) -8 NIL NIL NIL) (-156 257321 257566 257658 "COLONAST" 257773 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256961 257008 257133 "CMPLXRT" 257268 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256409 256661 256760 "CLLCTAST" 256882 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251909 252939 254019 "CLIP" 255349 T CLIP (NIL) -7 NIL NIL NIL) (-152 250255 251015 251254 "CLIF" 251736 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246430 248401 248442 "CLAGG" 249371 NIL CLAGG (NIL T) -9 NIL 249907 NIL) (-150 244852 245309 245892 "CLAGG-" 245897 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244396 244481 244621 "CINTSLPE" 244761 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241897 242368 242916 "CHVAR" 243924 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 241071 241625 241653 "CHARZ" 241658 T CHARZ (NIL) -9 NIL 241673 NIL) (-146 240825 240865 240943 "CHARPOL" 241025 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239883 240470 240498 "CHARNZ" 240545 T CHARNZ (NIL) -9 NIL 240601 NIL) (-144 237845 238573 238908 "CHAR" 239568 T CHAR (NIL) -8 NIL NIL NIL) (-143 237571 237632 237660 "CFCAT" 237771 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236816 236927 237109 "CDEN" 237455 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232781 235969 236249 "CCLASS" 236556 T CCLASS (NIL) -8 NIL NIL NIL) (-140 232088 232231 232394 "CATEGORY" 232638 T -10 (NIL) -8 NIL NIL NIL) (-139 231661 232007 232055 "CATCTOR" 232060 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 231112 231364 231462 "CATAST" 231583 T CATAST (NIL) -8 NIL NIL NIL) (-137 230588 230833 230925 "CASEAST" 231040 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225597 226617 227370 "CARTEN" 229891 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224705 224853 225074 "CARTEN2" 225444 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 223020 223855 224112 "CARD" 224468 T CARD (NIL) -8 NIL NIL NIL) (-133 222596 222824 222899 "CAPSLAST" 222965 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 222100 222308 222336 "CACHSET" 222468 T CACHSET (NIL) -9 NIL 222546 NIL) (-131 221570 221892 221920 "CABMON" 221970 T CABMON (NIL) -9 NIL 222026 NIL) (-130 221043 221274 221384 "BYTEORD" 221480 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 220019 220577 220719 "BYTE" 220882 T BYTE (NIL) -8 NIL NIL 221004) (-128 215369 219524 219696 "BYTEBUF" 219867 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212878 215061 215168 "BTREE" 215295 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 210327 212526 212648 "BTOURN" 212788 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207697 209797 209838 "BTCAT" 209906 NIL BTCAT (NIL T) -9 NIL 209983 NIL) (-124 207364 207444 207593 "BTCAT-" 207598 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202629 206507 206535 "BTAGG" 206757 T BTAGG (NIL) -9 NIL 206918 NIL) (-122 202119 202244 202450 "BTAGG-" 202455 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 199114 201397 201612 "BSTREE" 201936 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 198252 198378 198562 "BRILL" 198970 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194904 196978 197019 "BRAGG" 197668 NIL BRAGG (NIL T) -9 NIL 197926 NIL) (-118 193433 193839 194394 "BRAGG-" 194399 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186662 192779 192963 "BPADICRT" 193281 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184977 186599 186644 "BPADIC" 186649 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184675 184705 184819 "BOUNDZRO" 184941 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179903 181101 182013 "BOP" 183783 T BOP (NIL) -8 NIL NIL NIL) (-113 177684 178088 178563 "BOP1" 179461 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176509 177258 177407 "BOOLEAN" 177555 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175788 176192 176246 "BMODULE" 176251 NIL BMODULE (NIL T T) -9 NIL 176316 NIL) (-110 171589 175586 175659 "BITS" 175735 T BITS (NIL) -8 NIL NIL NIL) (-109 171010 171129 171269 "BINDING" 171469 T BINDING (NIL) -8 NIL NIL NIL) (-108 165017 170607 170755 "BINARY" 170882 T BINARY (NIL) -8 NIL NIL NIL) (-107 162797 164272 164313 "BGAGG" 164573 NIL BGAGG (NIL T) -9 NIL 164710 NIL) (-106 162628 162660 162751 "BGAGG-" 162756 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161699 162012 162217 "BFUNCT" 162443 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 160389 160567 160855 "BEZOUT" 161523 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156858 159241 159571 "BBTREE" 160092 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156592 156645 156673 "BASTYPE" 156792 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156444 156473 156546 "BASTYPE-" 156551 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155878 155954 156106 "BALFACT" 156355 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154734 155293 155479 "AUTOMOR" 155723 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154460 154465 154491 "ATTREG" 154496 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152712 153157 153509 "ATTRBUT" 154126 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 152320 152540 152606 "ATTRAST" 152664 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151856 151969 151995 "ATRIG" 152196 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151665 151706 151793 "ATRIG-" 151798 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 151310 151496 151522 "ASTCAT" 151527 T ASTCAT (NIL) -9 NIL 151557 NIL) (-92 151037 151096 151215 "ASTCAT-" 151220 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 149186 150813 150901 "ASTACK" 150980 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147691 147988 148353 "ASSOCEQ" 148868 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146723 147350 147474 "ASP9" 147598 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146486 146671 146710 "ASP8" 146715 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 145354 146091 146233 "ASP80" 146375 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 144252 144989 145121 "ASP7" 145253 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 143206 143929 144047 "ASP78" 144165 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 142175 142886 143003 "ASP77" 143120 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 141087 141813 141944 "ASP74" 142075 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139987 140722 140854 "ASP73" 140986 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 139091 139813 139913 "ASP6" 139918 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 138035 138768 138886 "ASP55" 139004 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136984 137709 137828 "ASP50" 137947 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 136072 136685 136795 "ASP4" 136905 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 135160 135773 135883 "ASP49" 135993 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133944 134699 134867 "ASP42" 135049 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132720 133477 133647 "ASP41" 133831 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131670 132397 132515 "ASP35" 132633 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 131435 131618 131657 "ASP34" 131662 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 131172 131239 131315 "ASP33" 131390 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 130065 130807 130939 "ASP31" 131071 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129830 130013 130052 "ASP30" 130057 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129565 129634 129710 "ASP29" 129785 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 129330 129513 129552 "ASP28" 129557 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 129095 129278 129317 "ASP27" 129322 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 128179 128793 128904 "ASP24" 129015 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 127255 127981 128093 "ASP20" 128098 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 126343 126956 127066 "ASP1" 127176 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 125285 126017 126136 "ASP19" 126255 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 125022 125089 125165 "ASP12" 125240 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123874 124621 124765 "ASP10" 124909 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121725 123718 123809 "ARRAY2" 123814 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117490 121373 121487 "ARRAY1" 121642 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116522 116695 116916 "ARRAY12" 117313 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110834 112752 112827 "ARR2CAT" 115457 NIL ARR2CAT (NIL T T T) -9 NIL 116215 NIL) (-56 108268 109012 109966 "ARR2CAT-" 109971 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107585 107895 108020 "ARITY" 108161 T ARITY (NIL) -8 NIL NIL NIL) (-54 106361 106513 106812 "APPRULE" 107421 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 106012 106060 106179 "APPLYORE" 106307 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104959 105277 105472 "ANY" 105835 T ANY (NIL) -8 NIL NIL NIL) (-51 104237 104360 104517 "ANY1" 104833 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101767 102674 103001 "ANTISYM" 103961 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101259 101474 101570 "ANON" 101689 T ANON (NIL) -8 NIL NIL NIL) (-48 95508 99798 100252 "AN" 100823 T AN (NIL) -8 NIL NIL NIL) (-47 91406 92794 92845 "AMR" 93593 NIL AMR (NIL T T) -9 NIL 94193 NIL) (-46 90518 90739 91102 "AMR-" 91107 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74957 90435 90496 "ALIST" 90501 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71759 74551 74720 "ALGSC" 74875 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68314 68869 69476 "ALGPKG" 71199 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67591 67692 67876 "ALGMFACT" 68200 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63542 64149 64767 "ALGMANIP" 67151 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54912 63168 63318 "ALGFF" 63475 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54108 54239 54418 "ALGFACT" 54770 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53049 53649 53687 "ALGEBRA" 53692 NIL ALGEBRA (NIL T) -9 NIL 53733 NIL) (-37 52767 52826 52958 "ALGEBRA-" 52963 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34860 50769 50821 "ALAGG" 50957 NIL ALAGG (NIL T T) -9 NIL 51118 NIL) (-35 34396 34509 34535 "AHYP" 34736 T AHYP (NIL) -9 NIL NIL NIL) (-34 33327 33575 33601 "AGG" 34100 T AGG (NIL) -9 NIL 34379 NIL) (-33 32761 32923 33137 "AGG-" 33142 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30567 30990 31395 "AF" 32403 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30047 30292 30382 "ADDAST" 30495 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29315 29574 29730 "ACPLOT" 29909 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18638 26442 26480 "ACFS" 27087 NIL ACFS (NIL T) -9 NIL 27326 NIL) (-28 16665 17155 17917 "ACFS-" 17922 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12783 14712 14738 "ACF" 15617 T ACF (NIL) -9 NIL 16030 NIL) (-26 11487 11821 12314 "ACF-" 12319 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11059 11254 11280 "ABELSG" 11372 T ABELSG (NIL) -9 NIL 11437 NIL) (-24 10926 10951 11017 "ABELSG-" 11022 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10269 10556 10582 "ABELMON" 10752 T ABELMON (NIL) -9 NIL 10864 NIL) (-22 9933 10017 10155 "ABELMON-" 10160 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9281 9653 9679 "ABELGRP" 9751 T ABELGRP (NIL) -9 NIL 9826 NIL) (-20 8744 8873 9089 "ABELGRP-" 9094 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8083 8122 "A1AGG" 8127 NIL A1AGG (NIL T) -9 NIL 8167 NIL) (-18 30 1251 2813 "A1AGG-" 2818 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 4aeae036..1ce621af 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,302 +1,329 @@
 
-(731707 . 3452645034)        
-(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-175))))) 
-(((*1 *1 *1)
-  (-12 (-5 *1 (-223 *2 *3)) (-4 *2 (-13 (-1045) (-846)))
-   (-14 *3 (-641 (-1170)))))) 
-(((*1 *1 *1 *2) (-12 (-4 *1 (-1008)) (-5 *2 (-858))))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846))
-   (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-112))))) 
-(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3)
-  (-12 (-5 *3 (-564)) (-5 *5 (-685 (-225))) (-5 *4 (-225))
-   (-5 *2 (-1031)) (-5 *1 (-748))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) 
+(731999 . 3452782370)        
+(((*1 *2 *1) (-12 (-5 *2 (-1267)) (-5 *1 (-819))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1155)) (-5 *2 (-1267)) (-5 *1 (-436))))) 
+(((*1 *2)
+  (-12 (-4 *2 (-13 (-430 *3) (-1000))) (-5 *1 (-276 *3 *2))
+   (-4 *3 (-556))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-225)) (-5 *2 (-1155)) (-5 *1 (-192))))
+ ((*1 *2 *3) (-12 (-5 *3 (-225)) (-5 *2 (-1155)) (-5 *1 (-300))))
+ ((*1 *2 *3) (-12 (-5 *3 (-225)) (-5 *2 (-1155)) (-5 *1 (-305))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-642 *3)) (-4 *3 (-1212)) (-4 *1 (-107 *3))))) 
+(((*1 *2 *1 *1)
+  (-12
+   (-5 *2
+    (-2 (|:| -2080 (-780 *3)) (|:| |coef1| (-780 *3))
+     (|:| |coef2| (-780 *3))))
+   (-5 *1 (-780 *3)) (-4 *3 (-556)) (-4 *3 (-1047))))
+ ((*1 *2 *1 *1)
+  (-12 (-4 *3 (-556)) (-4 *3 (-1047)) (-4 *4 (-791)) (-4 *5 (-848))
+   (-5 *2 (-2 (|:| -2080 *1) (|:| |coef1| *1) (|:| |coef2| *1)))
+   (-4 *1 (-1062 *3 *4 *5))))) 
+(((*1 *2 *2)
+  (-12 (-5 *2 (-642 *3)) (-4 *3 (-1238 (-564))) (-5 *1 (-486 *3))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-556)) (-5 *2 (-641 (-767))) (-5 *1 (-965 *4 *3))
-   (-4 *3 (-1235 *4))))) 
-(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5)
-  (-12 (-5 *3 (-225)) (-5 *4 (-564))
-   (-5 *5 (-3 (|:| |fn| (-388)) (|:| |fp| (-64 G)))) (-5 *2 (-1031))
-   (-5 *1 (-744))))) 
-(((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-917)) (-5 *2 (-1264)) (-5 *1 (-1260))))
- ((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-917)) (-5 *2 (-1264)) (-5 *1 (-1261))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1031))))) 
-(((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4407)) (-4 *1 (-489 *4))
-   (-4 *4 (-1209)) (-5 *2 (-112))))) 
+  (-12
+   (-5 *3
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-769)) (|:| |poli| *7)
+     (|:| |polj| *7)))
+   (-4 *5 (-791)) (-4 *7 (-947 *4 *5 *6)) (-4 *4 (-452)) (-4 *6 (-848))
+   (-5 *2 (-112)) (-5 *1 (-449 *4 *5 *6 *7))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-506)) (-5 *1 (-280))))
+ ((*1 *2 *1)
+  (-12 (-5 *2 (-3 (-564) (-225) (-506) (-1155) (-1178)))
+   (-5 *1 (-1178))))) 
+(((*1 *2 *1)
+  (-12 (-4 *1 (-693 *3)) (-4 *3 (-1097))
+   (-5 *2 (-642 (-2 (|:| -3778 *3) (|:| -4043 (-769)))))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-642 (-330))) (-5 *1 (-330))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-919)) (-5 *1 (-357 *3)) (-4 *3 (-349))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1283 *4 *2)) (-4 *1 (-374 *4 *2)) (-4 *4 (-846))
+  (-12 (-5 *3 (-1286 *4 *2)) (-4 *1 (-374 *4 *2)) (-4 *4 (-848))
    (-4 *2 (-172))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1276 *3 *2)) (-4 *3 (-846)) (-4 *2 (-1045))))
+  (-12 (-4 *1 (-1279 *3 *2)) (-4 *3 (-848)) (-4 *2 (-1047))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-815 *4)) (-4 *1 (-1276 *4 *2)) (-4 *4 (-846))
-   (-4 *2 (-1045))))
+  (-12 (-5 *3 (-817 *4)) (-4 *1 (-1279 *4 *2)) (-4 *4 (-848))
+   (-4 *2 (-1047))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *2 (-1045)) (-5 *1 (-1282 *2 *3)) (-4 *3 (-842))))) 
-(((*1 *2 *1 *3)
-  (-12 (-5 *3 (-564)) (-4 *1 (-323 *2 *4)) (-4 *4 (-131))
-   (-4 *2 (-1094))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-564)) (-5 *1 (-361 *2)) (-4 *2 (-1094))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-564)) (-5 *1 (-386 *2)) (-4 *2 (-1094))))
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-  (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1209))
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    (-5 *2 (-336 *9 *10 *11 *12))
    (-5 *1 (-333 *5 *6 *7 *8 *9 *10 *11 *12))
    (-4 *12 (-342 *9 *10 *11))))
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+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-338 *3)) (-4 *3 (-1097))))
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+  (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1216)) (-4 *8 (-1216))
+   (-4 *6 (-1238 *5)) (-4 *7 (-1238 (-407 *6))) (-4 *9 (-1238 *8))
    (-4 *2 (-342 *8 *9 *10)) (-5 *1 (-340 *5 *6 *7 *4 *8 *9 *10 *2))
-   (-4 *4 (-342 *5 *6 *7)) (-4 *10 (-1235 (-407 *9)))))
+   (-4 *4 (-342 *5 *6 *7)) (-4 *10 (-1238 (-407 *9)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1209)) (-4 *6 (-1209))
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1212)) (-4 *6 (-1212))
    (-4 *2 (-373 *6)) (-5 *1 (-371 *5 *4 *6 *2)) (-4 *4 (-373 *5))))
  ((*1 *1 *2 *1)
-  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-382 *3 *4)) (-4 *3 (-1045))
-   (-4 *4 (-1094))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-382 *3 *4)) (-4 *3 (-1047))
+   (-4 *4 (-1097))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-418 *5)) (-4 *5 (-556))
    (-4 *6 (-556)) (-5 *2 (-418 *6)) (-5 *1 (-405 *5 *6))))
@@ -305,36 +332,36 @@
    (-4 *6 (-556)) (-5 *2 (-407 *6)) (-5 *1 (-406 *5 *6))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-413 *5 *6 *7 *8)) (-4 *5 (-307))
-   (-4 *6 (-988 *5)) (-4 *7 (-1235 *6))
-   (-4 *8 (-13 (-409 *6 *7) (-1034 *6))) (-4 *9 (-307))
-   (-4 *10 (-988 *9)) (-4 *11 (-1235 *10))
+   (-4 *6 (-990 *5)) (-4 *7 (-1238 *6))
+   (-4 *8 (-13 (-409 *6 *7) (-1036 *6))) (-4 *9 (-307))
+   (-4 *10 (-990 *9)) (-4 *11 (-1238 *10))
    (-5 *2 (-413 *9 *10 *11 *12))
    (-5 *1 (-412 *5 *6 *7 *8 *9 *10 *11 *12))
-   (-4 *12 (-13 (-409 *10 *11) (-1034 *10)))))
+   (-4 *12 (-13 (-409 *10 *11) (-1036 *10)))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-172)) (-4 *6 (-172))
    (-4 *2 (-417 *6)) (-5 *1 (-415 *4 *5 *2 *6)) (-4 *4 (-417 *5))))
  ((*1 *1 *2 *1)
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    (-4 *2 (-425 *6)) (-5 *1 (-423 *5 *4 *6 *2)) (-4 *4 (-425 *5))))
  ((*1 *1 *2 *1)
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+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-489 *3)) (-4 *3 (-1212))))
  ((*1 *1 *2 *1)
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-   (-4 *4 (-846))))
+  (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-509 *3 *4)) (-4 *3 (-1097))
+   (-4 *4 (-848))))
  ((*1 *2 *3 *4)
   (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-585 *5)) (-4 *5 (-363))
    (-4 *6 (-363)) (-5 *2 (-585 *6)) (-5 *1 (-584 *5 *6))))
  ((*1 *2 *3 *4)
   (|partial| -12 (-5 *3 (-1 *6 *5))
-      (-5 *4 (-3 (-2 (|:| -2177 *5) (|:| |coeff| *5)) "failed"))
+      (-5 *4 (-3 (-2 (|:| -2116 *5) (|:| |coeff| *5)) "failed"))
       (-4 *5 (-363)) (-4 *6 (-363))
-      (-5 *2 (-2 (|:| -2177 *6) (|:| |coeff| *6)))
+      (-5 *2 (-2 (|:| -2116 *6) (|:| |coeff| *6)))
       (-5 *1 (-584 *5 *6))))
  ((*1 *2 *3 *4)
   (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed"))
@@ -345,3645 +372,3877 @@
        (-3
         (-2 (|:| |mainpart| *5)
          (|:| |limitedlogs|
-              (-641 (-2 (|:| |coeff| *5) (|:| |logand| *5)))))
+              (-642 (-2 (|:| |coeff| *5) (|:| |logand| *5)))))
         "failed"))
       (-4 *5 (-363)) (-4 *6 (-363))
       (-5 *2
        (-2 (|:| |mainpart| *6)
         (|:| |limitedlogs|
-             (-641 (-2 (|:| |coeff| *6) (|:| |logand| *6))))))
+             (-642 (-2 (|:| |coeff| *6) (|:| |logand| *6))))))
       (-5 *1 (-584 *5 *6))))
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+  (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-599 *5)) (-4 *5 (-1212))
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+   (-4 *6 (-1212)) (-4 *7 (-1212)) (-4 *8 (-1212)) (-5 *2 (-599 *8))
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+   (-4 *4 (-13 (-373 *5) (-10 -7 (-6 -4410))))))) 
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+ ((*1 *2 *3)
+  (-12 (-5 *3 (-642 (-263))) (-5 *2 (-1130 (-225))) (-5 *1 (-261))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1130 (-225))) (-5 *1 (-263))))) 
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+  (-12 (-5 *2 (-687 *5)) (-4 *5 (-1047)) (-5 *1 (-1052 *3 *4 *5))
+   (-14 *3 (-769)) (-14 *4 (-769))))) 
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+  (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-530 *3)) (-4 *3 (-13 (-724) (-25)))))) 
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+ ((*1 *1 *1 *2)
+  (-12 (-5 *2 (-769)) (-4 *1 (-738 *3 *4)) (-4 *3 (-1047))
+   (-4 *4 (-848))))
+ ((*1 *1 *1 *2) (-12 (-4 *1 (-867 *3)) (-5 *2 (-564))))
+ ((*1 *1 *1 *2)
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+ ((*1 *2 *3 *2)
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+ ((*1 *2 *3 *1)
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+ ((*1 *2 *3 *2)
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+ ((*1 *2 *3 *1)
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+ ((*1 *1 *1 *2)
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+   (-4 *5 (-848)) (-4 *2 (-1062 *3 *4 *5))))
+ ((*1 *1 *1 *2)
+  (-12 (-4 *1 (-1240 *3 *2)) (-4 *3 (-1047)) (-4 *2 (-790))))) 
 (((*1 *1 *1) (-4 *1 (-95)))
  ((*1 *2 *2)
   (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2))
-   (-4 *2 (-13 (-430 *3) (-998)))))
+   (-4 *2 (-13 (-430 *3) (-1000)))))
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-  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1250 *3))
-   (-5 *1 (-278 *3 *4 *2)) (-4 *2 (-1221 *3 *4))))
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-   (-5 *1 (-279 *3 *4 *2 *5)) (-4 *2 (-1242 *3 *4)) (-4 *5 (-979 *4))))
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  ((*1 *2 *2)
-  (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564))))
-   (-5 *1 (-1155 *3))))
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  ((*1 *2 *2)
-  (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564))))
-   (-5 *1 (-1156 *3))))) 
+  (-12 (-5 *2 (-1153 *3)) (-4 *3 (-38 (-407 (-564))))
+   (-5 *1 (-1159 *3))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3431 (-641 (-225)))))
-   (-5 *2 (-641 (-1170))) (-5 *1 (-267))))
+    (-2 (|:| |lfn| (-642 (-316 (-225)))) (|:| -3366 (-642 (-225)))))
+   (-5 *2 (-642 (-1173))) (-5 *1 (-267))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1166 *7)) (-4 *7 (-945 *6 *4 *5)) (-4 *4 (-789))
-   (-4 *5 (-846)) (-4 *6 (-1045)) (-5 *2 (-641 *5))
+  (-12 (-5 *3 (-1169 *7)) (-4 *7 (-947 *6 *4 *5)) (-4 *4 (-791))
+   (-4 *5 (-848)) (-4 *6 (-1047)) (-5 *2 (-642 *5))
    (-5 *1 (-321 *4 *5 *6 *7))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-641 (-1170))) (-5 *1 (-339 *3 *4 *5)) (-14 *3 *2)
+  (-12 (-5 *2 (-642 (-1173))) (-5 *1 (-339 *3 *4 *5)) (-14 *3 *2)
    (-14 *4 *2) (-4 *5 (-387))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-430 *3)) (-4 *3 (-1094)) (-5 *2 (-641 (-1170)))))
+  (-12 (-4 *1 (-430 *3)) (-4 *3 (-1097)) (-5 *2 (-642 (-1173)))))
  ((*1 *2 *1)
-  (-12 (-5 *2 (-641 (-888 *3))) (-5 *1 (-888 *3)) (-4 *3 (-1094))))
+  (-12 (-5 *2 (-642 (-890 *3))) (-5 *1 (-890 *3)) (-4 *3 (-1097))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-945 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-789))
-   (-4 *5 (-846)) (-5 *2 (-641 *5))))
+  (-12 (-4 *1 (-947 *3 *4 *5)) (-4 *3 (-1047)) (-4 *4 (-791))
+   (-4 *5 (-848)) (-5 *2 (-642 *5))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-789)) (-4 *5 (-846)) (-4 *6 (-1045))
-   (-4 *7 (-945 *6 *4 *5)) (-5 *2 (-641 *5))
-   (-5 *1 (-946 *4 *5 *6 *7 *3))
+  (-12 (-4 *4 (-791)) (-4 *5 (-848)) (-4 *6 (-1047))
+   (-4 *7 (-947 *6 *4 *5)) (-5 *2 (-642 *5))
+   (-5 *1 (-948 *4 *5 *6 *7 *3))
    (-4 *3
     (-13 (-363)
-     (-10 -8 (-15 -2423 ($ *7)) (-15 -2323 (*7 $)) (-15 -2336 (*7 $)))))))
+     (-10 -8 (-15 -2327 ($ *7)) (-15 -2245 (*7 $)) (-15 -2255 (*7 $)))))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-969 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-788))
-   (-4 *5 (-846)) (-5 *2 (-641 *5))))
+  (-12 (-4 *1 (-971 *3 *4 *5)) (-4 *3 (-1047)) (-4 *4 (-790))
+   (-4 *5 (-848)) (-5 *2 (-642 *5))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-972 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-789))
-   (-4 *5 (-846)) (-4 *6 (-1059 *3 *4 *5)) (-5 *2 (-641 *5))))
+  (-12 (-4 *1 (-974 *3 *4 *5 *6)) (-4 *3 (-1047)) (-4 *4 (-791))
+   (-4 *5 (-848)) (-4 *6 (-1062 *3 *4 *5)) (-5 *2 (-642 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-407 (-948 *4))) (-4 *4 (-556)) (-5 *2 (-641 (-1170)))
-   (-5 *1 (-1039 *4))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-561))))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-373 *3)) (-4 *3 (-1209)) (-4 *3 (-846)) (-5 *2 (-112))))
- ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *1 (-373 *4)) (-4 *4 (-1209))
-   (-5 *2 (-112))))) 
+  (-12 (-5 *3 (-407 (-950 *4))) (-4 *4 (-556)) (-5 *2 (-642 (-1173)))
+   (-5 *1 (-1041 *4))))) 
+(((*1 *2 *3 *3 *3)
+  (-12 (-5 *2 (-642 (-564))) (-5 *1 (-1107)) (-5 *3 (-564))))) 
+(((*1 *1 *1 *2)
+  (-12 (-5 *2 (-642 (-769))) (-5 *1 (-1161 *3 *4)) (-14 *3 (-919))
+   (-4 *4 (-1047))))) 
+(((*1 *2 *3 *3 *3)
+  (|partial| -12 (-4 *4 (-13 (-363) (-147) (-1036 (-564))))
+      (-4 *5 (-1238 *4)) (-5 *2 (-642 (-407 *5))) (-5 *1 (-1014 *4 *5))
+      (-5 *3 (-407 *5))))) 
+(((*1 *1 *1)
+  (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1047))))) 
 (((*1 *2 *3)
-  (-12
-   (-5 *3
-    (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3431 (-641 (-225)))))
-   (-5 *2 (-379)) (-5 *1 (-267))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1259 (-316 (-225)))) (-5 *2 (-379)) (-5 *1 (-305))))) 
+  (-12 (-4 *4 (-556)) (-5 *2 (-642 *3)) (-5 *1 (-43 *4 *3))
+   (-4 *3 (-417 *4))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1211)) (-5 *1 (-180))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1211)) (-5 *1 (-679))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1211)) (-5 *1 (-968))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1211)) (-5 *1 (-1070))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1178)) (-5 *1 (-1115))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *2 (-1 (-939 *3) (-939 *3))) (-5 *1 (-176 *3))
-   (-4 *3 (-13 (-363) (-1194) (-998)))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-180))))
- ((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-677))))
- ((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-966))))
- ((*1 *2 *1) (-12 (-5 *2 (-1208)) (-5 *1 (-1067))))
- ((*1 *2 *1) (-12 (-5 *2 (-1175)) (-5 *1 (-1112))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-818))))) 
-(((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-556) (-1034 (-564)))) (-4 *5 (-430 *4))
-   (-5 *2
-    (-3 (|:| |overq| (-1166 (-407 (-564))))
-     (|:| |overan| (-1166 (-48))) (|:| -3285 (-112))))
-   (-5 *1 (-435 *4 *5 *3)) (-4 *3 (-1235 *5))))) 
-(((*1 *2)
-  (-12 (-4 *4 (-1213)) (-4 *5 (-1235 *4)) (-4 *6 (-1235 (-407 *5)))
-   (-5 *2 (-767)) (-5 *1 (-341 *3 *4 *5 *6)) (-4 *3 (-342 *4 *5 *6))))
- ((*1 *2)
-  (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3))
-   (-4 *5 (-1235 (-407 *4))) (-5 *2 (-767))))) 
-(((*1 *1) (-4 *1 (-349)))) 
+  (-12 (-4 *4 (-556))
+   (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2022 *4)))
+   (-5 *1 (-967 *4 *3)) (-4 *3 (-1238 *4))))) 
+(((*1 *2 *3 *3 *3 *4)
+  (-12 (-5 *3 (-564)) (-5 *4 (-687 (-225))) (-5 *2 (-1033))
+   (-5 *1 (-755))))) 
+(((*1 *2 *1)
+  (-12 (-4 *3 (-1047)) (-5 *2 (-1262 *3)) (-5 *1 (-710 *3 *4))
+   (-4 *4 (-1238 *3))))) 
+(((*1 *2 *1)
+  (-12 (-5 *2 (-1153 (-407 *3))) (-5 *1 (-174 *3)) (-4 *3 (-307))))) 
 (((*1 *1 *1) (-4 *1 (-95)))
  ((*1 *2 *2)
   (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2))
-   (-4 *2 (-13 (-430 *3) (-998)))))
+   (-4 *2 (-13 (-430 *3) (-1000)))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1250 *3))
-   (-5 *1 (-278 *3 *4 *2)) (-4 *2 (-1221 *3 *4))))
+  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1253 *3))
+   (-5 *1 (-278 *3 *4 *2)) (-4 *2 (-1224 *3 *4))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1219 *3))
-   (-5 *1 (-279 *3 *4 *2 *5)) (-4 *2 (-1242 *3 *4)) (-4 *5 (-979 *4))))
+  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1222 *3))
+   (-5 *1 (-279 *3 *4 *2 *5)) (-4 *2 (-1245 *3 *4)) (-4 *5 (-981 *4))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564))))
-   (-5 *1 (-1155 *3))))
+  (-12 (-5 *2 (-1153 *3)) (-4 *3 (-38 (-407 (-564))))
+   (-5 *1 (-1158 *3))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564))))
-   (-5 *1 (-1156 *3))))) 
+  (-12 (-5 *2 (-1153 *3)) (-4 *3 (-38 (-407 (-564))))
+   (-5 *1 (-1159 *3))))) 
 (((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1166 (-407 (-1166 *2)))) (-5 *4 (-610 *2))
-   (-4 *2 (-13 (-430 *5) (-27) (-1194)))
-   (-4 *5 (-13 (-452) (-1034 (-564)) (-147) (-637 (-564))))
-   (-5 *1 (-560 *5 *2 *6)) (-4 *6 (-1094))))
+  (-12 (-5 *3 (-1169 (-407 (-1169 *2)))) (-5 *4 (-610 *2))
+   (-4 *2 (-13 (-430 *5) (-27) (-1197)))
+   (-4 *5 (-13 (-452) (-1036 (-564)) (-147) (-637 (-564))))
+   (-5 *1 (-560 *5 *2 *6)) (-4 *6 (-1097))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1166 *1)) (-4 *1 (-945 *4 *5 *3)) (-4 *4 (-1045))
-   (-4 *5 (-789)) (-4 *3 (-846))))
+  (-12 (-5 *2 (-1169 *1)) (-4 *1 (-947 *4 *5 *3)) (-4 *4 (-1047))
+   (-4 *5 (-791)) (-4 *3 (-848))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1166 *4)) (-4 *4 (-1045)) (-4 *1 (-945 *4 *5 *3))
-   (-4 *5 (-789)) (-4 *3 (-846))))
+  (-12 (-5 *2 (-1169 *4)) (-4 *4 (-1047)) (-4 *1 (-947 *4 *5 *3))
+   (-4 *5 (-791)) (-4 *3 (-848))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-407 (-1166 *2))) (-4 *5 (-789)) (-4 *4 (-846))
-   (-4 *6 (-1045))
+  (-12 (-5 *3 (-407 (-1169 *2))) (-4 *5 (-791)) (-4 *4 (-848))
+   (-4 *6 (-1047))
    (-4 *2
     (-13 (-363)
-     (-10 -8 (-15 -2423 ($ *7)) (-15 -2323 (*7 $)) (-15 -2336 (*7 $)))))
-   (-5 *1 (-946 *5 *4 *6 *7 *2)) (-4 *7 (-945 *6 *5 *4))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-407 (-1166 (-407 (-948 *5))))) (-5 *4 (-1170))
-   (-5 *2 (-407 (-948 *5))) (-5 *1 (-1039 *5)) (-4 *5 (-556))))) 
+     (-10 -8 (-15 -2327 ($ *7)) (-15 -2245 (*7 $)) (-15 -2255 (*7 $)))))
+   (-5 *1 (-948 *5 *4 *6 *7 *2)) (-4 *7 (-947 *6 *5 *4))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-407 (-1169 (-407 (-950 *5))))) (-5 *4 (-1173))
+   (-5 *2 (-407 (-950 *5))) (-5 *1 (-1041 *5)) (-4 *5 (-556))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-769)) (-5 *1 (-875 *2)) (-4 *2 (-1212))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-769)) (-5 *1 (-877 *2)) (-4 *2 (-1212))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-769)) (-5 *1 (-880 *2)) (-4 *2 (-1212))))) 
+(((*1 *1 *1) (-5 *1 (-1060)))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-917)) (-5 *4 (-1152)) (-5 *2 (-1264)) (-5 *1 (-1260))))) 
-(((*1 *2 *1)
-  (-12 (-5 *2 (-2 (|:| |var| (-641 (-1170))) (|:| |pred| (-52))))
-   (-5 *1 (-888 *3)) (-4 *3 (-1094))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-564))) (-5 *1 (-1043))))) 
-(((*1 *1 *1)
-  (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1045))))) 
+  (-12 (-5 *3 (-919)) (-5 *4 (-1155)) (-5 *2 (-1267)) (-5 *1 (-1263))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *4 (-919)) (-5 *2 (-1169 *3)) (-5 *1 (-1186 *3))
+   (-4 *3 (-363))))) 
+(((*1 *2 *2) (|partial| -12 (-4 *1 (-981 *2)) (-4 *2 (-1197))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2))
-   (-4 *2 (-13 (-430 *3) (-998)))))) 
-(((*1 *1 *2 *3)
-  (-12 (-5 *3 (-1150 *2)) (-4 *2 (-307)) (-5 *1 (-174 *2))))) 
-(((*1 *2 *1 *3) (-12 (-4 *1 (-302)) (-5 *3 (-1170)) (-5 *2 (-112))))
- ((*1 *2 *1 *1) (-12 (-4 *1 (-302)) (-5 *2 (-112))))) 
-(((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-564)) (-5 *1 (-136 *3 *4 *5)) (-14 *3 *2)
-   (-14 *4 (-767)) (-4 *5 (-172))))
- ((*1 *1 *1)
-  (-12 (-5 *1 (-136 *2 *3 *4)) (-14 *2 (-564)) (-14 *3 (-767))
-   (-4 *4 (-172))))
- ((*1 *1 *1)
-  (-12 (-4 *1 (-683 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-373 *2))
-   (-4 *4 (-373 *2))))
- ((*1 *1 *2)
-  (-12 (-4 *3 (-1045)) (-4 *1 (-683 *3 *2 *4)) (-4 *2 (-373 *3))
-   (-4 *4 (-373 *3))))
- ((*1 *1 *1)
-  (-12 (-5 *1 (-1136 *2 *3)) (-14 *2 (-767)) (-4 *3 (-1045))))) 
-(((*1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-755))))) 
-(((*1 *2 *1)
-  (-12 (-5 *2 (-858)) (-5 *1 (-1150 *3)) (-4 *3 (-1094))
-   (-4 *3 (-1209))))) 
+  (-12 (-4 *3 (-1238 (-407 (-564)))) (-5 *1 (-911 *3 *2))
+   (-4 *2 (-1238 (-407 *3)))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *3 (-1173)) (-4 *5 (-363)) (-5 *2 (-642 (-1206 *5)))
+   (-5 *1 (-1270 *5)) (-5 *4 (-1206 *5))))) 
+(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3)
+  (-12 (-5 *3 (-564)) (-5 *5 (-687 (-225))) (-5 *4 (-225))
+   (-5 *2 (-1033)) (-5 *1 (-750))))) 
+(((*1 *2 *3)
+  (-12 (-4 *4 (-1047)) (-5 *2 (-564)) (-5 *1 (-443 *4 *3 *5))
+   (-4 *3 (-1238 *4))
+   (-4 *5 (-13 (-404) (-1036 *4) (-363) (-1197) (-284)))))) 
+(((*1 *1) (-5 *1 (-186)))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-1169 *1)) (-4 *1 (-1010))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225)))
-     (|:| -2141 (-1088 (-839 (-225)))) (|:| |abserr| (-225))
+    (-2 (|:| |var| (-1173)) (|:| |fn| (-316 (-225)))
+     (|:| -3894 (-1091 (-841 (-225)))) (|:| |abserr| (-225))
      (|:| |relerr| (-225))))
    (-5 *2
     (-2
@@ -3998,10 +4257,10 @@
            (|:| |notEvaluated|
                 "End point continuity not yet evaluated")))
      (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1150 (-225)))
+          (-3 (|:| |str| (-1153 (-225)))
            (|:| |notEvaluated|
                 "Internal singularities not yet evaluated")))
-     (|:| -2141
+     (|:| -3894
           (-3 (|:| |finite| "The range is finite")
            (|:| |lowerInfinite| "The bottom of range is infinite")
            (|:| |upperInfinite| "The top of range is infinite")
@@ -4009,1962 +4268,2027 @@
                 "Both top and bottom points are infinite")
            (|:| |notEvaluated| "Range not yet evaluated")))))
    (-5 *1 (-559))))) 
-(((*1 *1) (-5 *1 (-186)))) 
+(((*1 *2 *3)
+  (-12 (-4 *4 (-1216)) (-4 *5 (-1238 *4))
+   (-5 *2 (-2 (|:| -4378 (-407 *5)) (|:| |poly| *3)))
+   (-5 *1 (-148 *4 *5 *3)) (-4 *3 (-1238 (-407 *5)))))) 
 (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-225)))
  ((*1 *2 *2)
   (-12 (-4 *3 (-556)) (-5 *1 (-276 *3 *2))
-   (-4 *2 (-13 (-430 *3) (-998)))))
+   (-4 *2 (-13 (-430 *3) (-1000)))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1250 *3))
-   (-5 *1 (-278 *3 *4 *2)) (-4 *2 (-1221 *3 *4))))
+  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1253 *3))
+   (-5 *1 (-278 *3 *4 *2)) (-4 *2 (-1224 *3 *4))))
  ((*1 *2 *2)
-  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1219 *3))
-   (-5 *1 (-279 *3 *4 *2 *5)) (-4 *2 (-1242 *3 *4)) (-4 *5 (-979 *4))))
+  (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1222 *3))
+   (-5 *1 (-279 *3 *4 *2 *5)) (-4 *2 (-1245 *3 *4)) (-4 *5 (-981 *4))))
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 (((*1 *2 *3)
-  (-12
-   (-5 *3
-    (-2
-     (|:| |endPointContinuity|
-          (-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")))
-     (|:| |singularitiesStream|
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-           (|:| |notEvaluated|
-                "Internal singularities not yet evaluated")))
-     (|:| -2141
-          (-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")))))
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-   (-4 *3 (-848 *5))))) 
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  ((*1 *2 *3)
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-   (-4 *3 (-1235 (-169 *4)))))
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 (((*1 *2 *1)
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@@ -5977,5281 +6301,5273 @@
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   (-12
    (-5 *2
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+      (|:| -3778
+           (-2
+            (|:| |endPointContinuity|
+                 (-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")))
+            (|:| |singularitiesStream|
+                 (-3 (|:| |str| (-1153 (-225)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -3894
+                 (-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"))))))))
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+           (|:| |relerr| (-225))))
+     (|:| -3778
+          (-2
+           (|:| |endPointContinuity|
+                (-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")))
+           (|:| |singularitiesStream|
+                (-3 (|:| |str| (-1153 (-225)))
+                 (|:| |notEvaluated|
+                      "Internal singularities not yet evaluated")))
+           (|:| -3894
+                (-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")))))))
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+           (|:| |intvals| (-642 (-225))) (|:| |g| (-316 (-225)))
+           (|:| |abserr| (-225)) (|:| |relerr| (-225))))
+     (|:| -3778
+          (-2 (|:| |stiffness| (-379)) (|:| |stability| (-379))
+           (|:| |expense| (-379)) (|:| |accuracy| (-379))
+           (|:| |intermediateResults| (-379))))))
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+  (-12
+   (-5 *3
+    (-2
+     (|:| |endPointContinuity|
+          (-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")))
+     (|:| |singularitiesStream|
+          (-3 (|:| |str| (-1153 (-225)))
+           (|:| |notEvaluated|
+                "Internal singularities not yet evaluated")))
+     (|:| -3894
+          (-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")))))
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+           (-2
+            (|:| |endPointContinuity|
+                 (-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")))
+            (|:| |singularitiesStream|
+                 (-3 (|:| |str| (-1153 (-225)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -3894
+                 (-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"))))))))
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+(((*1 *2 *1)
+  (|partial| -12 (-4 *3 (-13 (-1036 (-564)) (-637 (-564)) (-452)))
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+      (-14 *6 *4)))
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+      (-14 *6 *4)))) 
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+ ((*1 *2 *2)
+  (-12 (-4 *3 (-556)) (-5 *1 (-628 *3 *2))
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+      (-4 *5 (-884 (-564)))
+      (-4 *5 (-13 (-1036 (-564)) (-452) (-637 (-564))))
+      (-5 *2 (-2 (|:| |special| *3) (|:| |integrand| *3)))
+      (-5 *1 (-567 *5 *3)) (-4 *3 (-627))
+      (-4 *3 (-13 (-27) (-1197) (-430 *5)))))
+ ((*1 *2 *2 *3 *4 *4)
+  (|partial| -12 (-5 *3 (-1173)) (-5 *4 (-841 *2)) (-4 *2 (-1136))
+      (-4 *2 (-13 (-27) (-1197) (-430 *5)))
+      (-4 *5 (-612 (-890 (-564)))) (-4 *5 (-884 (-564)))
+      (-4 *5 (-13 (-1036 (-564)) (-452) (-637 (-564))))
+      (-5 *1 (-567 *5 *2))))) 
 (((*1 *2 *3)
   (|partial| -12
       (-5 *3
-       (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225)))
-        (|:| -2141 (-1088 (-839 (-225)))) (|:| |abserr| (-225))
+       (-2 (|:| |var| (-1173)) (|:| |fn| (-316 (-225)))
+        (|:| -3894 (-1091 (-841 (-225)))) (|:| |abserr| (-225))
         (|:| |relerr| (-225))))
       (-5 *2
        (-2
@@ -11266,10 +11582,10 @@
               (|:| |notEvaluated|
                    "End point continuity not yet evaluated")))
         (|:| |singularitiesStream|
-             (-3 (|:| |str| (-1150 (-225)))
+             (-3 (|:| |str| (-1153 (-225)))
               (|:| |notEvaluated|
                    "Internal singularities not yet evaluated")))
-        (|:| -2141
+        (|:| -3894
              (-3 (|:| |finite| "The range is finite")
               (|:| |lowerInfinite| "The bottom of range is infinite")
               (|:| |upperInfinite| "The top of range is infinite")
@@ -11277,546 +11593,520 @@
                    "Both top and bottom points are infinite")
               (|:| |notEvaluated| "Range not yet evaluated")))))
       (-5 *1 (-559))))) 
-(((*1 *2) (-12 (-5 *2 (-641 *3)) (-5 *1 (-1078 *3)) (-4 *3 (-132))))) 
-(((*1 *1 *1 *2 *2)
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-   (-14 *4 (-767)) (-4 *5 (-172))))
- ((*1 *1 *1 *2 *1 *2)
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- ((*1 *2 *2 *3)
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-   (-5 *1 (-505 *4 *5))))) 
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-(((*1 *2 *3)
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+(((*1 *2) (-12 (-5 *2 (-642 *3)) (-5 *1 (-1081 *3)) (-4 *3 (-132))))) 
 (((*1 *2 *3 *4)
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- ((*1 *2 *3 *4)
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 (((*1 *2 *3)
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 (((*1 *1 *2)
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@@ -11824,4944 +12114,4487 @@
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   (-12
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+   (-5 *2 (-2 (|:| |localSymbols| (-1177)) (|:| -3146 (-642 (-330)))))
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+     (|:| -3894 (-1091 (-841 (-225)))) (|:| |abserr| (-225))
+     (|:| |relerr| (-225))))
+   (-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 (-192))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-564)) (-5 *2 (-1267)) (-5 *1 (-1004))))) 
+(((*1 *2 *3)
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+   (-4 *5 (-13 (-29 *4) (-1197) (-957)))))) 
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- ((*1 *1 *1 *1) (-5 *1 (-1114)))) 
+ ((*1 *1 *1 *1) (-5 *1 (-1117)))) 
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+(((*1 *2 *1)
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 (((*1 *2 *3)
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-   (-4 *3 (-417 *4))))) 
-(((*1 *1 *1)
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-(((*1 *2 *1) (-12 (-5 *2 (-641 (-1208))) (-5 *1 (-604))))) 
+  (-12
+   (-5 *3
+    (-2 (|:| |var| (-1173)) (|:| |fn| (-316 (-225)))
+     (|:| -3894 (-1091 (-841 (-225)))) (|:| |abserr| (-225))
+     (|:| |relerr| (-225))))
+   (-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 (-192))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-379)) (-5 *2 (-1267)) (-5 *1 (-1264))))) 
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+(((*1 *2 *3 *3 *4 *4 *3 *3 *5 *3)
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-     (-10 -8 (-15 -3254 ($ $)) (-15 -2070 ($ $)))))
-   (-5 *2
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-     (|:| |%problem| (-2 (|:| |func| (-1152)) (|:| |prob| (-1152))))))
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-(((*1 *2 *1) (-12 (-4 *1 (-185)) (-5 *2 (-641 (-861)))))) 
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-  (|partial| -12 (-5 *4 (-1170))
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-      (-5 *2
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-(((*1 *2)
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- ((*1 *2)
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-   (-5 *2 (-641 (-1259 *3)))))) 
+ ((*1 *1 *1) (-4 *1 (-1136)))) 
+(((*1 *2 *3 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3 *2)
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-(((*1 *2 *3)
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 (((*1 *2 *1)
-  (-12
-   (-5 *2
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-            (|:| -2141 (-1088 (-839 (-225)))) (|:| |abserr| (-225))
-            (|:| |relerr| (-225))))
-      (|:| -3813
-           (-2
-            (|:| |endPointContinuity|
-                 (-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")))
-            (|:| |singularitiesStream|
-                 (-3 (|:| |str| (-1150 (-225)))
-                  (|:| |notEvaluated|
-                       "Internal singularities not yet evaluated")))
-            (|:| -2141
-                 (-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 (-559))))
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+  (-12 (-5 *2 (-506)) (-5 *3 (-642 (-1178))) (-5 *1 (-1178))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1132)) (-5 *1 (-517))))) 
+(((*1 *2 *3 *4)
+  (-12 (-4 *5 (-791)) (-4 *6 (-848)) (-4 *3 (-556))
+   (-4 *7 (-947 *3 *5 *6))
+   (-5 *2 (-2 (|:| -2700 (-769)) (|:| -4378 *8) (|:| |radicand| *8)))
+   (-5 *1 (-951 *5 *6 *3 *7 *8)) (-5 *4 (-769))
+   (-4 *8
+    (-13 (-363)
+     (-10 -8 (-15 -2327 ($ *7)) (-15 -2245 (*7 $)) (-15 -2255 (*7 $)))))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-407 (-564))) (-4 *4 (-1034 (-564))) (-4 *4 (-556))
+  (-12 (-5 *3 (-407 (-564))) (-4 *4 (-1036 (-564))) (-4 *4 (-556))
    (-5 *1 (-32 *4 *2)) (-4 *2 (-430 *4))))
  ((*1 *1 *1 *1) (-5 *1 (-134)))
  ((*1 *2 *2 *2)
@@ -16770,1531 +16603,1701 @@
  ((*1 *1 *1 *2) (-12 (-4 *1 (-243)) (-5 *2 (-564))))
  ((*1 *2 *2 *3)
   (-12 (-5 *3 (-407 (-564))) (-4 *4 (-363)) (-4 *4 (-38 *3))
-   (-4 *5 (-1250 *4)) (-5 *1 (-278 *4 *5 *2)) (-4 *2 (-1221 *4 *5))))
+   (-4 *5 (-1253 *4)) (-5 *1 (-278 *4 *5 *2)) (-4 *2 (-1224 *4 *5))))
  ((*1 *2 *2 *3)
   (-12 (-5 *3 (-407 (-564))) (-4 *4 (-363)) (-4 *4 (-38 *3))
-   (-4 *5 (-1219 *4)) (-5 *1 (-279 *4 *5 *2 *6)) (-4 *2 (-1242 *4 *5))
-   (-4 *6 (-979 *5))))
+   (-4 *5 (-1222 *4)) (-5 *1 (-279 *4 *5 *2 *6)) (-4 *2 (-1245 *4 *5))
+   (-4 *6 (-981 *5))))
  ((*1 *1 *1 *1) (-4 *1 (-284)))
- ((*1 *1 *2 *3) (-12 (-5 *3 (-564)) (-5 *1 (-361 *2)) (-4 *2 (-1094))))
+ ((*1 *1 *2 *3) (-12 (-5 *3 (-564)) (-5 *1 (-361 *2)) (-4 *2 (-1097))))
  ((*1 *1 *1 *1) (-5 *1 (-379)))
- ((*1 *1 *2 *3) (-12 (-5 *3 (-767)) (-5 *1 (-386 *2)) (-4 *2 (-1094))))
+ ((*1 *1 *2 *3) (-12 (-5 *3 (-769)) (-5 *1 (-386 *2)) (-4 *2 (-1097))))
  ((*1 *1 *1 *2)
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-   (-4 *3 (-1106))))
+  (-12 (-5 *2 (-769)) (-4 *1 (-430 *3)) (-4 *3 (-1097))
+   (-4 *3 (-1109))))
  ((*1 *1 *1 *2) (-12 (-4 *1 (-473)) (-5 *2 (-564))))
  ((*1 *1 *1 *2)
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-   (-5 *1 (-504 *3 *4 *5 *6)) (-4 *6 (-945 *3 *4 *5))))
+  (-12 (-5 *2 (-769)) (-4 *3 (-363)) (-4 *4 (-791)) (-4 *5 (-848))
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  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1259 *4)) (-5 *3 (-564)) (-4 *4 (-349))
+  (-12 (-5 *2 (-1262 *4)) (-5 *3 (-564)) (-4 *4 (-349))
    (-5 *1 (-528 *4))))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-536))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-767)) (-5 *1 (-536))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-769)) (-5 *1 (-536))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1 *4 *4)) (-5 *3 (-767)) (-4 *4 (-1094))
-   (-5 *1 (-678 *4))))
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  ((*1 *1 *1 *2)
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    (-4 *4 (-373 *3)) (-4 *5 (-373 *3)) (-4 *3 (-363))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-767)) (-4 *1 (-683 *3 *4 *5)) (-4 *3 (-1045))
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-  (-12 (-5 *2 (-685 *4)) (-5 *3 (-767)) (-4 *4 (-1045))
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  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-564)) (-4 *3 (-1045)) (-5 *1 (-710 *3 *4))
-   (-4 *4 (-644 *3))))
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  ((*1 *1 *2 *3)
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  ((*1 *1 *2 *3)
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  ((*1 *1 *1 *2)
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  ((*1 *2 *2 *2)
-  (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564))))
-   (-5 *1 (-1155 *3))))
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  ((*1 *2 *2 *2)
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  ((*1 *1 *1 *2)
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-   (-4 *2 (-1235 *4))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-678 *3)) (-4 *3 (-1094))))) 
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 (((*1 *2 *3 *4)
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-   (-5 *2 (-641 (-641 (-294 (-948 (-169 *4)))))) (-5 *1 (-378 *4))
-   (-4 *4 (-13 (-363) (-844)))))
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-      (-4 *4 (-1235 (-407 *2))) (-4 *2 (-1235 *3))))) 
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 (((*1 *2 *1)
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 (((*1 *2)
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 (((*1 *2 *1 *3)
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+ (-4331 . 31103) (-4332 . 30972) (-4333 . 30855) (-4334 . 30749)
+ (-4335 . 30618) (-4336 . 30280) (-4337 . 29954) (-4338 . 29785)
+ (-4339 . 29581) (-4340 . 29456) (-4341 . 29370) (-4342 . 29318)
+ (-4343 . 29117) (-4344 . 28940) (-4345 . 28758) (-4346 . 28466)
+ (-4347 . 28382) (-4348 . 27965) (-4349 . 27872) (-4350 . 27742)
+ (-4351 . 27618) (-4352 . 27339) (-4353 . 24994) (-4354 . 24909)
+ (-4355 . 24853) (-4356 . 24606) (-4357 . 24465) (-4358 . 10378)
+ (-4359 . 10346) (-4360 . 10258) (-4361 . 9557) (-4362 . 9523)
+ (-4363 . 9400) (-4364 . 8761) (-4365 . 8711) (-4366 . 8679)
+ (-4367 . 8583) (-4368 . 3484) (-4369 . 3411) (-4370 . 3309)
+ (-4371 . 3081) (-4372 . 2987) (-4373 . 2959) (-4374 . 2617)
+ (-4375 . 2456) (-4376 . 2021) (-4377 . 1950) (-4378 . 1592)
+ (-4379 . 1522) (-4380 . 1463) (-4381 . 1348) (-4382 . 1195)
+ (-4383 . 954) (-4384 . 871) (-4385 . 518) (-4386 . 444) (-4387 . 244)
+ (-4388 . 152) (-4389 . 83) (-4390 . 30)) 
+\ No newline at end of file
author	dos-reis <gdr@axiomatics.org>	2009-05-31 20:49:02 +0000
committer	dos-reis <gdr@axiomatics.org>	2009-05-31 20:49:02 +0000
commit	803d7a62fb91bb4083a0aaaaa20749574292e967 (patch)
tree	96fa55d12fe4f5e203c239e140f533b7a2824852
parent	748e67afa492ccf46498cfa33541327aa11ad584 (diff)
download	open-axiom-803d7a62fb91bb4083a0aaaaa20749574292e967.tar.gz