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authordos-reis <gdr@axiomatics.org>2008-10-09 18:40:38 +0000
committerdos-reis <gdr@axiomatics.org>2008-10-09 18:40:38 +0000
commit9d577a9fe12067a41ed4e60adb7edfba30996788 (patch)
treef8d95a5e091e45502a2bfeb22847d244cbc84fed /src
parent1e509eda4fa81af3f5954f50345dd3bc88c9252c (diff)
downloadopen-axiom-9d577a9fe12067a41ed4e60adb7edfba30996788.tar.gz
* algebra/domain.spad.pamphlet (ConstructorKinid): New domain.
(Constructor): Likewise. * algebra/Makefile.pamphlet (axiom_algebra_layer_0): Include CTORKIND. (axiom_algebra_layer_user): Include CTOR.
Diffstat (limited to 'src')
-rw-r--r--src/ChangeLog8
-rw-r--r--src/algebra/Makefile.in7
-rw-r--r--src/algebra/Makefile.pamphlet7
-rw-r--r--src/algebra/domain.spad.pamphlet59
-rw-r--r--src/share/algebra/browse.daase3440
-rw-r--r--src/share/algebra/category.daase5106
-rw-r--r--src/share/algebra/compress.daase26
-rw-r--r--src/share/algebra/interp.daase10220
-rw-r--r--src/share/algebra/operation.daase23935
9 files changed, 21453 insertions, 21355 deletions
diff --git a/src/ChangeLog b/src/ChangeLog
index 82504bb8..4d6e26a8 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,11 @@
+2008-10-09 Gabriel Dos Reis <gdr@cs.tamu.edu>
+
+ * algebra/domain.spad.pamphlet (ConstructorKinid): New domain.
+ (Constructor): Likewise.
+ * algebra/Makefile.pamphlet (axiom_algebra_layer_0): Include
+ CTORKIND.
+ (axiom_algebra_layer_user): Include CTOR.
+
2008-10-08 Gabriel Dos Reis <gdr@cs.tamu.edu>
SF/1872404 fixed.
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index 28d59a89..46e59144 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -363,7 +363,7 @@ axiom_algebra_layer_0 = \
ABELSG- ORDSET ORDSET- FNCAT FILECAT SEXCAT \
MKBCFUNC MKRECORD MKUCFUNC DROPT1 PLOT1 ITFUN2 \
ITFUN3 STREAM1 STREAM2 STREAM3 ANY1 SEGBIND2 \
- COMBOPC EQ2 NONE1 CONDUIT IOMODE
+ COMBOPC EQ2 NONE1 CONDUIT IOMODE CTORKIND
axiom_algebra_layer_0_nrlibs = \
$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_0))
@@ -826,7 +826,7 @@ axiom_algebra_layer_user = \
LETAST SUCHAST RDUCEAST COLONAST ADDAST CAPSLAST \
CASEAST HASAST ISAST CATAST WHEREAST COMMAAST \
QQUTAST DEFAST MACROAST SPADXPT SPADAST \
- INBFILE OUTBFILE RGBCMDL RGBCSPC
+ INBFILE OUTBFILE RGBCMDL RGBCSPC CTORKIND CTOR
axiom_algebra_layer_user_nrlibs = \
$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user))
@@ -886,6 +886,9 @@ INBFILE.NRLIB/code.$(FASLEXT): $(OUT)/FNAME.$(FASLEXT) \
OUTBFILE.NRLIB/code.$(FASLEXT): $(OUT)/FNAME.$(FASLEXT) \
$(OUT)/OUTBCON.$(FASLEXT) $(OUT)/STRING.$(FASLEXT)
+CTOR.NRLIB/code.$(FASLEXT): $(OUT)/CTORKIND.$(FASLEXT) \
+ $(OUT)/IDENT.$(FASLEXT)
+
.PHONY: all all-algebra mkdir-output-directory
all: all-ax
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index 53ce4b35..63c8c402 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -192,7 +192,7 @@ axiom_algebra_layer_0 = \
ABELSG- ORDSET ORDSET- FNCAT FILECAT SEXCAT \
MKBCFUNC MKRECORD MKUCFUNC DROPT1 PLOT1 ITFUN2 \
ITFUN3 STREAM1 STREAM2 STREAM3 ANY1 SEGBIND2 \
- COMBOPC EQ2 NONE1 CONDUIT IOMODE
+ COMBOPC EQ2 NONE1 CONDUIT IOMODE CTORKIND
axiom_algebra_layer_0_nrlibs = \
$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_0))
@@ -1253,7 +1253,7 @@ axiom_algebra_layer_user = \
LETAST SUCHAST RDUCEAST COLONAST ADDAST CAPSLAST \
CASEAST HASAST ISAST CATAST WHEREAST COMMAAST \
QQUTAST DEFAST MACROAST SPADXPT SPADAST \
- INBFILE OUTBFILE RGBCMDL RGBCSPC
+ INBFILE OUTBFILE RGBCMDL RGBCSPC CTORKIND CTOR
axiom_algebra_layer_user_nrlibs = \
$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user))
@@ -1312,6 +1312,9 @@ INBFILE.NRLIB/code.$(FASLEXT): $(OUT)/FNAME.$(FASLEXT) \
$(OUT)/INBCON.$(FASLEXT) $(OUT)/STRING.$(FASLEXT)
OUTBFILE.NRLIB/code.$(FASLEXT): $(OUT)/FNAME.$(FASLEXT) \
$(OUT)/OUTBCON.$(FASLEXT) $(OUT)/STRING.$(FASLEXT)
+
+CTOR.NRLIB/code.$(FASLEXT): $(OUT)/CTORKIND.$(FASLEXT) \
+ $(OUT)/IDENT.$(FASLEXT)
@
\section{Broken Files}
diff --git a/src/algebra/domain.spad.pamphlet b/src/algebra/domain.spad.pamphlet
index e4f11843..6619feb0 100644
--- a/src/algebra/domain.spad.pamphlet
+++ b/src/algebra/domain.spad.pamphlet
@@ -11,6 +11,61 @@
\tableofcontents
\eject
+\section{The Constructor domain}
+
+<<domain CTORKIND ConstructorKinid>>=
+)abbrev domain CTORKIND ConstructorKind
+++ Author: Gabriel Dos Reis
+++ Date Create: October 07, 2008.
+++ Date Last Updated: October 07, 2008.
+++ Related Constructors:
+++ Description:
+++ This domain enumerates the three kinds of constructors
+++ available in OpenAxiom: category constructors, domain
+++ constructors, and package constructors.
+ConstructorKind(): Public == Private where
+ Public == SetCategory with
+ category: % ++ `category' designates category constructors
+ domain: % ++ `domain' designates domain constructors
+ package: % ++ `package' designates package constructors.
+ Private == add
+ category == INTERN("category","KEYWORD")$Lisp
+ domain == INTERN("domain","KEYWORD")$Lisp
+ package == INTERN("package","KEYWORD")$Lisp
+ k1 = k2 == EQ(k1,k2)$Lisp
+ coerce(k: %): OutputForm ==
+ k = category => outputForm 'category
+ k = domain => outputForm 'domain
+ outputForm 'package
+@
+
+<<domain CTOR Constructor>>=
+)abbrev domain CTOR Constructor
+++ Author: Gabriel Dos Reis
+++ Date Create: October 07, 2008.
+++ Date Last Updated: October 07, 2008.
+++ Related Constructors: Domain, Category
+++ Basic Operations: name, kind, arity.
+++ Description:
+++ This domain provides implementations for constructors.
+Constructor(): Public == Private where
+ Public == SetCategory with
+ name: % -> Identifier
+ ++ name(ctor) returns the name of the constructor `ctor'.
+ kind: % -> ConstructorKind
+ ++ kind(ctor) returns the kind of the constructor `ctor'.
+ arity: % -> SingleInteger
+ ++ arity(ctor) returns the arity of the constructor `ctor'.
+ ++ A negative value means that the ctor takes a variable
+ ++ length argument list, e.g. Mapping, Record, etc.
+ Private == add
+ Rep == Identifier
+ name x == rep x
+ x = y == rep x = rep y
+ coerce(x: %): OutputForm == rep(x)::OutputForm
+@
+
+
\section{domain Category}
<<domain CATEGORY Category>>=
import CoercibleTo OutputForm
@@ -28,7 +83,6 @@ Category(): Public == Private where
outputDomainConstructor(x)$Lisp
@
-
\section{domain Domain}
<<domain DOMAIN Domain>>=
import SetCategory
@@ -111,6 +165,9 @@ Domain(): Public == Private where
<<*>>=
<<license>>
+
+<<domain CTORKIND ConstructorKinid>>
+
<<domain CATEGORY Category>>
<<domain DOMAIN Domain>>
@
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index c89ca2c0..dc9d5f7a 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
-(2266992 . 3432414584)
+(2267936 . 3432506631)
(-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.")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . 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}.")))
@@ -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}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
-((-4345 . T) (-4343 . T) (-4342 . T) ((-4350 "*") . T) (-4341 . T) (-4346 . T) (-4340 . T) (-2363 . T))
+((-4350 . T) (-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4346 . T) (-4351 . T) (-4345 . T) (-2368 . T))
NIL
(-30)
((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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.")))
@@ -56,17 +56,17 @@ 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 -3423)
+(-32 R -3428)
((|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 -1012) (QUOTE (-536)))))
+((|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))))
(-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 -4348)))
+((|HasAttribute| |#1| (QUOTE -4353)))
(-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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects.")))
-((-2363 . T))
+((-2368 . T))
NIL
(-35)
((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}.")))
@@ -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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}.")))
-((-4348 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4354 . T) (-2368 . T))
NIL
(-37 S R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra.")))
@@ -82,20 +82,20 @@ NIL
NIL
(-38 R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
+((-4347 . T) (-4348 . T) (-4350 . 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 -3423 UP UPUP -2938)
+(-40 -3428 UP UPUP -2943)
((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}")))
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-(-41 R -3423)
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+(-41 R -3428)
((|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 (-444))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -414) (|devaluate| |#1|)))))
+((-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|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
@@ -103,34 +103,34 @@ NIL
(-43 R A)
((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,{}A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note: right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note: left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,{}a) = 0} and \\spad{associator(x,{}a,{}b) = associator(a,{}x,{}b) = associator(a,{}b,{}x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,{}a,{}b) = associator(a,{}x,{}b) = associator(a,{}b,{}x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,{}x,{}b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,{}b,{}x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,{}a,{}b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,{}a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,{}j=1,{}...,{}n},{} where \\spad{b=[b1,{}...,{}bn]} is a basis. Note: if \\spad{A} has a unit,{} then \\spadfunFrom{doubleRank}{AlgebraPackage},{} \\spadfunFrom{weakBiRank}{AlgebraPackage} and \\spadfunFrom{biRank}{AlgebraPackage} coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,{}j=1,{}...,{}n},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")))
NIL
-((|HasCategory| |#1| (QUOTE (-300))))
+((|HasCategory| |#1| (QUOTE (-302))))
(-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.")))
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(-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.")))
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-((-3886 (-12 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-825)))) (-12 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072))))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-825))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-3886 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-825))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072))) (-3886 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (-12 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4353 . T) (-4354 . T))
+((-3891 (-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-827)))) (-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-827))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-827))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))))
(-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356))))
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-358))))
(-47 R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
(-48)
((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| $ (QUOTE (-1023))) (|HasCategory| $ (LIST (QUOTE -1012) (QUOTE (-536)))))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-538)))))
(-49)
((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}.")))
NIL
NIL
(-50 R |lVar|)
((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}.")))
-((-4345 . T))
+((-4350 . T))
NIL
(-51)
((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}.")))
@@ -144,7 +144,7 @@ NIL
((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}.")))
NIL
NIL
-(-54 |Base| R -3423)
+(-54 |Base| R -3428)
((|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
@@ -154,77 +154,77 @@ NIL
NIL
(-56 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")))
-((-4348 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4354 . T) (-2368 . T))
NIL
(-57 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}")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
(-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),{}...]}.")))
NIL
NIL
(-59 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}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-60 -3900)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-60 -3905)
((|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
-(-61 -3900)
+(-61 -3905)
((|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 -3900)
+(-62 -3905)
((|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 -3900)
+(-63 -3905)
((|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 -3900)
+(-64 -3905)
((|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}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-65 -3900)
+(-65 -3905)
((|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
-(-66 -3900)
+(-66 -3905)
((|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
-(-67 -3900)
+(-67 -3905)
((|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
-(-68 -3900)
+(-68 -3905)
((|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
-(-69 -3900)
+(-69 -3905)
((|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
-(-70 -3900)
+(-70 -3905)
((|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
-(-71 -3900)
+(-71 -3905)
((|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
-(-72 -3900)
+(-72 -3905)
((|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
-(-73 -3900)
+(-73 -3905)
((|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
-(-74 -3900)
+(-74 -3905)
((|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
@@ -236,62 +236,62 @@ 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 -3900)
+(-77 -3905)
((|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 -3900)
+(-78 -3905)
((|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
-(-79 -3900)
+(-79 -3905)
((|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
-(-80 -3900)
+(-80 -3905)
((|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}")) (|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 -3900)
+(-81 -3905)
((|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
-(-82 -3900)
+(-82 -3905)
((|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 -3900)
+(-83 -3905)
((|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 -3900)
+(-84 -3905)
((|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 -3900)
+(-85 -3905)
((|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 -3900)
+(-86 -3905)
((|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
-(-87 -3900)
+(-87 -3905)
((|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 -3900)
+(-88 -3905)
((|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
(-89 R L)
((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op,{} m)} returns \\spad{[w,{} eq,{} lw,{} lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,{}...,{}A_n]} such that if \\spad{y = [y_1,{}...,{}y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',{}y_j'',{}...,{}y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}\\spad{'s}.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op,{} m)} returns \\spad{[M,{}w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-356))))
+((|HasCategory| |#1| (QUOTE (-358))))
(-90 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}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
(-91 S)
((|constructor| (NIL "This is the category of Spad abstract syntax trees.")))
NIL
@@ -314,15 +314,15 @@ NIL
NIL
(-96)
((|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\".")))
-((-4348 . T))
+((-4353 . T))
NIL
(-97)
((|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.")))
-((-4348 . T) ((-4350 "*") . T) (-4349 . T) (-4345 . T) (-4343 . T) (-4342 . T) (-4341 . T) (-4346 . T) (-4340 . T) (-4339 . T) (-4338 . T) (-4337 . T) (-4336 . T) (-4344 . T) (-4347 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4335 . T))
+((-4353 . T) ((-4355 "*") . T) (-4354 . T) (-4350 . T) (-4348 . T) (-4347 . T) (-4346 . T) (-4351 . T) (-4345 . T) (-4344 . T) (-4343 . T) (-4342 . T) (-4341 . T) (-4349 . T) (-4352 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4340 . T))
NIL
(-98 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}.")))
-((-4345 . T))
+((-4350 . T))
NIL
(-99 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}.")))
@@ -338,15 +338,15 @@ NIL
NIL
(-102 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}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
(-103 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 (-4350 "*"))))
+((|HasAttribute| |#1| (QUOTE (-4355 "*"))))
(-104)
((|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")))
-((-4348 . T))
+((-4353 . T))
NIL
(-105 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.")))
@@ -354,12 +354,12 @@ NIL
NIL
(-106 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.")))
-((-4349 . T) (-2363 . T))
+((-4354 . T) (-2368 . T))
NIL
(-107)
((|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.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| (-536) (QUOTE (-884))) (|HasCategory| (-536) (LIST (QUOTE -1012) (QUOTE (-1147)))) (|HasCategory| (-536) (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-145))) (|HasCategory| (-536) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-536) (QUOTE (-994))) (|HasCategory| (-536) (QUOTE (-798))) (-3886 (|HasCategory| (-536) (QUOTE (-798))) (|HasCategory| (-536) (QUOTE (-825)))) (|HasCategory| (-536) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-536) (QUOTE (-1122))) (|HasCategory| (-536) (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-536) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-536) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-536) (QUOTE (-227))) (|HasCategory| (-536) (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| (-536) (LIST (QUOTE -505) (QUOTE (-1147)) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -302) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -279) (QUOTE (-536)) (QUOTE (-536)))) (|HasCategory| (-536) (QUOTE (-300))) (|HasCategory| (-536) (QUOTE (-535))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-536) (LIST (QUOTE -619) (QUOTE (-536)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-884)))) (-3886 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-884)))) (|HasCategory| (-536) (QUOTE (-143)))))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| (-538) (QUOTE (-886))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-538) (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-145))) (|HasCategory| (-538) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-996))) (|HasCategory| (-538) (QUOTE (-800))) (-3891 (|HasCategory| (-538) (QUOTE (-800))) (|HasCategory| (-538) (QUOTE (-827)))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-1124))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-538) (QUOTE (-229))) (|HasCategory| (-538) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-538) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -304) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -281) (QUOTE (-538)) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-302))) (|HasCategory| (-538) (QUOTE (-537))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-538) (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (|HasCategory| (-538) (QUOTE (-143)))))
(-108)
((|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| (($ (|Symbol|) (|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| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}")))
NIL
@@ -370,11 +370,11 @@ NIL
NIL
(-110)
((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| (-112) (QUOTE (-1072))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-112) (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-112) (QUOTE (-1072))) (|HasCategory| (-112) (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| (-112) (QUOTE (-1074))) (|HasCategory| (-112) (LIST (QUOTE -304) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-112) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-112) (QUOTE (-1074))) (|HasCategory| (-112) (LIST (QUOTE -597) (QUOTE (-840)))))
(-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}")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
NIL
(-112)
((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant.")))
@@ -387,26 +387,26 @@ NIL
(-114 A)
((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise.")))
NIL
-((|HasCategory| |#1| (QUOTE (-825))))
-(-115 -3423 UP)
+((|HasCategory| |#1| (QUOTE (-827))))
+(-115 -3428 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}.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . 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}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| (-116 |#1|) (QUOTE (-884))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1012) (QUOTE (-1147)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-116 |#1|) (QUOTE (-994))) (|HasCategory| (-116 |#1|) (QUOTE (-798))) (-3886 (|HasCategory| (-116 |#1|) (QUOTE (-798))) (|HasCategory| (-116 |#1|) (QUOTE (-825)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1122))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-227))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -505) (QUOTE (-1147)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-300))) (|HasCategory| (-116 |#1|) (QUOTE (-535))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-884)))) (-3886 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-884)))) (|HasCategory| (-116 |#1|) (QUOTE (-143)))))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| (-116 |#1|) (QUOTE (-886))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-116 |#1|) (QUOTE (-996))) (|HasCategory| (-116 |#1|) (QUOTE (-800))) (-3891 (|HasCategory| (-116 |#1|) (QUOTE (-800))) (|HasCategory| (-116 |#1|) (QUOTE (-827)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-1124))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-229))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -507) (QUOTE (-1149)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -304) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-302))) (|HasCategory| (-116 |#1|) (QUOTE (-537))) (|HasCategory| (-116 |#1|) (QUOTE (-827))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-886)))) (|HasCategory| (-116 |#1|) (QUOTE (-143)))))
(-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| (($ $) "\\spad{left(u)} returns the left child.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4349)))
+((|HasAttribute| |#1| (QUOTE -4354)))
(-119 S)
((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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.")))
-((-2363 . T))
+((-2368 . T))
NIL
(-120 UP)
((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive.")))
@@ -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")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
(-122 S)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")))
NIL
NIL
(-123)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
(-124 A S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
@@ -430,24 +430,24 @@ NIL
NIL
(-125 S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
-((-4348 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4354 . T) (-2368 . T))
NIL
(-126 S)
((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
(-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.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
(-128)
((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} views \\spad{`c'} a a byte. In particular \\spad{`c'} is supposed to have a numerical value less than 256.") (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|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
NIL
(-129)
((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes.")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| (-128) (QUOTE (-825))) (|HasCategory| (-128) (LIST (QUOTE -302) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1072))) (|HasCategory| (-128) (LIST (QUOTE -302) (QUOTE (-128)))))) (-3886 (-12 (|HasCategory| (-128) (QUOTE (-1072))) (|HasCategory| (-128) (LIST (QUOTE -302) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| (-128) (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| (-128) (QUOTE (-825))) (|HasCategory| (-128) (QUOTE (-1072)))) (|HasCategory| (-128) (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-128) (QUOTE (-1072))) (-12 (|HasCategory| (-128) (QUOTE (-1072))) (|HasCategory| (-128) (LIST (QUOTE -302) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| (-128) (QUOTE (-827))) (|HasCategory| (-128) (LIST (QUOTE -304) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1074))) (|HasCategory| (-128) (LIST (QUOTE -304) (QUOTE (-128)))))) (-3891 (-12 (|HasCategory| (-128) (QUOTE (-1074))) (|HasCategory| (-128) (LIST (QUOTE -304) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-128) (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| (-128) (QUOTE (-827))) (|HasCategory| (-128) (QUOTE (-1074)))) (|HasCategory| (-128) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-128) (QUOTE (-1074))) (-12 (|HasCategory| (-128) (QUOTE (-1074))) (|HasCategory| (-128) (LIST (QUOTE -304) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -597) (QUOTE (-840)))))
(-130)
((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")))
NIL
@@ -462,13 +462,13 @@ NIL
NIL
(-133)
((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")))
-(((-4350 "*") . T))
+(((-4355 "*") . T))
NIL
-(-134 |minix| -2945 R)
+(-134 |minix| -2950 R)
((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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
-(-135 |minix| -2945 S T$)
+(-135 |minix| -2950 S T$)
((|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
@@ -486,8 +486,8 @@ NIL
NIL
(-139)
((|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}.")))
-((-4348 . T) (-4338 . T) (-4349 . T))
-((-3886 (-12 (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1072))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1072))) (-12 (|HasCategory| (-142) (QUOTE (-1072))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-838)))))
+((-4353 . T) (-4343 . T) (-4354 . T))
+((-3891 (-12 (|HasCategory| (-142) (QUOTE (-363))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-142) (QUOTE (-363))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1074))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-840)))))
(-140 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
@@ -502,7 +502,7 @@ NIL
NIL
(-143)
((|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.")))
-((-4345 . T))
+((-4350 . T))
NIL
(-144 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}.")))
@@ -510,9 +510,9 @@ NIL
NIL
(-145)
((|constructor| (NIL "Rings of Characteristic Zero.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-146 -3423 UP UPUP)
+(-146 -3428 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
@@ -523,14 +523,14 @@ NIL
(-148 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 -596) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasAttribute| |#1| (QUOTE -4348)))
+((|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasAttribute| |#1| (QUOTE -4353)))
(-149 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.")))
-((-2363 . T))
+((-2368 . T))
NIL
(-150 |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.")))
-((-4343 . T) (-4342 . T) (-4345 . T))
+((-4348 . T) (-4347 . T) (-4350 . T))
NIL
(-151)
((|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.")))
@@ -552,7 +552,7 @@ 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
-(-156 R -3423)
+(-156 R -3428)
((|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
@@ -583,10 +583,10 @@ NIL
(-163 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 (-884))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1169))) (|HasCategory| |#2| (QUOTE (-1032))) (|HasCategory| |#2| (QUOTE (-994))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasAttribute| |#2| (QUOTE -4344)) (|HasAttribute| |#2| (QUOTE -4347)) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-825))))
+((|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-358))) (|HasAttribute| |#2| (QUOTE -4349)) (|HasAttribute| |#2| (QUOTE -4352)) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-827))))
(-164 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})")))
-((-4341 -3886 (|has| |#1| (-543)) (-12 (|has| |#1| (-300)) (|has| |#1| (-884)))) (-4346 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) (-4344 |has| |#1| (-6 -4344)) (-4347 |has| |#1| (-6 -4347)) (-1421 . T) (-2363 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 -3891 (|has| |#1| (-545)) (-12 (|has| |#1| (-302)) (|has| |#1| (-886)))) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4349 |has| |#1| (-6 -4349)) (-4352 |has| |#1| (-6 -4352)) (-1421 . T) (-2368 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
(-165 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.")))
@@ -594,8 +594,8 @@ NIL
NIL
(-166 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}.")))
-((-4341 -3886 (|has| |#1| (-543)) (-12 (|has| |#1| (-300)) (|has| |#1| (-884)))) (-4346 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) (-4344 |has| |#1| (-6 -4344)) (-4347 |has| |#1| (-6 -4347)) (-1421 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
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(QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| |#1| (QUOTE (-1034))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1171)))) (|HasCategory| |#1| (QUOTE (-537))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-886))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-358)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-229))) (-12 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasAttribute| |#1| (QUOTE -4349)) (|HasAttribute| |#1| (QUOTE -4352)) (-12 (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-345)))))
(-167 R S)
((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,{}u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}.")))
NIL
@@ -610,7 +610,7 @@ NIL
NIL
(-170)
((|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.")))
-(((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
(-171)
((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations.")))
@@ -618,7 +618,7 @@ NIL
NIL
(-172 R)
((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}.")))
-(((-4350 "*") . T) (-4341 . T) (-4346 . T) (-4340 . T) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") . T) (-4346 . T) (-4351 . T) (-4345 . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
(-173)
((|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| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|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}.")))
@@ -635,7 +635,7 @@ NIL
(-176 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| (-920 |#2|) (LIST (QUOTE -860) (|devaluate| |#1|))))
+((|HasCategory| (-922 |#2|) (LIST (QUOTE -862) (|devaluate| |#1|))))
(-177 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
@@ -653,4316 +653,4324 @@ NIL
NIL
NIL
(-181)
+((|constructor| (NIL "This domain provides implementations for constructors.")) (|arity| (((|SingleInteger|) $) "\\spad{arity(ctor)} returns the arity of the constructor `ctor'. \\indented{2}{A negative value means that the \\spad{ctor} takes a variable} \\indented{2}{length argument list,{} \\spadignore{e.g.} Mapping,{} Record,{} etc.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'.")) (|name| (((|Identifier|) $) "\\spad{name(ctor)} returns the name of the constructor `ctor'.")))
+NIL
+NIL
+(-182)
((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor")))
NIL
NIL
-(-182 R -3423)
+(-183)
+((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' designates package constructors.")) (|domain| (($) "`domain' designates domain constructors")) (|category| (($) "`category' designates category constructors")))
+NIL
+NIL
+(-184 R -3428)
((|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
-(-183 R)
+(-185 R)
((|constructor| (NIL "CoerceVectorMatrixPackage: an unexposed,{} technical package for data conversions")) (|coerce| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))) "\\spad{coerce(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Fraction Polynomial R}")) (|coerceP| (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|))) "\\spad{coerceP(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Polynomial R}")))
NIL
NIL
-(-184)
+(-186)
((|constructor| (NIL "Enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,{}li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|))) "\\spad{SFunction(\\spad{li})} is the \\spad{S}-function of the partition \\spad{\\spad{li}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,{}s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,{}s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,{}s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}")))
NIL
NIL
-(-185)
+(-187)
((|constructor| (NIL "This package \\undocumented{}")) (|cyclotomicFactorization| (((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicFactorization(n)} \\undocumented{}")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} \\undocumented{}")) (|cyclotomicDecomposition| (((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicDecomposition(n)} \\undocumented{}")))
NIL
NIL
-(-186)
+(-188)
((|constructor| (NIL "\\axiomType{d01AgentsPackage} is a package of numerical agents to be used to investigate attributes of an input function so as to decide the \\axiomFun{measure} of an appropriate numerical integration routine. It contains functions \\axiomFun{rangeIsFinite} to test the input range and \\axiomFun{functionIsContinuousAtEndPoints} to check for continuity at the end points of the range.")) (|changeName| (((|Result|) (|Symbol|) (|Symbol|) (|Result|)) "\\spad{changeName(s,{}t,{}r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to \\axiom{\\spad{t}}.")) (|commaSeparate| (((|String|) (|List| (|String|))) "\\spad{commaSeparate(l)} produces a comma separated string from a list of strings.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{singularitiesOf(args)} returns a list of potential singularities of the function within the given range")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function if it can be retracted to \\axiomType{Polynomial DoubleFloat}.")) (|functionIsOscillatory| (((|Float|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsOscillatory(a)} tests whether the function \\spad{a.fn} has many zeros of its derivative.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(x)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{x}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(x)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{x}}")) (|functionIsContinuousAtEndPoints| (((|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")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsContinuousAtEndPoints(args)} uses power series limits to check for problems at the end points of the range of \\spad{args}.")) (|rangeIsFinite| (((|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{rangeIsFinite(args)} tests the endpoints of \\spad{args.range} for infinite end points.")))
NIL
NIL
-(-187)
+(-189)
((|constructor| (NIL "\\axiomType{d01ajfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AJF,{} a general numerical integration routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine D01AJF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-188)
+(-190)
((|constructor| (NIL "\\axiomType{d01akfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AKF,{} a numerical integration routine which is is suitable for oscillating,{} non-singular functions. The function \\axiomFun{measure} measures the usefulness of the routine D01AKF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-189)
+(-191)
((|constructor| (NIL "\\axiomType{d01alfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ALF,{} a general numerical integration routine which can handle a list of singularities. The function \\axiomFun{measure} measures the usefulness of the routine D01ALF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-190)
+(-192)
((|constructor| (NIL "\\axiomType{d01amfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AMF,{} a general numerical integration routine which can handle infinite or semi-infinite range of the input function. The function \\axiomFun{measure} measures the usefulness of the routine D01AMF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-191)
+(-193)
((|constructor| (NIL "\\axiomType{d01anfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ANF,{} a numerical integration routine which can handle weight functions of the form cos(\\omega \\spad{x}) or sin(\\omega \\spad{x}). The function \\axiomFun{measure} measures the usefulness of the routine D01ANF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-192)
+(-194)
((|constructor| (NIL "\\axiomType{d01apfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01APF,{} a general numerical integration routine which can handle end point singularities of the algebraico-logarithmic form \\spad{w}(\\spad{x}) = (\\spad{x}-a)\\spad{^c} * (\\spad{b}-\\spad{x})\\spad{^d}. The function \\axiomFun{measure} measures the usefulness of the routine D01APF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-193)
+(-195)
((|constructor| (NIL "\\axiomType{d01aqfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AQF,{} a general numerical integration routine which can solve an integral of the form \\newline \\centerline{\\inputbitmap{/home/bjd/Axiom/anna/hypertex/bitmaps/d01aqf.\\spad{xbm}}} The function \\axiomFun{measure} measures the usefulness of the routine D01AQF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-194)
+(-196)
((|constructor| (NIL "\\axiomType{d01asfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ASF,{} a numerical integration routine which can handle weight functions of the form cos(\\omega \\spad{x}) or sin(\\omega \\spad{x}) on an semi-infinite range. The function \\axiomFun{measure} measures the usefulness of the routine D01ASF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-195)
+(-197)
((|constructor| (NIL "\\axiomType{d01fcfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01FCF,{} a numerical integration routine which can handle multi-dimensional quadrature over a finite region. The function \\axiomFun{measure} measures the usefulness of the routine D01GBF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-196)
+(-198)
((|constructor| (NIL "\\axiomType{d01gbfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01GBF,{} a numerical integration routine which can handle multi-dimensional quadrature over a finite region. The function \\axiomFun{measure} measures the usefulness of the routine D01GBF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-197)
+(-199)
NIL
NIL
NIL
-(-198)
+(-200)
((|constructor| (NIL "\\axiom{d01WeightsPackage} is a package for functions used to investigate whether a function can be divided into a simpler function and a weight function. The types of weights investigated are those giving rise to end-point singularities of the algebraico-logarithmic type,{} and trigonometric weights.")) (|exprHasLogarithmicWeights| (((|Integer|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasLogarithmicWeights} looks for logarithmic weights giving rise to singularities of the function at the end-points.")) (|exprHasAlgebraicWeight| (((|Union| (|List| (|DoubleFloat|)) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasAlgebraicWeight} looks for algebraic weights giving rise to singularities of the function at the end-points.")) (|exprHasWeightCosWXorSinWX| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |w| (|DoubleFloat|))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasWeightCosWXorSinWX} looks for trigonometric weights in an expression of the form \\axiom{cos \\omega \\spad{x}} or \\axiom{sin \\omega \\spad{x}},{} returning the value of \\omega (\\notequal 1) and the operator.")))
NIL
NIL
-(-199)
+(-201)
((|constructor| (NIL "\\axiom{d02AgentsPackage} contains a set of computational agents for use with Ordinary Differential Equation solvers.")) (|intermediateResultsIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{intermediateResultsIF(o)} returns a value corresponding to the required number of intermediate results required and,{} therefore,{} an indication of how much this would affect the step-length of the calculation. It returns a value in the range [0,{}1].")) (|accuracyIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{accuracyIF(o)} returns the intensity value of the accuracy requirements of the input ODE. A request of accuracy of 10^-6 corresponds to the neutral intensity. It returns a value in the range [0,{}1].")) (|expenseOfEvaluationIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{expenseOfEvaluationIF(o)} returns the intensity value of the cost of evaluating the input ODE. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].\\newline\\indent{20} 400 ``operation units\\spad{''} \\spad{->} 0.75 \\newline 200 ``operation units\\spad{''} \\spad{->} 0.5 \\newline 83 ``operation units\\spad{''} \\spad{->} 0.25 \\newline\\indent{15} exponentiation = 4 units ,{} function calls = 10 units.")) (|systemSizeIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{systemSizeIF(ode)} returns the intensity value of the size of the system of ODEs. 20 equations corresponds to the neutral value. It returns a value in the range [0,{}1].")) (|stiffnessAndStabilityOfODEIF| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityOfODEIF(ode)} calculates the intensity values of stiffness of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which \\spad{O}(10) equates to mildly stiff wheras stiffness ratios of \\spad{O}(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian). \\blankline It returns two values in the range [0,{}1].")) (|stiffnessAndStabilityFactor| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityFactor(me)} calculates the stability and stiffness factor of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which \\spad{O}(10) equates to mildly stiff wheras stiffness ratios of \\spad{O}(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian).")) (|eval| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Matrix| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{eval(mat,{}symbols,{}values)} evaluates a multivariable matrix at given \\spad{values} for each of a list of variables")) (|jacobian| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|))) "\\spad{jacobian(v,{}w)} is a local function to make a jacobian matrix")) (|sparsityIF| (((|Float|) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{sparsityIF(m)} calculates the sparsity of a jacobian matrix")) (|combineFeatureCompatibility| (((|Float|) (|Float|) (|List| (|Float|))) "\\spad{combineFeatureCompatibility(C1,{}L)} is for interacting attributes") (((|Float|) (|Float|) (|Float|)) "\\spad{combineFeatureCompatibility(C1,{}C2)} is for interacting attributes")))
NIL
NIL
-(-200)
+(-202)
((|constructor| (NIL "\\axiomType{d02bbfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02BBF,{} a ODE routine which uses an Runge-Kutta method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02BBF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}.")))
NIL
NIL
-(-201)
+(-203)
((|constructor| (NIL "\\axiomType{d02bhfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02BHF,{} a ODE routine which uses an Runge-Kutta method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02BHF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}.")))
NIL
NIL
-(-202)
+(-204)
((|constructor| (NIL "\\axiomType{d02cjfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02CJF,{} a ODE routine which uses an Adams-Moulton-Bashworth method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02CJF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}.")))
NIL
NIL
-(-203)
+(-205)
((|constructor| (NIL "\\axiomType{d02ejfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02EJF,{} a ODE routine which uses a backward differentiation formulae method to handle a stiff system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02EJF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}.")))
NIL
NIL
-(-204)
+(-206)
((|elliptic?| (((|Boolean|) (|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{elliptic?(r)} \\undocumented{}")) (|central?| (((|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{central?(f,{}g,{}l)} \\undocumented{}")) (|subscriptedVariables| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{subscriptedVariables(e)} \\undocumented{}")) (|varList| (((|List| (|Symbol|)) (|Symbol|) (|NonNegativeInteger|)) "\\spad{varList(s,{}n)} \\undocumented{}")))
NIL
NIL
-(-205)
+(-207)
((|constructor| (NIL "\\axiomType{d03eefAnnaType} is a domain of \\axiomType{PartialDifferentialEquationsSolverCategory} for the NAG routines D03EEF/D03EDF.")))
NIL
NIL
-(-206)
+(-208)
((|constructor| (NIL "\\axiomType{d03fafAnnaType} is a domain of \\axiomType{PartialDifferentialEquationsSolverCategory} for the NAG routine D03FAF.")))
NIL
NIL
-(-207 N T$)
+(-209 N T$)
((|constructor| (NIL "This domain provides for a fixed-sized homogeneous data buffer.")) (|setelt| ((|#2| $ (|NonNegativeInteger|) |#2|) "\\spad{setelt(b,{}i,{}x)} sets the \\spad{i}th entry of data buffer \\spad{`b'} to \\spad{`x'}. Indexing is 0-based.")) (|elt| ((|#2| $ (|NonNegativeInteger|)) "\\spad{elt(b,{}i)} returns the \\spad{i}th element in buffer \\spad{`b'}. Indexing is 0-based.")) (|new| (($) "\\spad{new()} returns a fresly allocated data buffer or length \\spad{N}.")))
NIL
NIL
-(-208 S)
+(-210 S)
((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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
-(-209 -3423 UP UPUP R)
+(-211 -3428 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
-(-210 -3423 FP)
+(-212 -3428 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
-(-211)
+(-213)
((|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.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| (-536) (QUOTE (-884))) (|HasCategory| (-536) (LIST (QUOTE -1012) (QUOTE (-1147)))) (|HasCategory| (-536) (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-145))) (|HasCategory| (-536) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-536) (QUOTE (-994))) (|HasCategory| (-536) (QUOTE (-798))) (-3886 (|HasCategory| (-536) (QUOTE (-798))) (|HasCategory| (-536) (QUOTE (-825)))) (|HasCategory| (-536) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-536) (QUOTE (-1122))) (|HasCategory| (-536) (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-536) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-536) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-536) (QUOTE (-227))) (|HasCategory| (-536) (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| (-536) (LIST (QUOTE -505) (QUOTE (-1147)) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -302) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -279) (QUOTE (-536)) (QUOTE (-536)))) (|HasCategory| (-536) (QUOTE (-300))) (|HasCategory| (-536) (QUOTE (-535))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-536) (LIST (QUOTE -619) (QUOTE (-536)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-884)))) (-3886 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-884)))) (|HasCategory| (-536) (QUOTE (-143)))))
-(-212)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| (-538) (QUOTE (-886))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-538) (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-145))) (|HasCategory| (-538) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-996))) (|HasCategory| (-538) (QUOTE (-800))) (-3891 (|HasCategory| (-538) (QUOTE (-800))) (|HasCategory| (-538) (QUOTE (-827)))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-1124))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-538) (QUOTE (-229))) (|HasCategory| (-538) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-538) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -304) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -281) (QUOTE (-538)) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-302))) (|HasCategory| (-538) (QUOTE (-537))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-538) (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (|HasCategory| (-538) (QUOTE (-143)))))
+(-214)
((|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
-(-213 R -3423)
+(-215 R -3428)
((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.")))
NIL
NIL
-(-214 R)
+(-216 R)
((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\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}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\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
-(-215 R1 R2)
+(-217 R1 R2)
((|constructor| (NIL "This package \\undocumented{}")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,{}n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}")))
NIL
NIL
-(-216 S)
+(-218 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}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-217 |CoefRing| |listIndVar|)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-219 |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}.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-218 R -3423)
+(-220 R -3428)
((|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
-(-219)
+(-221)
((|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}.")))
-((-4124 . T) (-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4129 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-220)
+(-222)
((|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)}.}")))
NIL
NIL
-(-221 R)
+(-223 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}")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-543))) (|HasAttribute| |#1| (QUOTE (-4350 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-222 A S)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-224 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
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+(-225 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.")))
-((-4349 . T) (-2363 . T))
+((-4354 . T) (-2368 . T))
NIL
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((|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 -874) (QUOTE (-1147)))) (|HasCategory| |#2| (QUOTE (-227))))
-(-225 R)
+((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))))
+(-227 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}.")))
-((-4345 . T))
+((-4350 . T))
NIL
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+(-228 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")))
NIL
NIL
-(-227)
+(-229)
((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")))
-((-4345 . T))
+((-4350 . T))
NIL
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((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4348)))
-(-229 S)
+((|HasAttribute| |#1| (QUOTE -4353)))
+(-231 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}.")))
-((-4349 . T) (-2363 . T))
+((-4354 . T) (-2368 . T))
NIL
-(-230)
+(-232)
((|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
-(-231 S -2945 R)
+(-233 S -2950 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 (-356))) (|HasCategory| |#3| (QUOTE (-771))) (|HasCategory| |#3| (QUOTE (-823))) (|HasAttribute| |#3| (QUOTE -4345)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (QUOTE (-705))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1023))) (|HasCategory| |#3| (QUOTE (-1072))))
-(-232 -2945 R)
+((|HasCategory| |#3| (QUOTE (-358))) (|HasCategory| |#3| (QUOTE (-773))) (|HasCategory| |#3| (QUOTE (-825))) (|HasAttribute| |#3| (QUOTE -4350)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-707))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (QUOTE (-1074))))
+(-234 -2950 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")))
-((-4342 |has| |#2| (-1023)) (-4343 |has| |#2| (-1023)) (-4345 |has| |#2| (-6 -4345)) ((-4350 "*") |has| |#2| (-170)) (-4348 . T) (-2363 . T))
+((-4347 |has| |#2| (-1025)) (-4348 |has| |#2| (-1025)) (-4350 |has| |#2| (-6 -4350)) ((-4355 "*") |has| |#2| (-170)) (-4353 . T) (-2368 . T))
NIL
-(-233 -2945 R)
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((|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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((|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
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((|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
NIL
-(-236 S)
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((|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}.")))
NIL
NIL
-(-237)
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((|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}.")))
-((-4341 . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-238 S)
+(-240 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.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-239 S)
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((|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}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}")))
-((-4349 . T) (-4348 . T))
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-(-240 M)
+((-4354 . T) (-4353 . T))
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((|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
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((|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")))
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((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: January 19,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall")) (|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'}.")))
NIL
NIL
-(-243 |n| R M S)
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((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view.")))
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(|HasCategory| |#3| (QUOTE (-1025)))) (-3891 (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#3| (QUOTE (-229))) (|HasCategory| |#3| (QUOTE (-1025)))) (|HasCategory| |#3| (QUOTE (-707)))) (-3891 (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#3| (QUOTE (-1025)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-1149))))) (|HasAttribute| |#3| (QUOTE -4350)) (-12 (|HasCategory| |#3| (QUOTE (-229))) (|HasCategory| |#3| (QUOTE (-1025))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-247 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 (-227))))
-(-246 R S V E)
+((|HasCategory| |#2| (QUOTE (-229))))
+(-248 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.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
NIL
-(-247 S)
+(-249 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}.")))
-((-4348 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4354 . T) (-2368 . T))
NIL
-(-248 |Ex|)
+(-250 |Ex|)
((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")))
NIL
NIL
-(-249)
+(-251)
((|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.")))
NIL
NIL
-(-250 R |Ex|)
+(-252 R |Ex|)
((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y) = g(x,{}y),{}x,{}y,{}l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched.")))
NIL
NIL
-(-251)
+(-253)
((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,{}rRange,{}iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f,{} -2..2,{} -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,{}rRange,{}iRange,{}arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f,{} 0.3..3,{} 0..2*\\%\\spad{pi},{} false)}} Parameter descriptions: \\indented{2}{\\spad{f:}\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")))
NIL
NIL
-(-252 R)
+(-254 R)
((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}.")))
NIL
NIL
-(-253)
+(-255)
((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}lz,{}l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly,{}lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,{}l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}.")))
NIL
NIL
-(-254)
+(-256)
((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}.")))
NIL
NIL
-(-255)
+(-257)
((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,{}u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,{}r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,{}ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned.")))
NIL
NIL
-(-256 S)
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((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,{}s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command.")))
NIL
NIL
-(-257 R S V)
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((|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")))
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-(-258 A S)
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+(-260 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
NIL
-(-259 S)
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((|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| (($ |#1|) "\\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| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate.")))
NIL
NIL
-(-260)
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((|optAttributes| (((|List| (|String|)) (|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{optAttributes(o)} is a function for supplying a list of attributes of an optimization problem.")) (|expenseOfEvaluation| (((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{expenseOfEvaluation(o)} returns the intensity value of the cost of evaluating the input set of functions. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].")) (|changeNameToObjf| (((|Result|) (|Symbol|) (|Result|)) "\\spad{changeNameToObjf(s,{}r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to objf.")) (|varList| (((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{varList(e,{}n)} returns a list of \\axiom{\\spad{n}} indexed variables with name as in \\axiom{\\spad{e}}.")) (|variables| (((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{variables(args)} returns the list of variables in \\axiom{\\spad{args}.\\spad{lfn}}")) (|quadratic?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{quadratic?(e)} tests if \\axiom{\\spad{e}} is a quadratic function.")) (|nonLinearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{nonLinearPart(l)} returns the list of non-linear functions of \\axiom{\\spad{l}}.")) (|linearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linearPart(l)} returns the list of linear functions of \\axiom{\\spad{l}}.")) (|linearMatrix| (((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|)) "\\spad{linearMatrix(l,{}n)} returns a matrix of coefficients of the linear functions in \\axiom{\\spad{l}}. If \\spad{l} is empty,{} the matrix has at least one row.")) (|linear?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{linear?(e)} tests if \\axiom{\\spad{e}} is a linear function.") (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linear?(l)} returns \\spad{true} if all the bounds \\spad{l} are either linear or simple.")) (|simpleBounds?| (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{simpleBounds?(l)} returns \\spad{true} if the list of expressions \\spad{l} are simple.")) (|splitLinear| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{splitLinear(f)} splits the linear part from an expression which it returns.")) (|sumOfSquares| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{sumOfSquares(f)} returns either an expression for which the square is the original function of \"failed\".")) (|sortConstraints| (((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{sortConstraints(args)} uses a simple bubblesort on the list of constraints using the degree of the expression on which to sort. Of course,{} it must match the bounds to the constraints.")) (|finiteBound| (((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|)) "\\spad{finiteBound(l,{}b)} repaces all instances of an infinite entry in \\axiom{\\spad{l}} by a finite entry \\axiom{\\spad{b}} or \\axiom{\\spad{-b}}.")))
NIL
NIL
-(-261)
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((|constructor| (NIL "\\axiomType{e04dgfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04DGF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04DGF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
-(-262)
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((|constructor| (NIL "\\axiomType{e04fdfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04FDF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04FDF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04gcfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04GCF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04GCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04jafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04JAF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04JAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04mbfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04MBF,{} an optimization routine for Linear functions. The function \\axiomFun{measure} measures the usefulness of the routine E04MBF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
-(-266)
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((|constructor| (NIL "\\axiomType{e04nafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04NAF,{} an optimization routine for Quadratic functions. The function \\axiomFun{measure} measures the usefulness of the routine E04NAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04ucfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04UCF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04UCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
-(-268)
+(-270)
((|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
-(-269 R -3423)
+(-271 R -3428)
((|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
-(-270 R -3423)
+(-272 R -3428)
((|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
-(-271 |Coef| UTS ULS)
+(-273 |Coef| UTS ULS)
((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}")))
NIL
-((|HasCategory| |#1| (QUOTE (-356))))
-(-272 |Coef| ULS UPXS EFULS)
+((|HasCategory| |#1| (QUOTE (-358))))
+(-274 |Coef| ULS UPXS EFULS)
((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}")))
NIL
-((|HasCategory| |#1| (QUOTE (-356))))
-(-273)
+((|HasCategory| |#1| (QUOTE (-358))))
+(-275)
((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Symbol|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Symbol|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|ConstructorCall|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter.")))
NIL
NIL
-(-274 A S)
+(-276 A S)
((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|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 (-825))) (|HasCategory| |#2| (QUOTE (-1072))))
-(-275 S)
+((|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))))
+(-277 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}.")))
-((-4349 . T) (-2363 . T))
+((-4354 . T) (-2368 . T))
NIL
-(-276 S)
+(-278 S)
((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}.")))
NIL
NIL
-(-277)
+(-279)
((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}.")))
NIL
NIL
-(-278 |Coef| UTS)
+(-280 |Coef| UTS)
((|constructor| (NIL "The elliptic functions \\spad{sn},{} \\spad{sc} and \\spad{dn} are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,{}c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,{}k)} expands the elliptic function \\spad{dn} as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,{}k)} expands the elliptic function \\spad{cn} as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,{}k)} expands the elliptic function \\spad{sn} as a Taylor \\indented{1}{series.}")))
NIL
NIL
-(-279 S |Index|)
+(-281 S |Index|)
((|constructor| (NIL "An eltable over domains \\spad{D} and \\spad{I} is a structure which can be viewed as a function from \\spad{D} to \\spad{I}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures,{} \\spadignore{e.g.} \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,{}i)} (also written: \\spad{u} . \\spad{i}) returns the element of \\spad{u} indexed by \\spad{i}. Error: if \\spad{i} is not an index of \\spad{u}.")))
NIL
NIL
-(-280 S |Dom| |Im|)
+(-282 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 -4349)))
-(-281 |Dom| |Im|)
+((|HasAttribute| |#1| (QUOTE -4354)))
+(-283 |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
-(-282 S R |Mod| -2147 -3867 |exactQuo|)
+(-284 S R |Mod| -2152 -3872 |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| $) "\\spad{modulus(x)} \\undocumented")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-283)
+(-285)
((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero.")))
-((-4341 . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-284)
+(-286)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment")))
NIL
NIL
-(-285 R)
+(-287 R)
((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,{}m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,{}m,{}k,{}g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,{}m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable.")))
NIL
NIL
-(-286 S)
+(-288 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.")))
-((-4345 -3886 (|has| |#1| (-1023)) (|has| |#1| (-465))) (-4342 |has| |#1| (-1023)) (-4343 |has| |#1| (-1023)))
-((|HasCategory| |#1| (QUOTE (-356))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1023)))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (-3886 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147))))) (-3886 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147))))) (-3886 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147))))) (-3886 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705)))) (|HasCategory| |#1| (QUOTE (-465))) (-3886 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1083))) (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147))))) (-3886 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1083)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1147)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-291))) (-3886 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465)))) (-3886 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705)))) (-3886 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1023)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1083))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))))
-(-287 S R)
+((-4350 -3891 (|has| |#1| (-1025)) (|has| |#1| (-467))) (-4347 |has| |#1| (-1025)) (-4348 |has| |#1| (-1025)))
+((|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025)))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (-3891 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707)))) (|HasCategory| |#1| (QUOTE (-467))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-293))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-467)))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707)))) (-3891 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))))
+(-289 S R)
((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,{}eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}")))
NIL
NIL
-(-288 |Key| |Entry|)
+(-290 |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.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1072))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-289)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-291)
((|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
-(-290 S)
+(-292 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 -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1023))))
-(-291)
+((|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1025))))
+(-293)
((|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
NIL
-(-292 -3423 S)
+(-294 -3428 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
-(-293 E -3423)
+(-295 E -3428)
((|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
-(-294)
+(-296)
((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}")))
NIL
NIL
-(-295 A B)
+(-297 A B)
((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]")))
NIL
NIL
-(-296)
+(-298)
((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|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{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}")))
NIL
NIL
-(-297 R1)
+(-299 R1)
((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage1} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}")))
NIL
NIL
-(-298 R1 R2)
+(-300 R1 R2)
((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage2} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,{}m)} applies a mapping f:R1 \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}")))
NIL
NIL
-(-299 S)
+(-301 S)
((|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}.")))
NIL
NIL
-(-300)
+(-302)
((|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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-301 S R)
+(-303 S R)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}.")))
NIL
NIL
-(-302 R)
+(-304 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| |#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
-(-303 -3423)
+(-305 -3428)
((|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
-(-304)
+(-306)
((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}.")))
NIL
NIL
-(-305)
+(-307)
((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'.")))
NIL
NIL
-(-306 R FE |var| |cen|)
+(-308 R FE |var| |cen|)
((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|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))}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
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-(-307 R)
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+(-309 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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-(-308 R S)
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+(-310 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
NIL
-(-309 R FE)
+(-311 R FE)
((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,{}x = a,{}n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,{}x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,{}n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}x = a,{}n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,{}x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,{}x = a,{}n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,{}x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,{}n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,{}n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series.")))
NIL
NIL
-(-310 R -3423)
+(-312 R -3428)
((|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
-(-311)
+(-313)
((|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.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n,{}s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n,{}s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}.")))
NIL
NIL
-(-312 FE |var| |cen|)
+(-314 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.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-170))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-536)) (QUOTE (-1083))) (|HasCategory| |#1| (QUOTE (-356))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543)))) (-3886 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasSignature| |#1| (LIST (QUOTE -4312) (LIST (|devaluate| |#1|) (QUOTE (-1147)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536)))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasSignature| |#1| (LIST (QUOTE -4167) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1147))))) (|HasSignature| |#1| (LIST (QUOTE -3412) (LIST (LIST (QUOTE -620) (QUOTE (-1147))) (|devaluate| |#1|)))))))
-(-313 M)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-538)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|)))))))
+(-315 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
NIL
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((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between \\spad{-k} and \\spad{k} as a member of \\spad{R}.")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,{}i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R}. An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of \\spad{upoly}.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly,{} lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly,{} lvar,{} lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R}.")))
NIL
NIL
-(-315 S)
+(-317 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.")))
-((-4343 . T) (-4342 . T))
-((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-770))))
-(-316 S E)
+((-4348 . T) (-4347 . T))
+((|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-772))))
+(-318 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}.")))
NIL
NIL
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((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative.")))
NIL
-((|HasCategory| (-749) (QUOTE (-770))))
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+((|HasCategory| (-751) (QUOTE (-772))))
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((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring.")))
NIL
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((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-320 S)
+(-322 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.")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-321 S -3423)
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-323 S -3428)
((|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 (-361))))
-(-322 -3423)
+((|HasCategory| |#2| (QUOTE (-363))))
+(-324 -3428)
((|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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-323)
+(-325)
((|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.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm.")))
NIL
NIL
-(-324 E)
+(-326 E)
((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series")))
NIL
NIL
-(-325)
+(-327)
((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and,{} where appropriate,{} naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables I1,{} I2,{} and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,{}p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,{}p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,{}b,{}d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,{}p,{}q)} uses loop variables in the Fortran,{} I1 and I2")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,{}p)} \\undocumented{}")))
NIL
NIL
-(-326 -3423 UP UPUP R)
+(-328 -3428 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
-(-327 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
+(-329 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
((|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
-(-328 S -3423 UP UPUP R)
+(-330 S -3428 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
-(-329 -3423 UP UPUP R)
+(-331 -3428 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|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}.")))
NIL
NIL
-(-330 S R)
+(-332 S R)
((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -505) (QUOTE (-1147)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -279) (|devaluate| |#2|) (|devaluate| |#2|))))
-(-331 R)
+((|HasCategory| |#2| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -281) (|devaluate| |#2|) (|devaluate| |#2|))))
+(-333 R)
((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex.")))
NIL
NIL
-(-332 |basicSymbols| |subscriptedSymbols| R)
+(-334 |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.}")))
-((-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-371)))) (|HasCategory| $ (QUOTE (-1023))) (|HasCategory| $ (LIST (QUOTE -1012) (QUOTE (-536)))))
-(-333 |p| |n|)
+((-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-373)))) (|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-538)))))
+(-335 |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}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| (-880 |#1|) (QUOTE (-143))) (|HasCategory| (-880 |#1|) (QUOTE (-361)))) (|HasCategory| (-880 |#1|) (QUOTE (-145))) (|HasCategory| (-880 |#1|) (QUOTE (-361))) (|HasCategory| (-880 |#1|) (QUOTE (-143))))
-(-334 S -3423 UP UPUP)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| (-882 |#1|) (QUOTE (-143))) (|HasCategory| (-882 |#1|) (QUOTE (-363)))) (|HasCategory| (-882 |#1|) (QUOTE (-145))) (|HasCategory| (-882 |#1|) (QUOTE (-363))) (|HasCategory| (-882 |#1|) (QUOTE (-143))))
+(-336 S -3428 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 (-361))) (|HasCategory| |#2| (QUOTE (-356))))
-(-335 -3423 UP UPUP)
+((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-358))))
+(-337 -3428 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.")))
-((-4341 |has| (-400 |#2|) (-356)) (-4346 |has| (-400 |#2|) (-356)) (-4340 |has| (-400 |#2|) (-356)) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 |has| (-402 |#2|) (-358)) (-4351 |has| (-402 |#2|) (-358)) (-4345 |has| (-402 |#2|) (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-336 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
+(-338 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
-(-337 |p| |extdeg|)
+(-339 |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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| (-880 |#1|) (QUOTE (-143))) (|HasCategory| (-880 |#1|) (QUOTE (-361)))) (|HasCategory| (-880 |#1|) (QUOTE (-145))) (|HasCategory| (-880 |#1|) (QUOTE (-361))) (|HasCategory| (-880 |#1|) (QUOTE (-143))))
-(-338 GF |defpol|)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| (-882 |#1|) (QUOTE (-143))) (|HasCategory| (-882 |#1|) (QUOTE (-363)))) (|HasCategory| (-882 |#1|) (QUOTE (-145))) (|HasCategory| (-882 |#1|) (QUOTE (-363))) (|HasCategory| (-882 |#1|) (QUOTE (-143))))
+(-340 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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
-(-339 GF |extdeg|)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143))))
+(-341 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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
-(-340 GF)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143))))
+(-342 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
NIL
-(-341 F1 GF F2)
+(-343 F1 GF F2)
((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}\\spad{GF},{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn\\spad{'t} divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn\\spad{'t} divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.")))
NIL
NIL
-(-342 S)
+(-344 S)
((|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.")))
NIL
NIL
-(-343)
+(-345)
((|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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-344 R UP -3423)
+(-346 R UP -3428)
((|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
-(-345 |p| |extdeg|)
+(-347 |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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| (-880 |#1|) (QUOTE (-143))) (|HasCategory| (-880 |#1|) (QUOTE (-361)))) (|HasCategory| (-880 |#1|) (QUOTE (-145))) (|HasCategory| (-880 |#1|) (QUOTE (-361))) (|HasCategory| (-880 |#1|) (QUOTE (-143))))
-(-346 GF |uni|)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| (-882 |#1|) (QUOTE (-143))) (|HasCategory| (-882 |#1|) (QUOTE (-363)))) (|HasCategory| (-882 |#1|) (QUOTE (-145))) (|HasCategory| (-882 |#1|) (QUOTE (-363))) (|HasCategory| (-882 |#1|) (QUOTE (-143))))
+(-348 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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
-(-347 GF |extdeg|)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143))))
+(-349 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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
-(-348 GF |defpol|)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143))))
+(-350 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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
-(-349 GF)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143))))
+(-351 GF)
((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\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
-(-350 -3423 GF)
+(-352 -3428 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
-(-351 -3423 FP FPP)
+(-353 -3428 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
-(-352 GF |n|)
+(-354 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}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
-(-353 R |ls|)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143))))
+(-355 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
-(-354 S)
+(-356 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-355 S)
+(-357 S)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
NIL
NIL
-(-356)
+(-358)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-357 S)
+(-359 S)
((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result.")))
NIL
NIL
-(-358 |Name| S)
+(-360 |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.")))
NIL
NIL
-(-359 S R)
+(-361 S 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| |#2|) $) "\\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| |#2|) $) "\\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| |#2|))) "\\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| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|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| |#2|) (|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| ((|#2| (|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| ((|#2| (|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| |#2|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|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| |#2|) $ (|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| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|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| |#2|) $ (|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| |#2|)) (|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| |#2|)) (|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.")))
NIL
-((|HasCategory| |#2| (QUOTE (-543))))
-(-360 R)
+((|HasCategory| |#2| (QUOTE (-545))))
+(-362 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis.")))
-((-4345 |has| |#1| (-543)) (-4343 . T) (-4342 . T))
+((-4350 |has| |#1| (-545)) (-4348 . T) (-4347 . T))
NIL
-(-361)
+(-363)
((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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.")))
NIL
NIL
-(-362 S R UP)
+(-364 S 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| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|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| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|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.")))
NIL
-((|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-356))))
-(-363 R UP)
+((|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-358))))
+(-365 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
+((-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-364 A S)
+(-366 A S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4349)) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1072))))
-(-365 S)
+((|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))))
+(-367 S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
-((-4348 . T) (-2363 . T))
+((-4353 . T) (-2368 . T))
NIL
-(-366 S A R B)
+(-368 S A R B)
((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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.")))
NIL
NIL
-(-367 |VarSet| R)
+(-369 |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) (-4343 . T) (-4342 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4348 . T) (-4347 . T))
NIL
-(-368 S V)
+(-370 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.")))
NIL
NIL
-(-369 S R)
+(-371 S 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}")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536)))))
-(-370 R)
+((|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))))
+(-372 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}")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-371)
+(-373)
((|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}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|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}.")))
-((-4331 . T) (-4339 . T) (-4124 . T) (-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4336 . T) (-4344 . T) (-4129 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-372 |Par|)
+(-374 |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}.")))
NIL
NIL
-(-373 |Par|)
+(-375 |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}.")))
NIL
NIL
-(-374 R S)
+(-376 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.")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
((|HasCategory| |#1| (QUOTE (-170))))
-(-375 R S)
+(-377 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}")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
((|HasCategory| |#1| (QUOTE (-170))))
-(-376)
+(-378)
((|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}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-377 R |Basis|)
+(-379 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}.")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
NIL
-(-378)
+(-380)
((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-379 S)
+(-381 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
NIL
-((|HasCategory| |#1| (QUOTE (-825))))
-(-380)
+((|HasCategory| |#1| (QUOTE (-827))))
+(-382)
((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-381)
+(-383)
((|constructor| (NIL "This domain provides an interface to names in the file system.")))
NIL
NIL
-(-382)
+(-384)
((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,{}pref,{}e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,{}n,{}e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used.")) (|coerce| (((|String|) $) "\\spad{coerce(fn)} produces a string for a file name according to operating system-dependent conventions.") (($ (|String|)) "\\spad{coerce(s)} converts a string to a file name according to operating system-dependent conventions.")))
NIL
NIL
-(-383 |n| |class| R)
+(-385 |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")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
NIL
-(-384)
+(-386)
((|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
-(-385 -3423 UP UPUP R)
+(-387 -3428 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
-(-386)
+(-388)
((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula 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 \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the 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 formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula 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.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format.")))
NIL
NIL
-(-387 S)
+(-389 S)
((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format.")))
NIL
NIL
-(-388)
+(-390)
((|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
-(-389)
+(-391)
((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-390)
+(-392)
((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-391 -3900 |returnType| -1464 |symbols|)
+(-393 -3905 |returnType| -1466 |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
-(-392 -3423 UP)
+(-394 -3428 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}")))
NIL
NIL
-(-393 R)
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((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers).")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-394 S)
+(-396 S)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
NIL
NIL
-(-395)
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((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
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NIL
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((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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
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((|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\".")))
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NIL
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((|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| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically.")))
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((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type.")))
NIL
NIL
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((|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.")))
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-(-401 A B)
+((-4340 -12 (|has| |#1| (-6 -4351)) (|has| |#1| (-446)) (|has| |#1| (-6 -4340))) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-996))) (|HasCategory| |#1| (QUOTE (-800))) (-3891 (|HasCategory| |#1| (QUOTE (-800))) (|HasCategory| |#1| (QUOTE (-827)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1124))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-537))) (-12 (|HasAttribute| |#1| (QUOTE -4340)) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-403 A B)
((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}.")))
NIL
NIL
-(-402 S R UP)
+(-404 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
-(-403 R UP)
+(-405 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
+((-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-404 A S)
+(-406 A S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))))
-(-405 S)
+((|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))))
+(-407 S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
NIL
-(-406 R -3423 UP A)
+(-408 R -3428 UP A)
((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-407 R1 F1 U1 A1 R2 F2 U2 A2)
+(-409 R1 F1 U1 A1 R2 F2 U2 A2)
((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}")))
NIL
NIL
-(-408 R -3423 UP A |ibasis|)
+(-410 R -3428 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")))
NIL
-((|HasCategory| |#4| (LIST (QUOTE -1012) (|devaluate| |#2|))))
-(-409 AR R AS S)
+((|HasCategory| |#4| (LIST (QUOTE -1014) (|devaluate| |#2|))))
+(-411 AR R AS S)
((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}.")))
NIL
NIL
-(-410 S R)
+(-412 S R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\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| |#2|))) "\\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| |#2|))) "\\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| |#2|) $) "\\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| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\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| |#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 \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\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| |#2|))) "\\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| ((|#2| $ (|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| |#2|) (|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| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
NIL
-((|HasCategory| |#2| (QUOTE (-356))))
-(-411 R)
+((|HasCategory| |#2| (QUOTE (-358))))
+(-413 R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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.")))
-((-4345 |has| |#1| (-543)) (-4343 . T) (-4342 . T))
+((-4350 |has| |#1| (-545)) (-4348 . T) (-4347 . T))
NIL
-(-412 R)
+(-414 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
NIL
-(-413 S R)
+(-415 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 -1012) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-1083))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))))
-(-414 R)
+((|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))))
+(-416 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}.")))
-((-4345 -3886 (|has| |#1| (-1023)) (|has| |#1| (-465))) (-4343 |has| |#1| (-170)) (-4342 |has| |#1| (-170)) ((-4350 "*") |has| |#1| (-543)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-543)) (-4340 |has| |#1| (-543)) (-2363 . T))
+((-4350 -3891 (|has| |#1| (-1025)) (|has| |#1| (-467))) (-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) ((-4355 "*") |has| |#1| (-545)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-545)) (-4345 |has| |#1| (-545)) (-2368 . T))
NIL
-(-415 R A S B)
+(-417 R A S B)
((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}.")))
NIL
NIL
-(-416 R FE |x| |cen|)
+(-418 R FE |x| |cen|)
((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed.")))
NIL
NIL
-(-417 R FE |Expon| UPS TRAN |x|)
+(-419 R FE |Expon| UPS TRAN |x|)
((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'")))
NIL
NIL
-(-418 A S)
+(-420 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 (-825))) (|HasCategory| |#2| (QUOTE (-361))))
-(-419 S)
+((|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-363))))
+(-421 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}.")))
-((-4348 . T) (-4338 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4343 . T) (-4354 . T) (-2368 . T))
NIL
-(-420 S A R B)
+(-422 S A R B)
((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain.")))
NIL
NIL
-(-421 R -3423)
+(-423 R -3428)
((|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
-(-422 R E)
+(-424 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")))
-((-4335 -12 (|has| |#1| (-6 -4335)) (|has| |#2| (-6 -4335))) (-4342 . T) (-4343 . T) (-4345 . T))
-((-12 (|HasAttribute| |#1| (QUOTE -4335)) (|HasAttribute| |#2| (QUOTE -4335))))
-(-423 R -3423)
+((-4340 -12 (|has| |#1| (-6 -4340)) (|has| |#2| (-6 -4340))) (-4347 . T) (-4348 . T) (-4350 . T))
+((-12 (|HasAttribute| |#1| (QUOTE -4340)) (|HasAttribute| |#2| (QUOTE -4340))))
+(-425 R -3428)
((|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
-(-424 R -3423)
+(-426 R -3428)
((|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
-(-425 R -3423)
+(-427 R -3428)
((|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))))
-(-426 R -3423)
+(-428 R -3428)
((|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
-(-427)
+(-429)
((|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
-(-428 R -3423 UP)
+(-430 R -3428 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 -1012) (QUOTE (-48)))))
-(-429)
+((|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-48)))))
+(-431)
((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}")))
NIL
NIL
-(-430)
+(-432)
((|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
NIL
-(-431 |f|)
+(-433 |f|)
((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-432)
+(-434)
((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|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.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-433)
+(-435)
((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-434 UP)
+(-436 UP)
((|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
-(-435 R UP -3423)
+(-437 R UP -3428)
((|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
-(-436 R UP)
+(-438 R UP)
((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored} (July 1994).")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,{}f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,{}f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,{}c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,{}c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1).")))
NIL
NIL
-(-437 R)
+(-439 R)
((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,{}r)} returns the binomial coefficient \\spad{C(n,{}r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation.")))
NIL
-((|HasCategory| |#1| (QUOTE (-397))))
-(-438)
+((|HasCategory| |#1| (QUOTE (-399))))
+(-440)
((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(\\spad{zi})} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p},{} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(\\spad{zi})} produces the complete factorization of the complex integer \\spad{zi}.")))
NIL
NIL
-(-439 |Dom| |Expon| |VarSet| |Dpol|)
+(-441 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-356))))
-(-440 |Dom| |Expon| |VarSet| |Dpol|)
+((|HasCategory| |#1| (QUOTE (-358))))
+(-442 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")))
NIL
NIL
-(-441 |Dom| |Expon| |VarSet| |Dpol|)
+(-443 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions,{} info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,{}info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}.")))
NIL
NIL
-(-442 |Dom| |Expon| |VarSet| |Dpol|)
+(-444 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented")))
NIL
NIL
-(-443 S)
+(-445 S)
((|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| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-444)
+(-446)
((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|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}.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-445 R |n| |ls| |gamma|)
+(-447 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")))
-((-4345 |has| (-400 (-920 |#1|)) (-543)) (-4343 . T) (-4342 . T))
-((|HasCategory| (-400 (-920 |#1|)) (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| (-400 (-920 |#1|)) (QUOTE (-543))))
-(-446 |vl| R E)
+((-4350 |has| (-402 (-922 |#1|)) (-545)) (-4348 . T) (-4347 . T))
+((|HasCategory| (-402 (-922 |#1|)) (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| (-402 (-922 |#1|)) (QUOTE (-545))))
+(-448 |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")))
-(((-4350 "*") |has| |#2| (-170)) (-4341 |has| |#2| (-543)) (-4346 |has| |#2| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#2| (QUOTE (-884))) (-3886 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-884)))) (-3886 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-884)))) (-3886 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-884)))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-170))) (-3886 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-543)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -860) (QUOTE (-371))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -860) (QUOTE (-536))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-356))) (-3886 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasAttribute| |#2| (QUOTE -4346)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| |#2| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (-3886 (-12 (|HasCategory| |#2| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143)))))
-(-447 R BP)
+(((-4355 "*") |has| |#2| (-170)) (-4346 |has| |#2| (-545)) (-4351 |has| |#2| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#2| (QUOTE (-886))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-358))) (-3891 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143)))))
+(-449 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
NIL
-(-448 OV E S R P)
+(-450 OV E S 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| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|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
-(-449 E OV R P)
+(-451 E OV R P)
((|constructor| (NIL "This package provides operations for \\spad{GCD} computations on polynomials")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{GCD} of \\spad{p} and \\spad{q}")))
NIL
NIL
-(-450 R)
+(-452 R)
((|constructor| (NIL "\\indented{1}{Description} This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}")))
NIL
NIL
-(-451 R FE)
+(-453 R FE)
((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),{}n,{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{series(a(n),{}n,{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n +-> a(n),{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),{}n,{}x=a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{series(a(n),{}n,{}x=a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),{}n,{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n +-> a(n),{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),{}n,{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{puiseux(a(n),{}n,{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n +-> a(n),{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{puiseux(n +-> a(n),{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),{}n,{}x=a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{laurent(a(n),{}n,{}x=a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{laurent(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),{}n,{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}; \\spad{taylor(a(n),{}n,{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n=n0..,{}a(n)*(x-a)**n)}; \\spad{taylor(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),{}n,{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n +-> a(n),{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.")))
NIL
NIL
-(-452 RP TP)
+(-454 RP TP)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni} General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,{}pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,{}lfact,{}prime,{}bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,{}lfacts,{}prime,{}bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done .")))
NIL
NIL
-(-453 |vl| R IS E |ff| P)
+(-455 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
NIL
-(-454 E V R P Q)
+(-456 E V R P Q)
((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}.")))
NIL
NIL
-(-455 R E |VarSet| P)
+(-457 R E |VarSet| P)
((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}.")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-456 S R E)
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-458 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
NIL
-(-457 R E)
+(-459 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
NIL
-(-458)
+(-460)
((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector {\\em ww} to start a loop using {\\em nextSubsetGray(ww,{}n)}")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,{}n)} returns a vector {\\em vv} whose components have the following meanings:\\begin{items} \\item {\\em vv.1}: a vector of length \\spad{n} whose entries are 0 or 1. This \\indented{3}{can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n};} \\indented{3}{{\\em vv.1} differs from {\\em ww.1} by exactly one entry;} \\item {\\em vv.2.1} is the number of the entry of {\\em vv.1} which \\indented{3}{will be changed next time;} \\item {\\em vv.2.1 = n+1} means that {\\em vv.1} is the last subset; \\indented{3}{trying to compute nextSubsetGray(\\spad{vv}) if {\\em vv.2.1 = n+1}} \\indented{3}{will produce an error!} \\end{items} The other components of {\\em vv.2} are needed to compute nextSubsetGray efficiently. Note: this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case {\\em r1 = r2 = ... = rn = 2}; Note: nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} {\\em nextSubsetGray(vv)} and {\\em vv := nextSubsetGray(vv)} will have the same effect.")))
NIL
NIL
-(-459)
+(-461)
((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n}.") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n}.")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is \\spad{false}.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is \\spad{true}.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done.")))
NIL
NIL
-(-460)
+(-462)
((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,{}lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(\\spad{gi})} returns the indicated graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}\\spad{pt}) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(\\spad{gi},{}pt,{}pal)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(\\spad{gi},{}pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{\\spad{gi}},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(\\spad{gi},{}pt,{}pal1,{}pal2,{}ps)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(\\spad{gi},{}pt)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(\\spad{gi},{}lp,{}pal1,{}pal2,{}p)} sets the components of the graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{\\spad{gi}} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(\\spad{gi},{}lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{\\spad{gi}}.") (((|List| (|Float|)) $) "\\spad{units(\\spad{gi})} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(\\spad{gi},{}lr)} modifies the list of ranges for the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{\\spad{gi}}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(\\spad{gi})} returns the list of ranges of the point components from the indicated graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(\\spad{gi})} returns the process ID of the given graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(\\spad{gi})} returns the list of lists of points which compose the given graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,{}lpal1,{}lpal2,{}lp,{}lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,{}lpal1,{}lpal2,{}lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(\\spad{gi})} takes the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} and sends it\\spad{'s} data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{\\spad{gi}} cannot be an empty graph,{} and it\\spad{'s} elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport.")))
NIL
NIL
-(-461 S R E)
+(-463 S R E)
((|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.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-462 R E)
+(-464 R E)
((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-463 |lv| -3423 R)
+(-465 |lv| -3428 R)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}.")))
NIL
NIL
-(-464 S)
+(-466 S)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
NIL
NIL
-(-465)
+(-467)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-466 |Coef| |var| |cen|)
+(-468 |Coef| |var| |cen|)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")))
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-(-467 |Key| |Entry| |Tbl| |dent|)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-538)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|)))))))
+(-469 |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.")))
-((-4349 . T))
-((-12 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-825))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-468 R E V P)
+((-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-827))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-470 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)}")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-469)
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-471)
((|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}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-470)
+(-472)
((|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'.")))
NIL
NIL
-(-471 |Key| |Entry| |hashfn|)
+(-473 |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.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1072))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-472)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-474)
((|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
-(-473 |vl| R)
+(-475 |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")))
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((|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}.")))
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(-538))))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))))) (|HasCategory| (-538) (QUOTE (-827))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (QUOTE (-1025)))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-1025)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#2| (QUOTE -4350)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-477)
((|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
-(-476 S)
+(-478 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}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-477 -3423 UP UPUP R)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-479 -3428 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
-(-478 BP)
+(-480 BP)
((|constructor| (NIL "This package provides the functions for the heuristic integer \\spad{gcd}. Geddes\\spad{'s} algorithm,{}for univariate polynomials with integer coefficients")) (|lintgcd| (((|Integer|) (|List| (|Integer|))) "\\spad{lintgcd([a1,{}..,{}ak])} = \\spad{gcd} of a list of integers")) (|content| (((|List| (|Integer|)) (|List| |#1|)) "\\spad{content([f1,{}..,{}fk])} = content of a list of univariate polynonials")) (|gcdcofactprim| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofactprim([f1,{}..fk])} = \\spad{gcd} and cofactors of \\spad{k} primitive polynomials.")) (|gcdcofact| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofact([f1,{}..fk])} = \\spad{gcd} and cofactors of \\spad{k} univariate polynomials.")) (|gcdprim| ((|#1| (|List| |#1|)) "\\spad{gcdprim([f1,{}..,{}fk])} = \\spad{gcd} of \\spad{k} PRIMITIVE univariate polynomials")) (|gcd| ((|#1| (|List| |#1|)) "\\spad{gcd([f1,{}..,{}fk])} = \\spad{gcd} of the polynomials \\spad{fi}.")))
NIL
NIL
-(-479)
+(-481)
((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| (-536) (QUOTE (-884))) (|HasCategory| (-536) (LIST (QUOTE -1012) (QUOTE (-1147)))) (|HasCategory| (-536) (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-145))) (|HasCategory| (-536) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-536) (QUOTE (-994))) (|HasCategory| (-536) (QUOTE (-798))) (-3886 (|HasCategory| (-536) (QUOTE (-798))) (|HasCategory| (-536) (QUOTE (-825)))) (|HasCategory| (-536) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-536) (QUOTE (-1122))) (|HasCategory| (-536) (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-536) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-536) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-536) (QUOTE (-227))) (|HasCategory| (-536) (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| (-536) (LIST (QUOTE -505) (QUOTE (-1147)) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -302) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -279) (QUOTE (-536)) (QUOTE (-536)))) (|HasCategory| (-536) (QUOTE (-300))) (|HasCategory| (-536) (QUOTE (-535))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-536) (LIST (QUOTE -619) (QUOTE (-536)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-884)))) (-3886 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-884)))) (|HasCategory| (-536) (QUOTE (-143)))))
-(-480 A S)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| (-538) (QUOTE (-886))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-538) (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-145))) (|HasCategory| (-538) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-996))) (|HasCategory| (-538) (QUOTE (-800))) (-3891 (|HasCategory| (-538) (QUOTE (-800))) (|HasCategory| (-538) (QUOTE (-827)))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-1124))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-538) (QUOTE (-229))) (|HasCategory| (-538) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-538) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -304) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -281) (QUOTE (-538)) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-302))) (|HasCategory| (-538) (QUOTE (-537))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-538) (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (|HasCategory| (-538) (QUOTE (-143)))))
+(-482 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 -4348)) (|HasAttribute| |#1| (QUOTE -4349)) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-481 S)
+((|HasAttribute| |#1| (QUOTE -4353)) (|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-483 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-482)
+(-484)
((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}.")))
NIL
NIL
-(-483 S)
+(-485 S)
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-484)
+(-486)
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-485 -3423 UP |AlExt| |AlPol|)
+(-487 -3428 UP |AlExt| |AlPol|)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP.")))
NIL
NIL
-(-486)
+(-488)
((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| $ (QUOTE (-1023))) (|HasCategory| $ (LIST (QUOTE -1012) (QUOTE (-536)))))
-(-487 S |mn|)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-538)))))
+(-489 S |mn|)
((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type.")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-488 R |mnRow| |mnCol|)
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-490 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.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-489 K R UP)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-491 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
-(-490 R UP -3423)
+(-492 R UP -3428)
((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}")))
NIL
NIL
-(-491 |mn|)
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((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}.")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| (-112) (QUOTE (-1072))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-112) (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-112) (QUOTE (-1072))) (|HasCategory| (-112) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-492 K R UP L)
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| (-112) (QUOTE (-1074))) (|HasCategory| (-112) (LIST (QUOTE -304) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-112) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-112) (QUOTE (-1074))) (|HasCategory| (-112) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-494 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
NIL
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((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts \\axiom{\\spad{s}} into an \\axiom{IndexCard}. Warning: if \\axiom{\\spad{s}} is not of the right format then an error will occur when using it.")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,{}s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}.")))
NIL
NIL
-(-494 R Q A B)
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((|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
-(-495 -3423 |Expon| |VarSet| |DPoly|)
+(-497 -3428 |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 -596) (QUOTE (-1147)))))
-(-496 |vl| |nv|)
+((|HasCategory| |#3| (LIST (QUOTE -598) (QUOTE (-1149)))))
+(-498 |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
NIL
-(-497)
+(-499)
((|constructor| (NIL "This domain represents identifer AST.")))
NIL
NIL
-(-498 A S)
+(-500 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored.")))
NIL
NIL
-(-499 A S)
+(-501 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored.")))
NIL
NIL
-(-500 A S)
+(-502 A S)
((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,{}s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}.")))
NIL
NIL
-(-501 A S)
+(-503 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support.")))
NIL
NIL
-(-502 A S)
+(-504 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored.")))
NIL
NIL
-(-503 A S)
+(-505 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored.")))
NIL
NIL
-(-504 S A B)
+(-506 S A B)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f,{} [x1,{}...,{}xn],{} [v1,{}...,{}vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f,{} x,{} v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
NIL
NIL
-(-505 A B)
+(-507 A B)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f,{} [x1,{}...,{}xn],{} [v1,{}...,{}vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f,{} x,{} v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
NIL
NIL
-(-506 S E |un|)
+(-508 S E |un|)
((|constructor| (NIL "Internal implementation of a free abelian monoid.")))
NIL
-((|HasCategory| |#2| (QUOTE (-770))))
-(-507 S |mn|)
+((|HasCategory| |#2| (QUOTE (-772))))
+(-509 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}")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-508)
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-510)
((|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
-(-509 |p| |n|)
+(-511 |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}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((-3886 (|HasCategory| (-565 |#1|) (QUOTE (-143))) (|HasCategory| (-565 |#1|) (QUOTE (-361)))) (|HasCategory| (-565 |#1|) (QUOTE (-145))) (|HasCategory| (-565 |#1|) (QUOTE (-361))) (|HasCategory| (-565 |#1|) (QUOTE (-143))))
-(-510 R |mnRow| |mnCol| |Row| |Col|)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((-3891 (|HasCategory| (-567 |#1|) (QUOTE (-143))) (|HasCategory| (-567 |#1|) (QUOTE (-363)))) (|HasCategory| (-567 |#1|) (QUOTE (-145))) (|HasCategory| (-567 |#1|) (QUOTE (-363))) (|HasCategory| (-567 |#1|) (QUOTE (-143))))
+(-512 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}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-511 S |mn|)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-513 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.")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-512 R |Row| |Col| M)
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-514 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 -4349)))
-(-513 R |Row| |Col| M QF |Row2| |Col2| M2)
+((|HasAttribute| |#3| (QUOTE -4354)))
+(-515 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 -4349)))
-(-514 R |mnRow| |mnCol|)
+((|HasAttribute| |#7| (QUOTE -4354)))
+(-516 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.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-543))) (|HasAttribute| |#1| (QUOTE (-4350 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-515)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-517)
((|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
NIL
-(-516)
+(-518)
((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Symbol|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'")))
NIL
NIL
-(-517 S)
+(-519 S)
((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{readBytes!(c,{}b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned.")) (|readByteIfCan!| (((|SingleInteger|) $) "\\spad{readByteIfCan!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise return \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every read attempt,{} which is overkill.}")))
NIL
NIL
-(-518)
+(-520)
((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{readBytes!(c,{}b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned.")) (|readByteIfCan!| (((|SingleInteger|) $) "\\spad{readByteIfCan!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise return \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every read attempt,{} which is overkill.}")))
NIL
NIL
-(-519 GF)
+(-521 GF)
((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}.")))
NIL
NIL
-(-520)
+(-522)
((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.")))
NIL
NIL
-(-521 R)
+(-523 R)
((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} \\spad{:=} increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} \\spad{:=} increment()} then \\spad{f x} is \\spad{x+1}.")))
NIL
NIL
-(-522 |Varset|)
+(-524 |Varset|)
((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables")))
NIL
NIL
-(-523 K -3423 |Par|)
+(-525 K -3428 |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
-(-524)
+(-526)
((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity.")))
NIL
NIL
-(-525)
+(-527)
((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter.")))
NIL
NIL
-(-526 R)
+(-528 R)
((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}.")))
NIL
NIL
-(-527 |Coef| UTS)
+(-529 |Coef| UTS)
((|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
-(-528 K -3423 |Par|)
+(-530 K -3428 |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
-(-529 R BP |pMod| |nextMod|)
+(-531 R BP |pMod| |nextMod|)
((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,{}p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the \\spad{gcd} of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,{}f2)} computes the \\spad{gcd} of the two polynomials \\spad{f1} and \\spad{f2} by modular methods.")))
NIL
NIL
-(-530 OV E R P)
+(-532 OV E R P)
((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,{}ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,{}ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}.")))
NIL
NIL
-(-531 K UP |Coef| UTS)
+(-533 K UP |Coef| UTS)
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|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| ((|#4| |#4|) "\\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| ((|#4| |#4|) "\\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| ((|#4| |#4|) "\\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
-(-532 |Coef| UTS)
+(-534 |Coef| UTS)
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|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
-(-533 R UP)
+(-535 R UP)
((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented")))
NIL
NIL
-(-534 S)
+(-536 S)
((|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|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd.")))
NIL
NIL
-(-535)
+(-537)
((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\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|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd.")))
-((-4346 . T) (-4347 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4351 . T) (-4352 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-536)
+(-538)
((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")))
-((-4330 . T) (-4336 . T) (-4340 . T) (-4335 . T) (-4346 . T) (-4347 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4335 . T) (-4341 . T) (-4345 . T) (-4340 . T) (-4351 . T) (-4352 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-537 |Key| |Entry| |addDom|)
+(-539 |Key| |Entry| |addDom|)
((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1072))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-538 R -3423)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-540 R -3428)
((|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
-(-539 R0 -3423 UP UPUP R)
+(-541 R0 -3428 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
-(-540)
+(-542)
((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,{}m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,{}m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})")))
NIL
NIL
-(-541 R)
+(-543 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.")))
-((-4124 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4129 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-542 S)
+(-544 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.")))
NIL
NIL
-(-543)
+(-545)
((|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.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-544 R -3423)
+(-546 R -3428)
((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\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|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise.")))
NIL
NIL
-(-545 I)
+(-547 I)
((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra\\spad{'s} eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}")))
NIL
NIL
-(-546)
+(-548)
((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions.")))
NIL
NIL
-(-547 R -3423 L)
+(-549 R -3428 L)
((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\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|))))) #3#) |#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|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}.")))
NIL
-((|HasCategory| |#3| (LIST (QUOTE -636) (|devaluate| |#2|))))
-(-548)
+((|HasCategory| |#3| (LIST (QUOTE -638) (|devaluate| |#2|))))
+(-550)
((|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
-(-549 -3423 UP UPUP R)
+(-551 -3428 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
-(-550 -3423 UP)
+(-552 -3428 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
-(-551)
+(-553)
((|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
-(-552 R -3423 L)
+(-554 R -3428 L)
((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\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 -636) (|devaluate| |#2|))))
-(-553 R -3423)
+((|HasCategory| |#3| (LIST (QUOTE -638) (|devaluate| |#2|))))
+(-555 R -3428)
((|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 -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1110)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-610)))))
-(-554 -3423 UP)
+((-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1112)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-612)))))
+(-556 -3428 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
-(-555 S)
+(-557 S)
((|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
-(-556 -3423)
+(-558 -3428)
((|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
-(-557 R)
+(-559 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.")))
-((-4124 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4129 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-558)
+(-560)
((|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
-(-559 R -3423)
+(-561 R -3428)
((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-277))) (|HasCategory| |#2| (QUOTE (-610))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1147))))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-277)))) (|HasCategory| |#1| (QUOTE (-543))))
-(-560 -3423 UP)
+((-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-279))) (|HasCategory| |#2| (QUOTE (-612))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149))))) (-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-279)))) (|HasCategory| |#1| (QUOTE (-545))))
+(-562 -3428 UP)
((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\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|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\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|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}.")))
NIL
NIL
-(-561 R -3423)
+(-563 R -3428)
((|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
-(-562)
+(-564)
((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations.")))
NIL
NIL
-(-563)
+(-565)
((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|bothWays| (($) "`bothWays' indicates that an IO conduit is for both input and output.")) (|output| (($) "`output' indicates that an IO conduit is for output")) (|input| (($) "`input' indicates that an IO conduit is for input.")))
NIL
NIL
-(-564 |p| |unBalanced?|)
+(-566 |p| |unBalanced?|)
((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-565 |p|)
+(-567 |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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-361))))
-(-566)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-363))))
+(-568)
((|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
-(-567 -3423)
+(-569 -3428)
((|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}.")))
-((-4343 . T) (-4342 . T))
-((|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-1147)))))
-(-568 E -3423)
+((-4348 . T) (-4347 . T))
+((|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-1149)))))
+(-570 E -3428)
((|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
-(-569 R -3423)
+(-571 R -3428)
((|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
-(-570 I)
+(-572 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
NIL
-(-571 GF)
+(-573 GF)
((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field.")))
NIL
NIL
-(-572 R)
+(-574 R)
((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\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
((|HasCategory| |#1| (QUOTE (-145))))
-(-573)
+(-575)
((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,{}2,{}...,{}n}} in Young\\spad{'s} natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,{}3,{}3,{}1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,{}listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young\\spad{'s} natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young\\spad{'s} natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,{}2,{}...,{}n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,{}\\spad{pi})} is the irreducible representation corresponding to partition {\\em lambda} in Young\\spad{'s} natural form of the permutation {\\em \\spad{pi}} in the symmetric group,{} whose elements permute {\\em {1,{}2,{}...,{}n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|Integer|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented.")))
NIL
NIL
-(-574 R E V P TS)
+(-576 R E V P TS)
((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,{}lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,{}univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial.")))
NIL
NIL
-(-575)
+(-577)
((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'.")))
NIL
NIL
-(-576 |mn|)
+(-578 |mn|)
((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1072))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (-3886 (-12 (|HasCategory| (-142) (QUOTE (-1072))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1072)))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1072))) (-12 (|HasCategory| (-142) (QUOTE (-1072))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-577 E V R P)
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (-3891 (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1074)))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1074))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-579 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
-(-578 |Coef|)
+(-580 |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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-543))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-536)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-536)) (|devaluate| |#1|)))) (|HasCategory| (-536) (QUOTE (-1083))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-536))))) (|HasSignature| |#1| (LIST (QUOTE -4312) (LIST (|devaluate| |#1|) (QUOTE (-1147)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-536))))))
-(-579 |Coef|)
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((|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.}")))
-((-4343 |has| |#1| (-543)) (-4342 |has| |#1| (-543)) ((-4350 "*") |has| |#1| (-543)) (-4341 |has| |#1| (-543)) (-4345 . T))
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-(-580 A B)
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+(-582 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),{}..]}.")))
NIL
NIL
-(-581 A B C)
+(-583 A B C)
((|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
-(-582 R -3423 FG)
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((|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
-(-583 S)
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((|constructor| (NIL "\\indented{1}{This package implements 'infinite tuples' for the interpreter.} The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}s)} returns \\spad{[s,{}f(s),{}f(f(s)),{}...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}.")))
NIL
NIL
-(-584 R |mn|)
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((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index.")))
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+(-587 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
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-(-586 |Index| |Entry|)
+((|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (QUOTE (-827))) (|HasAttribute| |#1| (QUOTE -4353)) (|HasCategory| |#3| (QUOTE (-1074))))
+(-588 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order.")))
-((-2363 . T))
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NIL
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((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode.")))
NIL
NIL
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((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join \\spad{`x'}.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'.")))
NIL
NIL
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((|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).")))
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((|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.")))
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((|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
-(-592 |Key| |Entry|)
+(-594 |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}.")))
-((-4349 . T) (-2363 . T))
+((-4354 . T) (-2368 . T))
NIL
-(-593 S)
+(-595 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 -596) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))))
-(-594 R S)
+((|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))))
+(-596 R S)
((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented")))
NIL
NIL
-(-595 S)
+(-597 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
NIL
-(-596 S)
+(-598 S)
((|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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}.")))
NIL
NIL
-(-597 -3423 UP)
+(-599 -3428 UP)
((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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
-(-598)
+(-600)
((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of \\spad{`x'} is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of \\spad{`x'} is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of \\spad{`x'} is `false'")) (|true| (($) "the definite truth value")) (|unknown| (($) "the indefinite `unknown'")) (|false| (($) "the definite falsehood value")))
NIL
NIL
-(-599 A R S)
+(-601 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}.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-823))))
-(-600 S R)
+((-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-825))))
+(-602 S R)
((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra.")))
NIL
NIL
-(-601 R)
+(-603 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.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-602 R -3423)
+(-604 R -3428)
((|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
-(-603 R UP)
+(-605 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")))
-((-4343 . T) (-4342 . T) ((-4350 "*") . T) (-4341 . T) (-4345 . T))
-((|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))))
-(-604 R E V P TS ST)
+((-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4346 . T) (-4350 . T))
+((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))))
+(-606 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
NIL
-(-605 OV E Z P)
+(-607 OV E Z P)
((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \\spad{\"F\"}.")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,{}unilist,{}plead,{}vl,{}lvar,{}lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod,{} numFacts,{} evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation.")))
NIL
NIL
-(-606)
+(-608)
((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'.")))
NIL
NIL
-(-607 |VarSet| R |Order|)
+(-609 |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}}.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-608 R |ls|)
+(-610 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}}.")))
NIL
NIL
-(-609 R -3423)
+(-611 R -3428)
((|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
-(-610)
+(-612)
((|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
-(-611 |lv| -3423)
+(-613 |lv| -3428)
((|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
-(-612)
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((|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.")))
-((-4349 . T))
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((|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).")))
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((|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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-356))))
-(-615 R)
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((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-4343 . T) (-4342 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4348 . T) (-4347 . T))
NIL
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((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}.")))
NIL
NIL
-(-617 R)
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((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")))
NIL
NIL
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((|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
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((|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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")))
-((-4345 . T))
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NIL
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((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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.")))
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-(-621 A B)
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((|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
-(-622 A B)
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((|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
-(-623 A B C)
+(-625 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
-(-624 T$)
+(-626 T$)
((|constructor| (NIL "This domain represents AST for Spad literals.")))
NIL
NIL
-(-625 S)
+(-627 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-626 R)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-628 R)
((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}.")))
NIL
NIL
-(-627 S E |un|)
+(-629 S E |un|)
((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|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
-(-628 A S)
+(-630 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 -4349)))
-(-629 S)
+((|HasAttribute| |#1| (QUOTE -4354)))
+(-631 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})}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-630 M R S)
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((|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}.")))
-((-4343 . T) (-4342 . T))
-((|HasCategory| |#1| (QUOTE (-769))))
-(-631 R -3423 L)
+((-4348 . T) (-4347 . T))
+((|HasCategory| |#1| (QUOTE (-771))))
+(-633 R -3428 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
-(-632 A -2743)
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((|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}}")))
-((-4342 . T) (-4343 . T) (-4345 . T))
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-(-633 A)
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((|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}}")))
-((-4342 . T) (-4343 . T) (-4345 . T))
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-(-634 A M)
+((-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358))))
+(-636 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}")))
-((-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
-(-635 S A)
+((-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358))))
+(-637 S A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-356))))
-(-636 A)
+((|HasCategory| |#2| (QUOTE (-358))))
+(-638 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}.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
+((-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-637 -3423 UP)
+(-639 -3428 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))))
-(-638 A L)
+(-640 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
-(-639 S)
+(-641 S)
((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}.")))
NIL
NIL
-(-640)
+(-642)
((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}.")))
NIL
NIL
-(-641 R)
+(-643 R)
((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists.")))
NIL
NIL
-(-642 |VarSet| R)
+(-644 |VarSet| R)
((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|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) (-4343 . T) (-4342 . T))
-((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-170))))
-(-643 A S)
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4348 . T) (-4347 . T))
+((|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-170))))
+(-645 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
-(-644 S)
+(-646 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}.")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-645 -3423 |Row| |Col| M)
+(-647 -3428 |Row| |Col| M)
((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.")))
NIL
NIL
-(-646 -3423)
+(-648 -3428)
((|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|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.")))
NIL
NIL
-(-647 R E OV P)
+(-649 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
-(-648 |n| R)
+(-650 |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.")))
-((-4345 . T) (-4348 . T) (-4342 . T) (-4343 . T))
-((|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4350 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))) (-3886 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1147)))))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-543))) (-3886 (|HasAttribute| |#2| (QUOTE (-4350 #1#))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1147))))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-170))))
-(-649)
+((-4350 . T) (-4353 . T) (-4347 . T) (-4348 . T))
+((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasAttribute| |#2| (QUOTE (-4355 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-545))) (-3891 (|HasAttribute| |#2| (QUOTE (-4355 #1#))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-170))))
+(-651)
((|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
-(-650 |VarSet|)
+(-652 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")))
NIL
NIL
-(-651 A S)
+(-653 A S)
((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}.")))
NIL
NIL
-(-652 S)
+(-654 S)
((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-653 R)
+(-655 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
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (QUOTE (-1023))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-654)
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-656)
((|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
-(-655 |VarSet|)
+(-657 |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
-(-656 A)
+(-658 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
-(-657 A C)
+(-659 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
-(-658 A B C)
+(-660 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
-(-659)
+(-661)
((|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
-(-660 A)
+(-662 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
-(-661 A C)
+(-663 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
-(-662 A B C)
+(-664 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
-(-663 S R |Row| |Col|)
+(-665 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 (-4350 "*"))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-543))))
-(-664 R |Row| |Col|)
+((|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-545))))
+(-666 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")))
-((-4348 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4354 . T) (-2368 . T))
NIL
-(-665 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
+(-667 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
-(-666 R |Row| |Col| M)
+(-668 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 (-356))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-543))))
-(-667 R)
+((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-545))))
+(-669 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.")))
-((-4348 . T) (-4349 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-543))) (|HasAttribute| |#1| (QUOTE (-4350 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-668 R)
+((-4353 . T) (-4354 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-670 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
-(-669 T$)
+(-671 T$)
((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} 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}.")))
NIL
NIL
-(-670 S -3423 FLAF FLAS)
+(-672 S -3428 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
-(-671 R Q)
+(-673 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
-(-672)
+(-674)
((|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")))
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-(-673 S)
+((-4346 . T) (-4351 |has| (-679) (-358)) (-4345 |has| (-679) (-358)) (-1421 . T) (-4352 |has| (-679) (-6 -4352)) (-4349 |has| (-679) (-6 -4349)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
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+(-675 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}.")))
-((-4349 . T) (-2363 . T))
+((-4354 . T) (-2368 . T))
NIL
-(-674 U)
+(-676 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
-(-675)
+(-677)
((|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|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented")))
NIL
NIL
-(-676 OV E -3423 PG)
+(-678 OV E -3428 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
-(-677)
+(-679)
((|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}")))
-((-4124 . T) (-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4129 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-678 R)
+(-680 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
-(-679)
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((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}")))
-((-4347 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4352 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-680 S D1 D2 I)
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((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function")))
NIL
NIL
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((|constructor| (NIL "MakeCachableSet(\\spad{S}) returns a cachable set which is equal to \\spad{S} as a set.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s} viewed as an element of \\%.")))
NIL
NIL
-(-682 S)
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((|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
-(-683 S)
+(-685 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
-(-684 S T$)
+(-686 S T$)
((|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
-(-685 S -2997 I)
+(-687 S -3002 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
-(-686 E OV R P)
+(-688 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
-(-687 R)
+(-689 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)}.}")))
-((-4342 . T) (-4343 . T) (-4345 . T))
+((-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-688 R1 UP1 UPUP1 R2 UP2 UPUP2)
+(-690 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
-(-689)
+(-691)
((|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
-(-690 R |Mod| -2147 -3867 |exactQuo|)
+(-692 R |Mod| -2152 -3872 |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| $) "\\spad{modulus(x)} \\undocumented")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-691 R |Rep|)
+(-693 R |Rep|)
((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(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")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4344 |has| |#1| (-356)) (-4346 |has| |#1| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
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-(-692 IS E |ff|)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1055) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1124))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-345))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-694 IS E |ff|)
((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented")))
NIL
NIL
-(-693 R M)
+(-695 R M)
((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}.")))
-((-4343 |has| |#1| (-170)) (-4342 |has| |#1| (-170)) (-4345 . T))
+((-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) (-4350 . T))
((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))))
-(-694 R |Mod| -2147 -3867 |exactQuo|)
+(-696 R |Mod| -2152 -3872 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-695 S R)
+(-697 S R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
NIL
NIL
-(-696 R)
+(-698 R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
NIL
-(-697 -3423)
+(-699 -3428)
((|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]]}.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-698 S)
+(-700 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation.")))
NIL
NIL
-(-699)
+(-701)
((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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
-(-700 S)
+(-702 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
-(-701)
+(-703)
((|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
-(-702 S R UP)
+(-704 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 (-343))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-361))))
-(-703 R UP)
+((|HasCategory| |#2| (QUOTE (-345))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-363))))
+(-705 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.")))
-((-4341 |has| |#1| (-356)) (-4346 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 |has| |#1| (-358)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-704 S)
+(-706 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
-(-705)
+(-707)
((|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
-(-706 -3423 UP)
+(-708 -3428 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
-(-707 |VarSet| E1 E2 R S PR PS)
+(-709 |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
-(-708 |Vars1| |Vars2| E1 E2 R PR1 PR2)
+(-710 |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
-(-709 E OV R PPR)
+(-711 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
-(-710 |vl| R)
+(-712 |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.")))
-(((-4350 "*") |has| |#2| (-170)) (-4341 |has| |#2| (-543)) (-4346 |has| |#2| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#2| (QUOTE (-884))) (-3886 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-884)))) (-3886 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-884)))) (-3886 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-884)))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-170))) (-3886 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-543)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -860) (QUOTE (-371))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -860) (QUOTE (-536))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-356))) (-3886 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasAttribute| |#2| (QUOTE -4346)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| |#2| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (-3886 (-12 (|HasCategory| |#2| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143)))))
-(-711 E OV R PRF)
+(((-4355 "*") |has| |#2| (-170)) (-4346 |has| |#2| (-545)) (-4351 |has| |#2| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#2| (QUOTE (-886))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-358))) (-3891 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143)))))
+(-713 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
NIL
-(-712 E OV R P)
+(-714 E OV R P)
((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}.")))
NIL
NIL
-(-713 R S M)
+(-715 R S M)
((|constructor| (NIL "MonoidRingFunctions2 implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,{}u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}.")))
NIL
NIL
-(-714 R M)
+(-716 R M)
((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}.")))
-((-4343 |has| |#1| (-170)) (-4342 |has| |#1| (-170)) (-4345 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-825))))
-(-715 S)
+((-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) (-4350 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-827))))
+(-717 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}.")))
-((-4348 . T) (-4338 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-716 S)
+((-4353 . T) (-4343 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-718 S)
((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements.")))
-((-4338 . T) (-4349 . T) (-2363 . T))
+((-4343 . T) (-4354 . T) (-2368 . T))
NIL
-(-717)
+(-719)
((|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
-(-718 S)
+(-720 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
-(-719 |Coef| |Var|)
+(-721 |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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4343 . T) (-4342 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4348 . T) (-4347 . T) (-4350 . T))
NIL
-(-720 OV E R P)
+(-722 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
-(-721 E OV R P)
+(-723 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
-(-722 S R)
+(-724 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
-(-723 R)
+(-725 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}.")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
NIL
-(-724)
+(-726)
((|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
-(-725)
+(-727)
((|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
-(-726)
+(-728)
((|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
-(-727)
+(-729)
((|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
-(-728)
+(-730)
((|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
-(-729)
+(-731)
((|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
-(-730)
+(-732)
((|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
-(-731)
+(-733)
((|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
-(-732)
+(-734)
((|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
-(-733)
+(-735)
((|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
-(-734)
+(-736)
((|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
-(-735)
+(-737)
((|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
-(-736)
+(-738)
((|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
-(-737)
+(-739)
((|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
-(-738)
+(-740)
((|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
-(-739 S)
+(-741 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| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}.")))
NIL
NIL
-(-740)
+(-742)
((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}.")))
NIL
NIL
-(-741 S)
+(-743 S)
((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|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
-(-742)
+(-744)
((|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
-(-743 |Par|)
+(-745 |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
-(-744 -3423)
+(-746 -3428)
((|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
-(-745 P -3423)
+(-747 P -3428)
((|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
-(-746 UP -3423)
+(-748 UP -3428)
((|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
-(-747)
+(-749)
((|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| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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
-(-748 R)
+(-750 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
-(-749)
+(-751)
((|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.")))
-(((-4350 "*") . T))
+(((-4355 "*") . T))
NIL
-(-750 R -3423)
+(-752 R -3428)
((|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
-(-751)
+(-753)
((|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
-(-752 S)
+(-754 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
-(-753 R |PolR| E |PolE|)
+(-755 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
-(-754 R E V P TS)
+(-756 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
-(-755 -3423 |ExtF| |SUEx| |ExtP| |n|)
+(-757 -3428 |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
-(-756 BP E OV R P)
+(-758 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
-(-757 |Par|)
+(-759 |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
-(-758 R |VarSet|)
+(-760 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.")))
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+(-761 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)}")))
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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| (((|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
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((|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
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+(-764 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.}")))
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NIL
-(-763 S)
+(-765 S)
((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-170))))
-(-764)
+((-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-827)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-170))))
+(-766)
((|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
-(-765)
+(-767)
((|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
-(-766)
+(-768)
((|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
-(-767)
+(-769)
((|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
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((|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
-(-769)
+(-771)
((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")))
NIL
NIL
-(-770)
+(-772)
((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")))
NIL
NIL
-(-771)
+(-773)
((|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| (($ $ $) "\\spad{sup(x,{}y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted.")))
NIL
NIL
-(-772)
+(-774)
((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}")))
NIL
NIL
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((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-1032))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-361))))
-(-774 R)
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+(-776 R)
((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
+((-4347 . T) (-4348 . T) (-4350 . T))
NIL
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((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering.")))
NIL
NIL
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((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1147)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (-3886 (|HasCategory| (-970 |#1|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (-3886 (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-970 |#1|) (LIST (QUOTE -1012) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-535))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-970 |#1|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| (-970 |#1|) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))))
-(-777 -3886 R OS S)
+((-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (-3891 (|HasCategory| (-972 |#1|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-972 |#1|) (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-972 |#1|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-972 |#1|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))))
+(-779 -3891 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
-(-778)
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((|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
-(-779 R -3423 L)
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((|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
-(-780 R -3423)
+(-782 R -3428)
((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.")))
NIL
NIL
-(-781)
+(-783)
((|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
-(-782 R -3423)
+(-784 R -3428)
((|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
-(-783)
+(-785)
((|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
-(-784 -3423 UP UPUP R)
+(-786 -3428 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
-(-785 -3423 UP L LQ)
+(-787 -3428 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
-(-786)
+(-788)
((|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| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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
-(-787 -3423 UP L LQ)
+(-789 -3428 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
-(-788 -3423 UP)
+(-790 -3428 UP)
((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\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|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.")))
NIL
NIL
-(-789 -3423 L UP A LO)
+(-791 -3428 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
-(-790 -3423 UP)
+(-792 -3428 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))))
-(-791 -3423 LO)
+(-793 -3428 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
-(-792 -3423 LODO)
+(-794 -3428 LODO)
((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.")))
NIL
NIL
-(-793 -2945 S |f|)
+(-795 -2950 S |f|)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
-((-4342 |has| |#2| (-1023)) (-4343 |has| |#2| (-1023)) (-4345 |has| |#2| (-6 -4345)) ((-4350 "*") |has| |#2| (-170)) (-4348 . T))
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((|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")))
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-(-795 |Kernels| R |var|)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
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+(-797 |Kernels| R |var|)
((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring.")))
-(((-4350 "*") |has| |#2| (-356)) (-4341 |has| |#2| (-356)) (-4346 |has| |#2| (-356)) (-4340 |has| |#2| (-356)) (-4345 . T) (-4343 . T) (-4342 . T))
-((|HasCategory| |#2| (QUOTE (-356))))
-(-796 S)
+(((-4355 "*") |has| |#2| (-358)) (-4346 |has| |#2| (-358)) (-4351 |has| |#2| (-358)) (-4345 |has| |#2| (-358)) (-4350 . T) (-4348 . T) (-4347 . T))
+((|HasCategory| |#2| (QUOTE (-358))))
+(-798 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
-(-797 S)
+(-799 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
-(-798)
+(-800)
((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-799)
+(-801)
((|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
-(-800)
+(-802)
((|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
-(-801)
+(-803)
((|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
-(-802)
+(-804)
((|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
-(-803)
+(-805)
((|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
-(-804)
+(-806)
((|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
-(-805 R)
+(-807 R)
((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath.")))
NIL
NIL
-(-806 P R)
+(-808 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}.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-227))))
-(-807)
+((-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-229))))
+(-809)
((|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
-(-808 S)
+(-810 S)
((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}.")))
-((-4348 . T) (-4338 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4343 . T) (-4354 . T) (-2368 . T))
NIL
-(-809)
+(-811)
((|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
-(-810 R)
+(-812 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.")))
-((-4345 |has| |#1| (-823)))
-((|HasCategory| |#1| (QUOTE (-823))) (-3886 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-535))) (-3886 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-21))))
-(-811 R S)
+((-4350 |has| |#1| (-825)))
+((|HasCategory| |#1| (QUOTE (-825))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-537))) (-3891 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-21))))
+(-813 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
-(-812 R)
+(-814 R)
((|constructor| (NIL "Algebra of ADDITIVE operators over a ring.")))
-((-4343 |has| |#1| (-170)) (-4342 |has| |#1| (-170)) (-4345 . T))
+((-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) (-4350 . T))
((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))))
-(-813)
+(-815)
((|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
-(-814)
+(-816)
((|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
-(-815)
+(-817)
((|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
-(-816)
+(-818)
((|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| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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
-(-817 R)
+(-819 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.")))
-((-4345 |has| |#1| (-823)))
-((|HasCategory| |#1| (QUOTE (-823))) (-3886 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-535))) (-3886 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-21))))
-(-818 R S)
+((-4350 |has| |#1| (-825)))
+((|HasCategory| |#1| (QUOTE (-825))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-537))) (-3891 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-21))))
+(-820 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
-(-819)
+(-821)
((|constructor| (NIL "Ordered finite sets.")))
NIL
NIL
-(-820 -2945 S)
+(-822 -2950 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
-(-821)
+(-823)
((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline")))
NIL
NIL
-(-822 S)
+(-824 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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0.")))
NIL
NIL
-(-823)
+(-825)
((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-824 S)
+(-826 S)
((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set.")))
NIL
NIL
-(-825)
+(-827)
((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set.")))
NIL
NIL
-(-826 S R)
+(-828 S R)
((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")))
NIL
-((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-170))))
-(-827 R)
+((|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))))
+(-829 R)
((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}")))
-((-4342 . T) (-4343 . T) (-4345 . T))
+((-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-828 R C)
+(-830 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 (-356))) (|HasCategory| |#1| (QUOTE (-543))))
-(-829 R |sigma| -3590)
+((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545))))
+(-831 R |sigma| -3595)
((|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.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
-(-830 |x| R |sigma| -3590)
+((-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358))))
+(-832 |x| R |sigma| -3595)
((|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}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-356))))
-(-831 R)
+((-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-358))))
+(-833 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 -400) (QUOTE (-536))))))
-(-832)
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))))
+(-834)
((|constructor| (NIL "Semigroups with compatible ordering.")))
NIL
NIL
-(-833)
+(-835)
((|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
-(-834)
+(-836)
((|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
-(-835 S)
+(-837 S)
((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}")))
NIL
NIL
-(-836)
+(-838)
((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}")))
NIL
NIL
-(-837)
+(-839)
((|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
-(-838)
+(-840)
((|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
-(-839 |VariableList|)
+(-841 |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
-(-840 R |vl| |wl| |wtlevel|)
+(-842 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights")))
-((-4343 |has| |#1| (-170)) (-4342 |has| |#1| (-170)) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))))
-(-841 R PS UP)
+((-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))))
+(-843 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
-(-842 R |x| |pt|)
+(-844 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
-(-843 |p|)
+(-845 |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).")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-844 |p|)
+(-846 |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}.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-845 |p|)
+(-847 |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).")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| (-843 |#1|) (QUOTE (-884))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -1012) (QUOTE (-1147)))) (|HasCategory| (-843 |#1|) (QUOTE (-143))) (|HasCategory| (-843 |#1|) (QUOTE (-145))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-843 |#1|) (QUOTE (-994))) (|HasCategory| (-843 |#1|) (QUOTE (-798))) (-3886 (|HasCategory| (-843 |#1|) (QUOTE (-798))) (|HasCategory| (-843 |#1|) (QUOTE (-825)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-843 |#1|) (QUOTE (-1122))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| (-843 |#1|) (QUOTE (-227))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -505) (QUOTE (-1147)) (LIST (QUOTE -843) (|devaluate| |#1|)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -843) (|devaluate| |#1|)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -843) (|devaluate| |#1|)) (LIST (QUOTE -843) (|devaluate| |#1|)))) (|HasCategory| (-843 |#1|) (QUOTE (-300))) (|HasCategory| (-843 |#1|) (QUOTE (-535))) (|HasCategory| (-843 |#1|) (QUOTE (-825))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-843 |#1|) (QUOTE (-884)))) (-3886 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-843 |#1|) (QUOTE (-884)))) (|HasCategory| (-843 |#1|) (QUOTE (-143)))))
-(-846 |p| PADIC)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| (-845 |#1|) (QUOTE (-886))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-845 |#1|) (QUOTE (-143))) (|HasCategory| (-845 |#1|) (QUOTE (-145))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-845 |#1|) (QUOTE (-996))) (|HasCategory| (-845 |#1|) (QUOTE (-800))) (-3891 (|HasCategory| (-845 |#1|) (QUOTE (-800))) (|HasCategory| (-845 |#1|) (QUOTE (-827)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-845 |#1|) (QUOTE (-1124))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-845 |#1|) (QUOTE (-229))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -507) (QUOTE (-1149)) (LIST (QUOTE -845) (|devaluate| |#1|)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -304) (LIST (QUOTE -845) (|devaluate| |#1|)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -845) (|devaluate| |#1|)) (LIST (QUOTE -845) (|devaluate| |#1|)))) (|HasCategory| (-845 |#1|) (QUOTE (-302))) (|HasCategory| (-845 |#1|) (QUOTE (-537))) (|HasCategory| (-845 |#1|) (QUOTE (-827))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-845 |#1|) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-845 |#1|) (QUOTE (-886)))) (|HasCategory| (-845 |#1|) (QUOTE (-143)))))
+(-848 |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)}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#2| (QUOTE (-884))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1147)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-994))) (|HasCategory| |#2| (QUOTE (-798))) (-3886 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1122))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| |#2| (LIST (QUOTE -505) (QUOTE (-1147)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -279) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-825))) (-12 (|HasCategory| |#2| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (-3886 (-12 (|HasCategory| |#2| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143)))))
-(-847 S T$)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-800))) (-3891 (|HasCategory| |#2| (QUOTE (-800))) (|HasCategory| |#2| (QUOTE (-827)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1124))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -281) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-827))) (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143)))))
+(-849 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 (-1072))) (|HasCategory| |#2| (QUOTE (-1072)))) (-3886 (-12 (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838))))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#2| (QUOTE (-1072))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838))))))
-(-848)
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-1074)))) (-3891 (-12 (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))))
+(-850)
((|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
-(-849)
+(-851)
((|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
-(-850 CF1 CF2)
+(-852 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-851 |ComponentFunction|)
+(-853 |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
-(-852 CF1 CF2)
+(-854 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-853 |ComponentFunction|)
+(-855 |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
-(-854)
+(-856)
((|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
-(-855 CF1 CF2)
+(-857 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-856 |ComponentFunction|)
+(-858 |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
-(-857)
+(-859)
((|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
-(-858 R)
+(-860 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
-(-859 R S L)
+(-861 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
-(-860 S)
+(-862 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
-(-861 |Base| |Subject| |Pat|)
+(-863 |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 (-3671 (|HasCategory| |#2| (QUOTE (-1023)))) (-3671 (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1147)))))) (-12 (|HasCategory| |#2| (QUOTE (-1023))) (-3671 (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1147)))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1147)))))
-(-862 R S)
+((-12 (-3676 (|HasCategory| |#2| (QUOTE (-1025)))) (-3676 (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (-3676 (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))))
+(-864 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
-(-863 R A B)
+(-865 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
-(-864 R)
+(-866 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
-(-865 R -2997)
+(-867 R -3002)
((|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
-(-866 R S)
+(-868 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
-(-867 |VarSet|)
+(-869 |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
-(-868 UP R)
+(-870 UP R)
((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented")))
NIL
NIL
-(-869)
+(-871)
((|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
-(-870 UP -3423)
+(-872 UP -3428)
((|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
-(-871)
+(-873)
((|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
-(-872)
+(-874)
((|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| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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
-(-873 A S)
+(-875 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
-(-874 S)
+(-876 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}.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-875 S)
+(-877 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}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-876 S)
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-878 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation.")))
-((-4345 . T))
-((-3886 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-825))))
-(-877 |n| R)
+((-4350 . T))
+((-3891 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-827)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-827))))
+(-879 |n| R)
((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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
-(-878 S)
+(-880 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.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-879 S)
+(-881 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
-(-880 |p|)
+(-882 |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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-361))))
-(-881 R E |VarSet| S)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-363))))
+(-883 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
-(-882 R S)
+(-884 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
-(-883 S)
+(-885 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 (-143))))
-(-884)
+(-886)
((|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}.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-885 R0 -3423 UP UPUP R)
+(-887 R0 -3428 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
-(-886 UP UPUP R)
+(-888 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
-(-887 UP UPUP)
+(-889 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
-(-888 R)
+(-890 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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-889 R)
+(-891 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
-(-890 E OV R P)
+(-892 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
-(-891)
+(-893)
((|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
-(-892 -3423)
+(-894 -3428)
((|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
-(-893)
+(-895)
((|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}.")))
-(((-4350 "*") . T))
+(((-4355 "*") . T))
NIL
-(-894 R)
+(-896 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
-(-895)
+(-897)
((|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)}")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-896 |xx| -3423)
+(-898 |xx| -3428)
((|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
-(-897 -3423 P)
+(-899 -3428 P)
((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented")))
NIL
NIL
-(-898 R |Var| |Expon| GR)
+(-900 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
-(-899)
+(-901)
((|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
-(-900 S)
+(-902 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
-(-901)
+(-903)
((|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
-(-902)
+(-904)
((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented")))
NIL
NIL
-(-903)
+(-905)
((|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|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}.")))
NIL
NIL
-(-904 R -3423)
+(-906 R -3428)
((|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| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol.")))
NIL
NIL
-(-905 S A B)
+(-907 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
-(-906 S R -3423)
+(-908 S R -3428)
((|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
-(-907 I)
+(-909 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
-(-908 S E)
+(-910 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
-(-909 S R L)
+(-911 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
-(-910 S E V R P)
+(-912 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 -860) (|devaluate| |#1|))))
-(-911 -2997)
+((|HasCategory| |#3| (LIST (QUOTE -862) (|devaluate| |#1|))))
+(-913 -3002)
((|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
-(-912 R -3423 -2997)
+(-914 R -3428 -3002)
((|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
-(-913 S R Q)
+(-915 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
-(-914 S)
+(-916 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
-(-915 S R P)
+(-917 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
-(-916)
+(-918)
((|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
-(-917 R)
+(-919 R)
((|constructor| (NIL "This domain implements points in coordinate space")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1023))) (-12 (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1023)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-918 |lv| R)
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-920 |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
-(-919 |TheField| |ThePols|)
+(-921 |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 (-823))))
-(-920 R)
+((|HasCategory| |#1| (QUOTE (-825))))
+(-922 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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-884))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-884)))) (-3886 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-884)))) (-3886 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-884)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-170))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-1147) (LIST (QUOTE -860) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-1147) (LIST (QUOTE -860) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-1147) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-1147) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-1147) (LIST (QUOTE -596) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-356))) (-3886 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasAttribute| |#1| (QUOTE -4346)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))))
-(-921 R S)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-886))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1149) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1149) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1149) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1149) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1149) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-923 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
-(-922 |x| R)
+(-924 |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
-(-923 S R E |VarSet|)
+(-925 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 (-884))) (|HasAttribute| |#2| (QUOTE -4346)) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| |#4| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| |#4| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| |#4| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-825))))
-(-924 R E |VarSet|)
+((|HasCategory| |#2| (QUOTE (-886))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#4| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#4| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#4| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-827))))
+(-926 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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
NIL
-(-925 E V R P -3423)
+(-927 E V R P -3428)
((|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
-(-926 E |Vars| R P S)
+(-928 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
-(-927 E V R P -3423)
+(-929 E V R P -3428)
((|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)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented")))
NIL
-((|HasCategory| |#3| (QUOTE (-444))))
-(-928)
+((|HasCategory| |#3| (QUOTE (-446))))
+(-930)
((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}.")))
NIL
NIL
-(-929)
+(-931)
((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}.")))
NIL
NIL
-(-930 R E)
+(-932 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-6 -4346)) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-543))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-130)))) (-3886 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasAttribute| |#1| (QUOTE -4346)))
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((|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
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((|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")))
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((|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
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((|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
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((|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
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((|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
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((|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
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((|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")))
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((|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| (($ (|Symbol|) (|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| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}")))
NIL
NIL
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((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|equivOperands| (((|Pair| $ $) $) "\\spad{equivOperands p} extracts the operands to the logical equivalence; otherwise errors.")) (|equiv?| (((|Boolean|) $) "\\spad{equiv? p} is \\spad{true} when \\spad{`p'} is a logical equivalence.")) (|impliesOperands| (((|Pair| $ $) $) "\\spad{impliesOperands p} extracts the operands to the logical implication; otherwise errors.")) (|implies?| (((|Boolean|) $) "\\spad{implies? p} is \\spad{true} when \\spad{`p'} is a logical implication.")) (|orOperands| (((|Pair| $ $) $) "\\spad{orOperands p} extracts the operands to the logical disjunction; otherwise errors.")) (|or?| (((|Boolean|) $) "\\spad{or? p} is \\spad{true} when \\spad{`p'} is a logical disjunction.")) (|andOperands| (((|Pair| $ $) $) "\\spad{andOperands p} extracts the operands of the logical conjunction; otherwise errors.")) (|and?| (((|Boolean|) $) "\\spad{and? p} is \\spad{true} when \\spad{`p'} is a logical conjunction.")) (|notOperand| (($ $) "\\spad{notOperand returns} the operand to the logical `not' operator; otherwise errors.")) (|not?| (((|Boolean|) $) "\\spad{not? p} is \\spad{true} when \\spad{`p'} is a logical negation")) (|variable| (((|Symbol|) $) "\\spad{variable p} extracts the variable name from \\spad{`p'}; otherwise errors.")) (|variable?| (((|Boolean|) $) "variables? \\spad{p} returns \\spad{true} when \\spad{`p'} really is a variable.")) (|term| ((|#1| $) "\\spad{term p} extracts the term value from \\spad{`p'}; otherwise errors.")) (|term?| (((|Boolean|) $) "\\spad{term? p} returns \\spad{true} when \\spad{`p'} really is a term")) (|variables| (((|Set| (|Symbol|)) $) "\\spad{variables(p)} returns the set of propositional variables appearing in the proposition \\spad{`p'}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional variable.") (($ |#1|) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional formula")))
NIL
NIL
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((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}.")))
NIL
NIL
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((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}.")))
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NIL
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((|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 (-444))))
-(-944)
+((|HasCategory| |#1| (QUOTE (-446))))
+(-946)
((|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
-(-945)
+(-947)
((|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}.")) (|coerce| (((|List| (|Integer|)) $) "\\spad{coerce(p)} coerces a partition into a list of integers")) (|conjugate| (($ $) "\\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
-(-946 S |Coef| |Expon| |Var|)
+(-948 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
-(-947 |Coef| |Expon| |Var|)
+(-949 |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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-948)
+(-950)
((|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
-(-949 S R E |VarSet| P)
+(-951 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 (-543))))
-(-950 R E |VarSet| P)
+((|HasCategory| |#2| (QUOTE (-545))))
+(-952 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.")))
-((-4348 . T) (-2363 . T))
+((-4353 . T) (-2368 . T))
NIL
-(-951 R E V P)
+(-953 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 (-145))) (|HasCategory| |#1| (QUOTE (-300)))) (|HasCategory| |#1| (QUOTE (-444))))
-(-952 K)
+((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-302)))) (|HasCategory| |#1| (QUOTE (-446))))
+(-954 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
-(-953 |VarSet| E RC P)
+(-955 |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
-(-954 R)
+(-956 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| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|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}.")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-955 R1 R2)
+(-957 R1 R2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented")))
NIL
NIL
-(-956 R)
+(-958 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
-(-957 K)
+(-959 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
-(-958 R E OV PPR)
+(-960 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
-(-959 K R UP -3423)
+(-961 K R UP -3428)
((|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
-(-960 R |Var| |Expon| |Dpoly|)
+(-962 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|) #1="failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-300)))))
-(-961 |vl| |nv|)
+((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-302)))))
+(-963 |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
-(-962 R E V P TS)
+(-964 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
-(-963)
+(-965)
((|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
-(-964 A S)
+(-966 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 (-884))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1147)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-994))) (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1122))))
-(-965 S)
+((|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-800))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1124))))
+(-967 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}.")))
-((-2363 . T) (-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-2368 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-966 A B R S)
+(-968 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
-(-967 |n| K)
+(-969 |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
-(-968)
+(-970)
((|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
-(-969 S)
+(-971 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.")))
-((-4348 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4354 . T) (-2368 . T))
NIL
-(-970 R)
+(-972 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.}")))
-((-4341 |has| |#1| (-283)) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-356))) (-3886 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1147)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-535))) (-3886 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))))
-(-971 S R)
+((-4346 |has| |#1| (-285)) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-285))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-285))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-537))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))))
+(-973 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 (-535))) (|HasCategory| |#2| (QUOTE (-1032))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-283))))
-(-972 R)
+((|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-285))))
+(-974 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}.")))
-((-4341 |has| |#1| (-283)) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 |has| |#1| (-285)) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-973 QR R QS S)
+(-975 QR R QS S)
((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}.")))
NIL
NIL
-(-974 S)
+(-976 S)
((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-975 S)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-977 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
NIL
NIL
-(-976)
+(-978)
((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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
-(-977 -3423 UP UPUP |radicnd| |n|)
+(-979 -3428 UP UPUP |radicnd| |n|)
((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x}).")))
-((-4341 |has| (-400 |#2|) (-356)) (-4346 |has| (-400 |#2|) (-356)) (-4340 |has| (-400 |#2|) (-356)) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-343))) (-3886 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-343)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-3886 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-343)))) (-3886 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1147))))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-343))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1147)))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-3886 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1147))))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))))
-(-978 |bb|)
+((-4346 |has| (-402 |#2|) (-358)) (-4351 |has| (-402 |#2|) (-358)) (-4345 |has| (-402 |#2|) (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| (-402 |#2|) (QUOTE (-143))) (|HasCategory| (-402 |#2|) (QUOTE (-145))) (|HasCategory| (-402 |#2|) (QUOTE (-345))) (-3891 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-345)))) (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-363))) (-3891 (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (|HasCategory| (-402 |#2|) (QUOTE (-345)))) (-3891 (-12 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-345))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363))) (-3891 (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))))
+(-980 |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.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| (-536) (QUOTE (-884))) (|HasCategory| (-536) (LIST (QUOTE -1012) (QUOTE (-1147)))) (|HasCategory| (-536) (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-145))) (|HasCategory| (-536) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-536) (QUOTE (-994))) (|HasCategory| (-536) (QUOTE (-798))) (-3886 (|HasCategory| (-536) (QUOTE (-798))) (|HasCategory| (-536) (QUOTE (-825)))) (|HasCategory| (-536) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-536) (QUOTE (-1122))) (|HasCategory| (-536) (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-536) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-536) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-536) (QUOTE (-227))) (|HasCategory| (-536) (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| (-536) (LIST (QUOTE -505) (QUOTE (-1147)) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -302) (QUOTE (-536)))) (|HasCategory| (-536) (LIST (QUOTE -279) (QUOTE (-536)) (QUOTE (-536)))) (|HasCategory| (-536) (QUOTE (-300))) (|HasCategory| (-536) (QUOTE (-535))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-536) (LIST (QUOTE -619) (QUOTE (-536)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-884)))) (-3886 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-536) (QUOTE (-884)))) (|HasCategory| (-536) (QUOTE (-143)))))
-(-979)
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| (-538) (QUOTE (-886))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-538) (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-145))) (|HasCategory| (-538) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-996))) (|HasCategory| (-538) (QUOTE (-800))) (-3891 (|HasCategory| (-538) (QUOTE (-800))) (|HasCategory| (-538) (QUOTE (-827)))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-1124))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-538) (QUOTE (-229))) (|HasCategory| (-538) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-538) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -304) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -281) (QUOTE (-538)) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-302))) (|HasCategory| (-538) (QUOTE (-537))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-538) (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (|HasCategory| (-538) (QUOTE (-143)))))
+(-981)
((|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
-(-980)
+(-982)
((|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
-(-981 RP)
+(-983 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
-(-982 S)
+(-984 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
-(-983 A S)
+(-985 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 -4349)) (|HasCategory| |#2| (QUOTE (-1072))))
-(-984 S)
+((|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (QUOTE (-1074))))
+(-986 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}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-985 S)
+(-987 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
-(-986)
+(-988)
((|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}}")))
-((-4341 . T) (-4346 . T) (-4340 . T) (-4343 . T) (-4342 . T) ((-4350 "*") . T) (-4345 . T))
+((-4346 . T) (-4351 . T) (-4345 . T) (-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4350 . T))
NIL
-(-987 R -3423)
+(-989 R -3428)
((|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
-(-988 R -3423)
+(-990 R -3428)
((|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
-(-989 -3423 UP)
+(-991 -3428 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
-(-990 -3423 UP)
+(-992 -3428 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
-(-991 S)
+(-993 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
-(-992 F1 UP UPUP R F2)
+(-994 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
-(-993)
+(-995)
((|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
-(-994)
+(-996)
((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats.")))
NIL
NIL
-(-995 |Pol|)
+(-997 |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
-(-996 |Pol|)
+(-998 |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
-(-997)
+(-999)
((|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
-(-998 |TheField|)
+(-1000 |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")))
-((-4341 . T) (-4346 . T) (-4340 . T) (-4343 . T) (-4342 . T) ((-4350 "*") . T) (-4345 . T))
-((-3886 (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-400 (-536)) (LIST (QUOTE -1012) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-400 (-536)) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| (-400 (-536)) (LIST (QUOTE -1012) (QUOTE (-536)))))
-(-999 -3423 L)
+((-4346 . T) (-4351 . T) (-4345 . T) (-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4350 . T))
+((-3891 (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-402 (-538)) (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-402 (-538)) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-402 (-538)) (LIST (QUOTE -1014) (QUOTE (-538)))))
+(-1001 -3428 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
-(-1000 S)
+(-1002 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 (-1072))))
-(-1001 R E V P)
+((|HasCategory| |#1| (QUOTE (-1074))))
+(-1003 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.")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1002)
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1004)
((|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
-(-1003 R)
+(-1005 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 (-4350 "*"))))
-(-1004 R)
+((|HasAttribute| |#1| (QUOTE (-4355 "*"))))
+(-1006 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 (-356))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-300))))
-(-1005 S)
+((-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-302))))
+(-1007 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.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}")))
NIL
NIL
-(-1006 S)
+(-1008 S)
((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}")))
NIL
NIL
-(-1007 S)
+(-1009 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
-(-1008 -3423 |Expon| |VarSet| |FPol| |LFPol|)
+(-1010 -3428 |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")))
-(((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1009)
+(-1011)
((|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.}")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (QUOTE (-1147))) (LIST (QUOTE |:|) (QUOTE -2186) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (QUOTE (-1072)))) (-3886 (|HasCategory| (-51) (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-51) (QUOTE (-1072))) (|HasCategory| (-51) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| (-51) (QUOTE (-1072))) (|HasCategory| (-51) (LIST (QUOTE -302) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (QUOTE (-1072))) (|HasCategory| (-1147) (QUOTE (-825))) (|HasCategory| (-51) (QUOTE (-1072))) (-3886 (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-51) (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| (-51) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1010)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (QUOTE (-1149))) (LIST (QUOTE |:|) (QUOTE -2191) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -304) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074))) (|HasCategory| (-1149) (QUOTE (-827))) (|HasCategory| (-51) (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1012)
((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'.")))
NIL
NIL
-(-1011 A S)
+(-1013 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") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%.")))
NIL
NIL
-(-1012 S)
+(-1014 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") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#1|) "\\spad{coerce(a)} transforms a into an element of \\%.")))
NIL
NIL
-(-1013 Q R)
+(-1015 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
-(-1014 R)
+(-1016 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
-(-1015)
+(-1017)
((|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
-(-1016 UP)
+(-1018 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
-(-1017 R)
+(-1019 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
-(-1018 T$)
+(-1020 T$)
((|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| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}.")))
NIL
NIL
-(-1019 T$)
+(-1021 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
-(-1020 R |ls|)
+(-1022 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}.")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| (-758 |#1| (-839 |#2|)) (QUOTE (-1072))) (|HasCategory| (-758 |#1| (-839 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -758) (|devaluate| |#1|) (LIST (QUOTE -839) (|devaluate| |#2|)))))) (|HasCategory| (-758 |#1| (-839 |#2|)) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-758 |#1| (-839 |#2|)) (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| (-839 |#2|) (QUOTE (-361))) (|HasCategory| (-758 |#1| (-839 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1021)
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| (-760 |#1| (-841 |#2|)) (QUOTE (-1074))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -760) (|devaluate| |#1|) (LIST (QUOTE -841) (|devaluate| |#2|)))))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-760 |#1| (-841 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| (-841 |#2|) (QUOTE (-363))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1023)
((|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
-(-1022 S)
+(-1024 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\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|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
-(-1023)
+(-1025)
((|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\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|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.")))
-((-4345 . T))
+((-4350 . T))
NIL
-(-1024 |xx| -3423)
+(-1026 |xx| -3428)
((|constructor| (NIL "This package exports rational interpolation algorithms")))
NIL
NIL
-(-1025 S |m| |n| R |Row| |Col|)
+(-1027 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 (-300))) (|HasCategory| |#4| (QUOTE (-356))) (|HasCategory| |#4| (QUOTE (-543))) (|HasCategory| |#4| (QUOTE (-170))))
-(-1026 |m| |n| R |Row| |Col|)
+((|HasCategory| |#4| (QUOTE (-302))) (|HasCategory| |#4| (QUOTE (-358))) (|HasCategory| |#4| (QUOTE (-545))) (|HasCategory| |#4| (QUOTE (-170))))
+(-1028 |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")))
-((-4348 . T) (-2363 . T) (-4343 . T) (-4342 . T))
+((-4353 . T) (-2368 . T) (-4348 . T) (-4347 . T))
NIL
-(-1027 |m| |n| R)
+(-1029 |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.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}.")))
-((-4348 . T) (-4343 . T) (-4342 . T))
-((-3886 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1072))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356)))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-1072))) (|HasCategory| |#3| (QUOTE (-300))) (|HasCategory| |#3| (QUOTE (-543))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -595) (QUOTE (-838)))) (-12 (|HasCategory| |#3| (QUOTE (-1072))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))))
-(-1028 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
+((-4353 . T) (-4348 . T) (-4347 . T))
+((-3891 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-358))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-358)))) (|HasCategory| |#3| (QUOTE (-358))) (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (QUOTE (-302))) (|HasCategory| |#3| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -597) (QUOTE (-840)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))))
+(-1030 |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
-(-1029 R)
+(-1031 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}.")))
NIL
NIL
-(-1030)
+(-1032)
((|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
-(-1031 S)
+(-1033 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value.")))
NIL
NIL
-(-1032)
+(-1034)
((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1033 |TheField| |ThePolDom|)
+(-1035 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval")))
NIL
NIL
-(-1034)
+(-1036)
((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(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.")))
-((-4336 . T) (-4340 . T) (-4335 . T) (-4346 . T) (-4347 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4341 . T) (-4345 . T) (-4340 . T) (-4351 . T) (-4352 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1035)
+(-1037)
((|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}")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (QUOTE (-1147))) (LIST (QUOTE |:|) (QUOTE -2186) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (QUOTE (-1072)))) (-3886 (|HasCategory| (-51) (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-51) (QUOTE (-1072))) (|HasCategory| (-51) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| (-51) (QUOTE (-1072))) (|HasCategory| (-51) (LIST (QUOTE -302) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (QUOTE (-1072))) (|HasCategory| (-1147) (QUOTE (-825))) (|HasCategory| (-51) (QUOTE (-1072))) (-3886 (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-51) (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| (-51) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 (-1147)) (|:| -2186 (-51))) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1036 S R E V)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (QUOTE (-1149))) (LIST (QUOTE |:|) (QUOTE -2191) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -304) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074))) (|HasCategory| (-1149) (QUOTE (-827))) (|HasCategory| (-51) (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1038 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -965) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-1147)))))
-(-1037 R E V)
+((|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-1149)))))
+(-1039 R E V)
((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
NIL
-(-1038)
+(-1040)
((|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
-(-1039 S |TheField| |ThePols|)
+(-1041 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
-(-1040 |TheField| |ThePols|)
+(-1042 |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
-(-1041 R E V P TS)
+(-1043 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
-(-1042 S R E V P)
+(-1044 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
-(-1043 R E V P)
+(-1045 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}.")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-1044 R E V P TS)
+(-1046 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
-(-1045)
+(-1047)
((|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
-(-1046 |Base| R -3423)
+(-1048 |Base| R -3428)
((|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
-(-1047 |f|)
+(-1049 |f|)
((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-1048 |Base| R -3423)
+(-1050 |Base| R -3428)
((|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
-(-1049 R |ls|)
+(-1051 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
-(-1050 R UP M)
+(-1052 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.")))
-((-4341 |has| |#1| (-356)) (-4346 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-343))) (-3886 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-343)))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147))))) (-3886 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))))
-(-1051 UP SAE UPA)
+((-4346 |has| |#1| (-358)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-345))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-345)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-345)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#1| (QUOTE (-345))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358)))))
+(-1053 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
-(-1052 UP SAE UPA)
+(-1054 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
-(-1053)
+(-1055)
((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable")))
NIL
NIL
-(-1054)
+(-1056)
((|constructor| (NIL "This is the category of Spad syntax objects.")))
NIL
NIL
-(-1055 S)
+(-1057 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
-(-1056)
+(-1058)
((|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| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(n,{}s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `failed'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope.")))
NIL
NIL
-(-1057 R)
+(-1059 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
-(-1058 R)
+(-1060 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")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-884))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-884)))) (-3886 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-884)))) (-3886 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-884)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-170))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| (-1059 (-1147)) (LIST (QUOTE -860) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| (-1059 (-1147)) (LIST (QUOTE -860) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| (-1059 (-1147)) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| (-1059 (-1147)) (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-1059 (-1147)) (LIST (QUOTE -596) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| |#1| (QUOTE (-356))) (-3886 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasAttribute| |#1| (QUOTE -4346)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))))
-(-1059 S)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-886))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-1061 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
-(-1060 S)
+(-1062 S)
((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1072))))
-(-1061 R S)
+((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1074))))
+(-1063 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 (-823))))
-(-1062)
+((|HasCategory| |#1| (QUOTE (-825))))
+(-1064)
((|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
-(-1063 S)
+(-1065 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 (-1072))))
-(-1064 R S)
+((|HasCategory| |#1| (QUOTE (-1074))))
+(-1066 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
-(-1065 S)
+(-1067 S)
((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|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.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-1066 S L)
+(-1068 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]}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-1067)
+(-1069)
((|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
-(-1068 S)
+(-1070 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)}}")))
-((-4348 . T) (-4338 . T) (-4349 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-825))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1069 A S)
+((-4353 . T) (-4343 . T) (-4354 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1071 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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}.")))
NIL
NIL
-(-1070 S)
+(-1072 S)
((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}.")))
-((-4338 . T) (-2363 . T))
+((-4343 . T) (-2368 . T))
NIL
-(-1071 S)
+(-1073 S)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
NIL
NIL
-(-1072)
+(-1074)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
NIL
NIL
-(-1073 |m| |n|)
+(-1075 |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| $ #1="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| $ #1#) $ (|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
-(-1074)
+(-1076)
((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values.")))
NIL
NIL
-(-1075 |Str| |Sym| |Int| |Flt| |Expr|)
+(-1077 |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|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|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|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp.")))
NIL
NIL
-(-1076 |Str| |Sym| |Int| |Flt| |Expr|)
+(-1078 |Str| |Sym| |Int| |Flt| |Expr|)
((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types.")))
NIL
NIL
-(-1077 R FS)
+(-1079 R FS)
((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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
-(-1078 R E V P TS)
+(-1080 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
-(-1079 R E V P TS)
+(-1081 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
-(-1080 R E V P)
+(-1082 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.}")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-1081)
+(-1083)
((|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
-(-1082 S)
+(-1084 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-1083)
+(-1085)
((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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
-(-1084 |dimtot| |dim1| S)
+(-1086 |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}.")))
-((-4342 |has| |#3| (-1023)) (-4343 |has| |#3| (-1023)) (-4345 |has| |#3| (-6 -4345)) ((-4350 "*") |has| |#3| (-170)) (-4348 . T))
-((-3886 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-705))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-771))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-823))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1072))) (|HasCategory| |#3| (LIST (QUOTE 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|#3| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#3| (QUOTE (-356))) (-3886 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-1023)))) (-3886 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356)))) (|HasCategory| |#3| (QUOTE (-1023))) (|HasCategory| |#3| (QUOTE (-771))) (-3886 (|HasCategory| |#3| (QUOTE (-771))) (|HasCategory| |#3| (QUOTE (-823)))) (|HasCategory| |#3| (QUOTE (-823))) (|HasCategory| |#3| (QUOTE (-705))) (|HasCategory| |#3| (QUOTE (-170))) (-3886 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-1023)))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -874) (QUOTE (-1147)))) (-3886 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-361))) 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-(-1085 R |x|)
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(-538))))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538)))))) (|HasCategory| (-538) (QUOTE (-827))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#3| (QUOTE (-229))) (|HasCategory| |#3| (QUOTE (-1025)))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538))))) (-3891 (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#3| (QUOTE (-1025)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#3| (QUOTE -4350)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1087 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 (-444))))
-(-1086)
+((|HasCategory| |#1| (QUOTE (-446))))
+(-1088)
((|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
-(-1087)
+(-1089)
((|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
-(-1088 R -3423)
+(-1090 R -3428)
((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere.")))
NIL
NIL
-(-1089 R)
+(-1091 R)
((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere.")))
NIL
NIL
-(-1090)
+(-1092)
((|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
-(-1091)
+(-1093)
((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|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.")))
-((-4336 . T) (-4340 . T) (-4335 . T) (-4346 . T) (-4347 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4341 . T) (-4345 . T) (-4340 . T) (-4351 . T) (-4352 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1092 S)
+(-1094 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.")))
-((-4348 . T) (-4349 . T) (-2363 . T))
+((-4353 . T) (-4354 . T) (-2368 . T))
NIL
-(-1093 S |ndim| R |Row| |Col|)
+(-1095 S |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-356))) (|HasAttribute| |#3| (QUOTE (-4350 "*"))) (|HasCategory| |#3| (QUOTE (-170))))
-(-1094 |ndim| R |Row| |Col|)
+((|HasCategory| |#3| (QUOTE (-358))) (|HasAttribute| |#3| (QUOTE (-4355 "*"))) (|HasCategory| |#3| (QUOTE (-170))))
+(-1096 |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.")))
-((-2363 . T) (-4348 . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-2368 . T) (-4353 . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1095 R |Row| |Col| M)
+(-1097 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
-(-1096 R |VarSet|)
+(-1098 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.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-884))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-884)))) (-3886 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-884)))) (-3886 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-884)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-170))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-371)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-371)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (QUOTE (-536)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-356))) (-3886 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasAttribute| |#1| (QUOTE -4346)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-884))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))))
-(-1097 |Coef| |Var| SMP)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-886))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-1099 |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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-356))))
-(-1098 R E V P)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-358))))
+(-1100 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}")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-1099 UP -3423)
+(-1101 UP -3428)
((|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
-(-1100 R)
+(-1102 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
-(-1101 R)
+(-1103 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
-(-1102 R)
+(-1104 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
-(-1103 S A)
+(-1105 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 (-825))))
-(-1104 R)
+((|HasCategory| |#1| (QUOTE (-827))))
+(-1106 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
-(-1105 R)
+(-1107 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
-(-1106)
+(-1108)
((|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
-(-1107)
+(-1109)
((|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
-(-1108)
+(-1110)
((|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.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-1109)
+(-1111)
((|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
-(-1110)
+(-1112)
((|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
-(-1111 V C)
+(-1113 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
-(-1112 V C)
+(-1114 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| (-1111 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1111) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1111 |#1| |#2|) (QUOTE (-1072)))) (|HasCategory| (-1111 |#1| |#2|) (QUOTE (-1072))) (-3886 (-12 (|HasCategory| (-1111 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1111) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1111 |#1| |#2|) (QUOTE (-1072)))) (|HasCategory| (-1111 |#1| |#2|) (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| (-1111 |#1| |#2|) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1113 |ndim| R)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -304) (LIST (QUOTE -1113) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1074)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1074))) (-3891 (-12 (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -304) (LIST (QUOTE -1113) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1074)))) (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1115 |ndim| R)
((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}.")))
-((-4345 . T) (-4337 |has| |#2| (-6 (-4350 "*"))) (-4348 . T) (-4342 . T) (-4343 . T))
-((|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4350 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-536)))) (-3886 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1147)))))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (QUOTE (-356))) (-3886 (|HasAttribute| |#2| (QUOTE (-4350 "*"))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1147))))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-170))))
-(-1114 S)
+((-4350 . T) (-4342 |has| |#2| (-6 (-4355 "*"))) (-4353 . T) (-4347 . T) (-4348 . T))
+((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-358))) (-3891 (|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-170))))
+(-1116 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
NIL
NIL
-(-1115)
+(-1117)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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.")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-1116 R E V P TS)
+(-1118 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
-(-1117 R E V P)
+(-1119 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.")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1118 S)
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1120 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}.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1119 A S)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1121 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
-(-1120 S)
+(-1122 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})}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-1121 |Key| |Ent| |dent|)
+(-1123 |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.")))
-((-4349 . T))
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-(-1122)
+((-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-827))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1124)
((|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
-(-1123 |Coef|)
+(-1125 |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
-(-1124 S)
+(-1126 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}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries.")))
-((-4349 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1125 S)
+((-4354 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1127 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
-(-1126 A B)
+(-1128 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
-(-1127 A B C)
+(-1129 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
-(-1128)
+(-1130)
((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-1129)
+(-1131)
NIL
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1072))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1072))) (-12 (|HasCategory| (-142) (QUOTE (-1072))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1130 |Entry|)
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1074))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1132 |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used.")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (QUOTE (-1129))) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (QUOTE (-1072)))) (-3886 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (QUOTE (-1072))) (|HasCategory| (-1129) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 (-1129)) (|:| -2186 |#1|)) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1131 A)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (QUOTE (-1131))) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074))) (|HasCategory| (-1131) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1133 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 (-356))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))))
-(-1132 |Coef|)
+((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))))
+(-1134 |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
-(-1133 |Coef|)
+(-1135 |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
-(-1134 R UP)
+(-1136 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 (-300))))
-(-1135 |n| R)
+((|HasCategory| |#1| (QUOTE (-302))))
+(-1137 |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
-(-1136 S1 S2)
+(-1138 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
-(-1137)
+(-1139)
((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'.")))
NIL
NIL
-(-1138 |Coef| |var| |cen|)
+(-1140 |Coef| |var| |cen|)
((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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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((|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
-(-1140 R)
+(-1142 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
-(-1141 R)
+(-1143 R)
((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable.")))
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-(-1142 R S)
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+(-1144 R S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
-(-1143 E OV R P)
+(-1145 E OV R P)
((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}.")))
NIL
NIL
-(-1144 |Coef| |var| |cen|)
+(-1146 |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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series.")))
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-(-1145 |Coef| |var| |cen|)
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+(-1147 |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}.")))
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+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|)))) (|HasCategory| (-751) (QUOTE (-1085))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|)))))))
+(-1148)
((|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
-(-1147)
+(-1149)
((|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|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts the string \\spad{s} to a symbol.")) (|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
-(-1148 R)
+(-1150 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
-(-1149 R)
+(-1151 R)
((|constructor| (NIL "This domain implements symmetric polynomial")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-6 -4346)) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-543))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| (-945) (QUOTE (-130)))) (-3886 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasAttribute| |#1| (QUOTE -4346)))
-(-1150)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| (-947) (QUOTE (-130)))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)))
+(-1152)
((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table.")))
NIL
NIL
-(-1151)
+(-1153)
((|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
-(-1152)
+(-1154)
((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} building complete representation of Spad programs as objects of a term algebra built from ground terms of type integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity in a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} Symbol,{} String,{} SExpression. See Also: SExpression,{} SetCategory. 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|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} if \\spad{`x'} really is a Symbol") (((|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|) (|Symbol|) (|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| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|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.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo 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|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (($ (|String|)) "\\spad{coerce(s)} injects the string value \\spad{`s'} into the syntax domain") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (($ (|Symbol|)) "\\spad{coerce(s)} injects the symbol \\spad{`s'} into the Syntax domain.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (($ (|DoubleFloat|)) "\\spad{coerce(f)} injects the float value \\spad{`f'} into the Syntax domain") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}") (($ (|Integer|)) "\\spad{coerce(i)} injects the integer value `i' into the Syntax domain.")) (|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
-(-1153 R)
+(-1155 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
-(-1154)
+(-1156)
((|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()} returns a string representation of a filename extension for native modules.")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform()} returns 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
-(-1155 S)
+(-1157 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
-(-1156 |Key| |Entry|)
+(-1158 |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}")))
-((-4348 . T) (-4349 . T))
-((-12 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4215) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2186) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -596) (QUOTE (-525)))) (-12 (|HasCategory| |#2| (QUOTE (-1072))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1072))) (-3886 (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-838)))) (|HasCategory| (-2 (|:| -4215 |#1|) (|:| -2186 |#2|)) (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1157 S)
+((-4353 . T) (-4354 . T))
+((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1159 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
-(-1158 R)
+(-1160 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
-(-1159 S |Key| |Entry|)
+(-1161 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
-(-1160 |Key| |Entry|)
+(-1162 |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})}.")))
-((-4349 . T) (-2363 . T))
+((-4354 . T) (-2368 . T))
NIL
-(-1161 |Key| |Entry|)
+(-1163 |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
-(-1162)
+(-1164)
((|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
-(-1163)
+(-1165)
((|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.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format.")))
NIL
NIL
-(-1164 S)
+(-1166 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
-(-1165)
+(-1167)
((|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
-(-1166 R)
+(-1168 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
-(-1167)
+(-1169)
((|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
-(-1168 S)
+(-1170 S)
((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}.")))
NIL
NIL
-(-1169)
+(-1171)
((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}.")))
NIL
NIL
-(-1170 S)
+(-1172 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}.")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1072))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1171 S)
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1173 S)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1172)
+(-1174)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1173 R -3423)
+(-1175 R -3428)
((|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
-(-1174 R |Row| |Col| M)
+(-1176 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
-(-1175 R -3423)
+(-1177 R -3428)
((|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 -596) (LIST (QUOTE -864) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -860) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -864) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -860) (|devaluate| |#1|)))))
-(-1176 |Coef|)
+((-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -862) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -862) (|devaluate| |#1|)))))
+(-1178 |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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-356))))
-(-1177 S R E V P)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-358))))
+(-1179 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 (-361))))
-(-1178 R E V P)
+((|HasCategory| |#4| (QUOTE (-363))))
+(-1180 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-1179 |Curve|)
+(-1181 |Curve|)
((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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
-(-1180)
+(-1182)
((|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
-(-1181 S)
+(-1183 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")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a")))
NIL
-((|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1182 -3423)
+((|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1184 -3428)
((|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
-(-1183)
+(-1185)
((|constructor| (NIL "The fundamental Type.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-1184)
+(-1186)
((|constructor| (NIL "This domain represents a type AST.")))
NIL
NIL
-(-1185 S)
+(-1187 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 (-825))))
-(-1186)
+((|HasCategory| |#1| (QUOTE (-827))))
+(-1188)
((|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
-(-1187 S)
+(-1189 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
-(-1188)
+(-1190)
((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element.")))
-((-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1189 |Coef| |var| |cen|)
+(-1191 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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.")))
-(((-4350 "*") -3886 (-3186 (|has| |#1| (-356)) (|has| (-1219 |#1| |#2| |#3|) (-798))) (|has| |#1| (-170)) (-3186 (|has| |#1| (-356)) (|has| (-1219 |#1| |#2| |#3|) (-884)))) (-4341 -3886 (-3186 (|has| |#1| (-356)) (|has| (-1219 |#1| |#2| |#3|) (-798))) (|has| |#1| (-543)) (-3186 (|has| |#1| (-356)) (|has| (-1219 |#1| |#2| |#3|) (-884)))) (-4346 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) (-4342 . T) (-4343 . T) (-4345 . T))
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|#2| |#3|) (LIST (QUOTE -505) (QUOTE (-1147)) (LIST (QUOTE -1219) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -619) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -860) (QUOTE (-371))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -860) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -1012) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -1012) (QUOTE (-1147))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-825)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-994)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-1122)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-170))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143)))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-145)))) (|HasCategory| |#1| (QUOTE (-145)))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -874) (QUOTE (-1147))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-536)) (|devaluate| |#1|)))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-227)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-536)) (|devaluate| |#1|))))) (|HasCategory| (-536) (QUOTE (-1083))) (-3886 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-884)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -1012) (QUOTE (-1147))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -596) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-994)))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-798)))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-825))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -1012) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (QUOTE (-1122)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -279) (LIST (QUOTE -1219) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1219) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -302) (LIST (QUOTE -1219) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 |#1| |#2| |#3|) (LIST (QUOTE -505) (QUOTE (-1147)) (LIST (QUOTE -1219) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-1219 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-(-1190 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
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|#1| |#2| |#3|) (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1221 |#1| |#2| |#3|) (QUOTE (-886)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1221 |#1| |#2| |#3|) (QUOTE (-800)))) (|HasCategory| |#1| (QUOTE (-170)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1221 |#1| |#2| |#3|) (QUOTE (-827)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1221 |#1| |#2| |#3|) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1221 |#1| |#2| |#3|) (QUOTE (-143)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1221 |#1| |#2| |#3|) (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-1192 |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
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((|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.")))
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NIL
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((|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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|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 (-356))))
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((|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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}.")))
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NIL
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((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")))
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((|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
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((|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
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((|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
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((|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| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial.")))
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+(-1201 |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
-(-1200 R Q UP)
+(-1202 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
-(-1201 R UP)
+(-1203 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
-(-1202 R UP)
+(-1204 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
-(-1203 R U)
+(-1205 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
-(-1204 S R)
+(-1206 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 -400) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1122))))
-(-1205 R)
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1124))))
+(-1207 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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4344 |has| |#1| (-356)) (-4346 |has| |#1| (-6 -4346)) (-4343 . T) (-4342 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T))
NIL
-(-1206 R PR S PS)
+(-1208 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
-(-1207 S |Coef| |Expon|)
+(-1209 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 -874) (QUOTE (-1147)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1083))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4312) (LIST (|devaluate| |#2|) (QUOTE (-1147))))))
-(-1208 |Coef| |Expon|)
+((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1085))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4317) (LIST (|devaluate| |#2|) (QUOTE (-1149))))))
+(-1210 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1209 RC P)
+(-1211 RC P)
((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}.")))
NIL
NIL
-(-1210 |Coef| |var| |cen|)
+(-1212 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series.")))
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-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-170))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-536)) (QUOTE (-1083))) (|HasCategory| |#1| (QUOTE (-356))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543)))) (-3886 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasSignature| |#1| (LIST (QUOTE -4312) (LIST (|devaluate| |#1|) (QUOTE (-1147)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536)))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasSignature| |#1| (LIST (QUOTE -4167) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1147))))) (|HasSignature| |#1| (LIST (QUOTE -3412) (LIST (LIST (QUOTE -620) (QUOTE (-1147))) (|devaluate| |#1|)))))))
-(-1211 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
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+(-1213 |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
-(-1212 |Coef|)
+(-1214 |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.")))
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+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1213 S |Coef| ULS)
+(-1215 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| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|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
-(-1214 |Coef| ULS)
+(-1216 |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| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|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)}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1215 |Coef| ULS)
+(-1217 |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)}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4346 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) (-4342 . T) (-4343 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-170))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-543)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1147)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-536)) (QUOTE (-1083))) (|HasCategory| |#1| (QUOTE (-356))) (-3886 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543)))) (-3886 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-543)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasSignature| |#1| (LIST (QUOTE -4312) (LIST (|devaluate| |#1|) (QUOTE (-1147)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-536)))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-536))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasSignature| |#1| (LIST (QUOTE -4167) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1147))))) (|HasSignature| |#1| (LIST (QUOTE -3412) (LIST (LIST (QUOTE -620) (QUOTE (-1147))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))))
-(-1216 R FE |var| |cen|)
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+((|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-538)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))))
+(-1218 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))}.")))
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-((|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -1012) (QUOTE (-536)))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-356))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-444))) (-3886 (|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| (-1210 |#2| |#3| |#4|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-536)))))) (|HasCategory| (-1210 |#2| |#3| |#4|) (QUOTE (-543))))
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+(((-4355 "*") |has| (-1212 |#2| |#3| |#4|) (-170)) (-4346 |has| (-1212 |#2| |#3| |#4|) (-545)) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-358))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-446))) (-3891 (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-545))))
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((|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4349)))
-(-1218 S)
+((|HasAttribute| |#1| (QUOTE -4354)))
+(-1220 S)
((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-1219 |Coef| |var| |cen|)
+(-1221 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4342 . T) (-4343 . T) (-4345 . T))
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-(-1220 |Coef1| |Coef2| UTS1 UTS2)
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|)))) (|HasCategory| (-751) (QUOTE (-1085))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|)))))))
+(-1222 |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
-(-1221 S |Coef|)
+(-1223 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 (-536)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-1169))) (|HasSignature| |#2| (LIST (QUOTE -3412) (LIST (LIST (QUOTE -620) (QUOTE (-1147))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4167) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1147))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-356))))
-(-1222 |Coef|)
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-936))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasSignature| |#2| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4172) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1149))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-358))))
+(-1224 |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.")))
-(((-4350 "*") |has| |#1| (-170)) (-4341 |has| |#1| (-543)) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1223 |Coef| UTS)
+(-1225 |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
-(-1224 -3423 UP L UTS)
+(-1226 -3428 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 (-543))))
-(-1225)
+((|HasCategory| |#1| (QUOTE (-545))))
+(-1227)
((|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.")))
-((-2363 . T))
+((-2368 . T))
NIL
-(-1226 |sym|)
+(-1228 |sym|)
((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol")))
NIL
NIL
-(-1227 S R)
+(-1229 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 (-976))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-705))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))))
-(-1228 R)
+((|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-707))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))))
+(-1230 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")))
-((-4349 . T) (-4348 . T) (-2363 . T))
+((-4354 . T) (-4353 . T) (-2368 . T))
NIL
-(-1229 R)
+(-1231 R)
((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector.")))
-((-4349 . T) (-4348 . T))
-((-3886 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-3886 (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-525)))) (-3886 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-536) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1023))) (-12 (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1023)))) (-12 (|HasCategory| |#1| (QUOTE (-1072))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1230 A B)
+((-4354 . T) (-4353 . T))
+((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1232 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
-(-1231)
+(-1233)
((|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
-(-1232)
+(-1234)
((|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
-(-1233)
+(-1235)
((|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
-(-1234)
+(-1236)
((|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
-(-1235)
+(-1237)
((|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.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object.")))
NIL
NIL
-(-1236 A S)
+(-1238 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
-(-1237 S)
+(-1239 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}.")))
-((-4343 . T) (-4342 . T))
+((-4348 . T) (-4347 . T))
NIL
-(-1238 R)
+(-1240 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
-(-1239 K R UP -3423)
+(-1241 K R UP -3428)
((|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
-(-1240)
+(-1242)
((|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
-(-1241)
+(-1243)
((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'.")))
NIL
NIL
-(-1242 R |VarSet| E P |vl| |wl| |wtlevel|)
+(-1244 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights")))
-((-4343 |has| |#1| (-170)) (-4342 |has| |#1| (-170)) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))))
-(-1243 R E V P)
+((-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))))
+(-1245 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}}.")))
-((-4349 . T) (-4348 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-525)))) (|HasCategory| |#4| (QUOTE (-1072))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-838)))))
-(-1244 R)
+((-4354 . T) (-4353 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840)))))
+(-1246 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})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}.")))
-((-4342 . T) (-4343 . T) (-4345 . T))
+((-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1245 |vl| R)
+(-1247 |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.")))
-((-4345 . T) (-4341 |has| |#2| (-6 -4341)) (-4343 . T) (-4342 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4341)))
-(-1246 R |VarSet| XPOLY)
+((-4350 . T) (-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4346)))
+(-1248 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
-(-1247 S -3423)
+(-1249 S -3428)
((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))))
-(-1248 -3423)
+((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))))
+(-1250 -3428)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}.")))
-((-4340 . T) (-4346 . T) (-4341 . T) ((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
-(-1249 |vl| R)
+(-1251 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}.")))
-((-4341 |has| |#2| (-6 -4341)) (-4343 . T) (-4342 . T) (-4345 . T))
+((-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T))
NIL
-(-1250 |VarSet| R)
+(-1252 |VarSet| R)
((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}.")))
-((-4341 |has| |#2| (-6 -4341)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -696) (LIST (QUOTE -400) (QUOTE (-536))))) (|HasAttribute| |#2| (QUOTE -4341)))
-(-1251 R)
+((-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -698) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasAttribute| |#2| (QUOTE -4346)))
+(-1253 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.")))
-((-4341 |has| |#1| (-6 -4341)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasAttribute| |#1| (QUOTE -4341)))
-(-1252 |vl| R)
+((-4346 |has| |#1| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasAttribute| |#1| (QUOTE -4346)))
+(-1254 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}.")))
-((-4341 |has| |#2| (-6 -4341)) (-4343 . T) (-4342 . T) (-4345 . T))
+((-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T))
NIL
-(-1253 R E)
+(-1255 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}.")))
-((-4345 . T) (-4346 |has| |#1| (-6 -4346)) (-4341 |has| |#1| (-6 -4341)) (-4343 . T) (-4342 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasAttribute| |#1| (QUOTE -4345)) (|HasAttribute| |#1| (QUOTE -4346)) (|HasAttribute| |#1| (QUOTE -4341)))
-(-1254 |VarSet| R)
+((-4350 . T) (-4351 |has| |#1| (-6 -4351)) (-4346 |has| |#1| (-6 -4346)) (-4348 . T) (-4347 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasAttribute| |#1| (QUOTE -4350)) (|HasAttribute| |#1| (QUOTE -4351)) (|HasAttribute| |#1| (QUOTE -4346)))
+(-1256 |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.")))
-((-4341 |has| |#2| (-6 -4341)) (-4343 . T) (-4342 . T) (-4345 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4341)))
-(-1255 A)
+((-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4346)))
+(-1257 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
-(-1256 R |ls| |ls2|)
+(-1258 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
-(-1257 R)
+(-1259 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
-(-1258 |p|)
+(-1260 |p|)
((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}.")))
-(((-4350 "*") . T) (-4342 . T) (-4343 . T) (-4345 . T))
+(((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T))
NIL
NIL
NIL
@@ -4980,4 +4988,4 @@ NIL
NIL
NIL
NIL
-((-3 NIL 2266972 2266977 2266982 2266987) (-2 NIL 2266952 2266957 2266962 2266967) (-1 NIL 2266932 2266937 2266942 2266947) (0 NIL 2266912 2266917 2266922 2266927) (-1258 "ZMOD.spad" 2266721 2266734 2266850 2266907) (-1257 "ZLINDEP.spad" 2265765 2265776 2266711 2266716) (-1256 "ZDSOLVE.spad" 2255614 2255636 2265755 2265760) (-1255 "YSTREAM.spad" 2255107 2255118 2255604 2255609) (-1254 "XRPOLY.spad" 2254327 2254347 2254963 2255032) (-1253 "XPR.spad" 2252056 2252069 2254045 2254144) (-1252 "XPOLYC.spad" 2251373 2251389 2251982 2252051) (-1251 "XPOLY.spad" 2250928 2250939 2251229 2251298) (-1250 "XPBWPOLY.spad" 2249365 2249385 2250708 2250777) (-1249 "XFALG.spad" 2246389 2246405 2249291 2249360) (-1248 "XF.spad" 2244850 2244865 2246291 2246384) (-1247 "XF.spad" 2243291 2243308 2244734 2244739) (-1246 "XEXPPKG.spad" 2242542 2242568 2243281 2243286) (-1245 "XDPOLY.spad" 2242156 2242172 2242398 2242467) (-1244 "XALG.spad" 2241754 2241765 2242112 2242151) (-1243 "WUTSET.spad" 2237593 2237610 2241400 2241427) (-1242 "WP.spad" 2236607 2236651 2237451 2237518) (-1241 "WHILEAST.spad" 2236405 2236414 2236597 2236602) (-1240 "WHEREAST.spad" 2236076 2236085 2236395 2236400) (-1239 "WFFINTBS.spad" 2233639 2233661 2236066 2236071) (-1238 "WEIER.spad" 2231853 2231864 2233629 2233634) (-1237 "VSPACE.spad" 2231526 2231537 2231821 2231848) (-1236 "VSPACE.spad" 2231219 2231232 2231516 2231521) (-1235 "VOID.spad" 2230809 2230818 2231209 2231214) (-1234 "VIEWDEF.spad" 2226006 2226015 2230799 2230804) (-1233 "VIEW3D.spad" 2209841 2209850 2225996 2226001) (-1232 "VIEW2D.spad" 2197578 2197587 2209831 2209836) (-1231 "VIEW.spad" 2195200 2195209 2197568 2197573) (-1230 "VECTOR2.spad" 2193827 2193840 2195190 2195195) (-1229 "VECTOR.spad" 2192502 2192513 2192753 2192780) (-1228 "VECTCAT.spad" 2190390 2190401 2192458 2192497) (-1227 "VECTCAT.spad" 2188098 2188111 2190168 2190173) (-1226 "VARIABLE.spad" 2187878 2187893 2188088 2188093) (-1225 "UTYPE.spad" 2187512 2187521 2187858 2187873) (-1224 "UTSODETL.spad" 2186805 2186829 2187468 2187473) (-1223 "UTSODE.spad" 2184993 2185013 2186795 2186800) (-1222 "UTSCAT.spad" 2182444 2182460 2184891 2184988) (-1221 "UTSCAT.spad" 2179539 2179557 2181988 2181993) (-1220 "UTS2.spad" 2179132 2179167 2179529 2179534) (-1219 "UTS.spad" 2173921 2173949 2177599 2177696) (-1218 "URAGG.spad" 2168543 2168554 2173901 2173916) (-1217 "URAGG.spad" 2163139 2163152 2168499 2168504) (-1216 "UPXSSING.spad" 2160782 2160808 2162220 2162353) (-1215 "UPXSCONS.spad" 2158539 2158559 2158914 2159063) (-1214 "UPXSCCA.spad" 2156997 2157017 2158385 2158534) (-1213 "UPXSCCA.spad" 2155597 2155619 2156987 2156992) (-1212 "UPXSCAT.spad" 2154178 2154194 2155443 2155592) (-1211 "UPXS2.spad" 2153719 2153772 2154168 2154173) (-1210 "UPXS.spad" 2150746 2150774 2151851 2152000) (-1209 "UPSQFREE.spad" 2149159 2149173 2150736 2150741) (-1208 "UPSCAT.spad" 2146752 2146776 2149057 2149154) (-1207 "UPSCAT.spad" 2144051 2144077 2146358 2146363) (-1206 "UPOLYC2.spad" 2143520 2143539 2144041 2144046) (-1205 "UPOLYC.spad" 2138498 2138509 2143362 2143515) (-1204 "UPOLYC.spad" 2133368 2133381 2138234 2138239) (-1203 "UPMP.spad" 2132258 2132271 2133358 2133363) (-1202 "UPDIVP.spad" 2131821 2131835 2132248 2132253) (-1201 "UPDECOMP.spad" 2130058 2130072 2131811 2131816) (-1200 "UPCDEN.spad" 2129265 2129281 2130048 2130053) (-1199 "UP2.spad" 2128627 2128648 2129255 2129260) (-1198 "UP.spad" 2125669 2125684 2126177 2126330) (-1197 "UNISEG2.spad" 2125162 2125175 2125625 2125630) (-1196 "UNISEG.spad" 2124515 2124526 2125081 2125086) (-1195 "UNIFACT.spad" 2123616 2123628 2124505 2124510) (-1194 "ULSCONS.spad" 2117655 2117675 2118027 2118176) (-1193 "ULSCCAT.spad" 2115252 2115272 2117475 2117650) (-1192 "ULSCCAT.spad" 2112983 2113005 2115208 2115213) (-1191 "ULSCAT.spad" 2111199 2111215 2112829 2112978) (-1190 "ULS2.spad" 2110711 2110764 2111189 2111194) (-1189 "ULS.spad" 2101265 2101293 2102358 2102787) (-1188 "UFD.spad" 2100330 2100339 2101191 2101260) (-1187 "UFD.spad" 2099457 2099468 2100320 2100325) (-1186 "UDVO.spad" 2098304 2098313 2099447 2099452) (-1185 "UDPO.spad" 2095731 2095742 2098260 2098265) (-1184 "TYPEAST.spad" 2095650 2095659 2095721 2095726) (-1183 "TYPE.spad" 2095572 2095581 2095630 2095645) (-1182 "TWOFACT.spad" 2094222 2094237 2095562 2095567) (-1181 "TUPLE.spad" 2093608 2093619 2094121 2094126) (-1180 "TUBETOOL.spad" 2090445 2090454 2093598 2093603) (-1179 "TUBE.spad" 2089086 2089103 2090435 2090440) (-1178 "TSETCAT.spad" 2076201 2076218 2089042 2089081) (-1177 "TSETCAT.spad" 2063314 2063333 2076157 2076162) (-1176 "TS.spad" 2061903 2061919 2062879 2062976) (-1175 "TRMANIP.spad" 2056269 2056286 2061609 2061614) (-1174 "TRIMAT.spad" 2055228 2055253 2056259 2056264) (-1173 "TRIGMNIP.spad" 2053745 2053762 2055218 2055223) (-1172 "TRIGCAT.spad" 2053257 2053266 2053735 2053740) (-1171 "TRIGCAT.spad" 2052767 2052778 2053247 2053252) (-1170 "TREE.spad" 2051338 2051349 2052374 2052401) (-1169 "TRANFUN.spad" 2051169 2051178 2051328 2051333) (-1168 "TRANFUN.spad" 2050998 2051009 2051159 2051164) (-1167 "TOPSP.spad" 2050672 2050681 2050988 2050993) (-1166 "TOOLSIGN.spad" 2050335 2050346 2050662 2050667) (-1165 "TEXTFILE.spad" 2048892 2048901 2050325 2050330) (-1164 "TEX1.spad" 2048448 2048459 2048882 2048887) (-1163 "TEX.spad" 2045465 2045474 2048438 2048443) (-1162 "TEMUTL.spad" 2045020 2045029 2045455 2045460) (-1161 "TBCMPPK.spad" 2043113 2043136 2045010 2045015) (-1160 "TBAGG.spad" 2042137 2042160 2043081 2043108) (-1159 "TBAGG.spad" 2041181 2041206 2042127 2042132) (-1158 "TANEXP.spad" 2040557 2040568 2041171 2041176) (-1157 "TABLEAU.spad" 2040038 2040049 2040547 2040552) (-1156 "TABLE.spad" 2038449 2038472 2038719 2038746) (-1155 "TABLBUMP.spad" 2035232 2035243 2038439 2038444) (-1154 "SYSTEM.spad" 2034506 2034515 2035222 2035227) (-1153 "SYSSOLP.spad" 2031979 2031990 2034496 2034501) (-1152 "SYNTAX.spad" 2028171 2028180 2031969 2031974) (-1151 "SYMTAB.spad" 2026227 2026236 2028161 2028166) (-1150 "SYMS.spad" 2022218 2022227 2026217 2026222) (-1149 "SYMPOLY.spad" 2021225 2021236 2021307 2021434) (-1148 "SYMFUNC.spad" 2020700 2020711 2021215 2021220) (-1147 "SYMBOL.spad" 2018036 2018045 2020690 2020695) (-1146 "SWITCH.spad" 2014793 2014802 2018026 2018031) (-1145 "SUTS.spad" 2011692 2011720 2013260 2013357) (-1144 "SUPXS.spad" 2008706 2008734 2009824 2009973) (-1143 "SUPFRACF.spad" 2007811 2007829 2008696 2008701) (-1142 "SUP2.spad" 2007201 2007214 2007801 2007806) (-1141 "SUP.spad" 2003970 2003981 2004751 2004904) (-1140 "SUMRF.spad" 2002936 2002947 2003960 2003965) (-1139 "SUMFS.spad" 2002569 2002586 2002926 2002931) (-1138 "SULS.spad" 1993110 1993138 1994216 1994645) (-1137 "SUCHTAST.spad" 1992879 1992888 1993100 1993105) (-1136 "SUCH.spad" 1992559 1992574 1992869 1992874) (-1135 "SUBSPACE.spad" 1984566 1984581 1992549 1992554) (-1134 "SUBRESP.spad" 1983726 1983740 1984522 1984527) (-1133 "STTFNC.spad" 1980194 1980210 1983716 1983721) (-1132 "STTF.spad" 1976293 1976309 1980184 1980189) (-1131 "STTAYLOR.spad" 1968691 1968702 1976174 1976179) (-1130 "STRTBL.spad" 1967196 1967213 1967345 1967372) (-1129 "STRING.spad" 1966605 1966614 1966619 1966646) (-1128 "STRICAT.spad" 1966381 1966390 1966561 1966600) (-1127 "STREAM3.spad" 1965926 1965941 1966371 1966376) (-1126 "STREAM2.spad" 1964994 1965007 1965916 1965921) (-1125 "STREAM1.spad" 1964698 1964709 1964984 1964989) (-1124 "STREAM.spad" 1961466 1961477 1964223 1964238) (-1123 "STINPROD.spad" 1960372 1960388 1961456 1961461) (-1122 "STEP.spad" 1959573 1959582 1960362 1960367) (-1121 "STBL.spad" 1958099 1958127 1958266 1958281) (-1120 "STAGG.spad" 1957164 1957175 1958079 1958094) (-1119 "STAGG.spad" 1956237 1956250 1957154 1957159) (-1118 "STACK.spad" 1955588 1955599 1955844 1955871) (-1117 "SREGSET.spad" 1953292 1953309 1955234 1955261) (-1116 "SRDCMPK.spad" 1951837 1951857 1953282 1953287) (-1115 "SRAGG.spad" 1946922 1946931 1951793 1951832) (-1114 "SRAGG.spad" 1942039 1942050 1946912 1946917) (-1113 "SQMATRIX.spad" 1939655 1939673 1940571 1940658) (-1112 "SPLTREE.spad" 1934207 1934220 1939091 1939118) (-1111 "SPLNODE.spad" 1930795 1930808 1934197 1934202) (-1110 "SPFCAT.spad" 1929572 1929581 1930785 1930790) (-1109 "SPECOUT.spad" 1928122 1928131 1929562 1929567) (-1108 "SPADXPT.spad" 1920251 1920260 1928102 1928117) (-1107 "spad-parser.spad" 1919716 1919725 1920241 1920246) (-1106 "SPADAST.spad" 1919417 1919426 1919706 1919711) (-1105 "SPACEC.spad" 1903430 1903441 1919407 1919412) (-1104 "SPACE3.spad" 1903206 1903217 1903420 1903425) (-1103 "SORTPAK.spad" 1902751 1902764 1903162 1903167) (-1102 "SOLVETRA.spad" 1900508 1900519 1902741 1902746) (-1101 "SOLVESER.spad" 1899028 1899039 1900498 1900503) (-1100 "SOLVERAD.spad" 1895038 1895049 1899018 1899023) (-1099 "SOLVEFOR.spad" 1893458 1893476 1895028 1895033) (-1098 "SNTSCAT.spad" 1893046 1893063 1893414 1893453) (-1097 "SMTS.spad" 1891306 1891332 1892611 1892708) (-1096 "SMP.spad" 1888745 1888765 1889135 1889262) (-1095 "SMITH.spad" 1887588 1887613 1888735 1888740) (-1094 "SMATCAT.spad" 1885686 1885716 1887520 1887583) (-1093 "SMATCAT.spad" 1883728 1883760 1885564 1885569) (-1092 "SKAGG.spad" 1882677 1882688 1883684 1883723) (-1091 "SINT.spad" 1880985 1880994 1882543 1882672) (-1090 "SIMPAN.spad" 1880713 1880722 1880975 1880980) (-1089 "SIGNRF.spad" 1879828 1879839 1880703 1880708) (-1088 "SIGNEF.spad" 1879104 1879121 1879818 1879823) (-1087 "SIGAST.spad" 1878485 1878494 1879094 1879099) (-1086 "SIG.spad" 1877813 1877822 1878475 1878480) (-1085 "SHP.spad" 1875731 1875746 1877769 1877774) (-1084 "SHDP.spad" 1866716 1866743 1867225 1867356) (-1083 "SGROUP.spad" 1866324 1866333 1866706 1866711) (-1082 "SGROUP.spad" 1865930 1865941 1866314 1866319) (-1081 "SGCF.spad" 1858811 1858820 1865920 1865925) (-1080 "SFRTCAT.spad" 1857727 1857744 1858767 1858806) (-1079 "SFRGCD.spad" 1856790 1856810 1857717 1857722) (-1078 "SFQCMPK.spad" 1851427 1851447 1856780 1856785) (-1077 "SFORT.spad" 1850862 1850876 1851417 1851422) (-1076 "SEXOF.spad" 1850705 1850745 1850852 1850857) (-1075 "SEXCAT.spad" 1847809 1847849 1850695 1850700) (-1074 "SEX.spad" 1847701 1847710 1847799 1847804) (-1073 "SETMN.spad" 1846137 1846154 1847691 1847696) (-1072 "SETCAT.spad" 1845622 1845631 1846127 1846132) (-1071 "SETCAT.spad" 1845105 1845116 1845612 1845617) (-1070 "SETAGG.spad" 1841614 1841625 1845073 1845100) (-1069 "SETAGG.spad" 1838143 1838156 1841604 1841609) (-1068 "SET.spad" 1836443 1836454 1837564 1837603) (-1067 "SEQAST.spad" 1836146 1836155 1836433 1836438) (-1066 "SEGXCAT.spad" 1835258 1835271 1836126 1836141) (-1065 "SEGCAT.spad" 1834077 1834088 1835238 1835253) (-1064 "SEGBIND2.spad" 1833773 1833786 1834067 1834072) (-1063 "SEGBIND.spad" 1832845 1832856 1833728 1833733) (-1062 "SEGAST.spad" 1832559 1832568 1832835 1832840) (-1061 "SEG2.spad" 1831984 1831997 1832515 1832520) (-1060 "SEG.spad" 1831797 1831808 1831903 1831908) (-1059 "SDVAR.spad" 1831073 1831084 1831787 1831792) (-1058 "SDPOL.spad" 1828463 1828474 1828754 1828881) (-1057 "SCPKG.spad" 1826542 1826553 1828453 1828458) (-1056 "SCOPE.spad" 1825687 1825696 1826532 1826537) (-1055 "SCACHE.spad" 1824369 1824380 1825677 1825682) (-1054 "SASTCAT.spad" 1824278 1824287 1824359 1824364) (-1053 "SAOS.spad" 1824150 1824159 1824268 1824273) (-1052 "SAERFFC.spad" 1823863 1823883 1824140 1824145) (-1051 "SAEFACT.spad" 1823564 1823584 1823853 1823858) (-1050 "SAE.spad" 1821739 1821755 1822350 1822485) (-1049 "RURPK.spad" 1819380 1819396 1821729 1821734) (-1048 "RULESET.spad" 1818821 1818845 1819370 1819375) (-1047 "RULECOLD.spad" 1818673 1818686 1818811 1818816) (-1046 "RULE.spad" 1816877 1816901 1818663 1818668) (-1045 "RSTRCAST.spad" 1816594 1816603 1816867 1816872) (-1044 "RSETGCD.spad" 1812972 1812992 1816584 1816589) (-1043 "RSETCAT.spad" 1802744 1802761 1812928 1812967) (-1042 "RSETCAT.spad" 1792548 1792567 1802734 1802739) (-1041 "RSDCMPK.spad" 1791000 1791020 1792538 1792543) (-1040 "RRCC.spad" 1789384 1789414 1790990 1790995) (-1039 "RRCC.spad" 1787766 1787798 1789374 1789379) (-1038 "RPTAST.spad" 1787468 1787477 1787756 1787761) (-1037 "RPOLCAT.spad" 1766828 1766843 1787336 1787463) (-1036 "RPOLCAT.spad" 1745902 1745919 1766412 1766417) (-1035 "ROUTINE.spad" 1741765 1741774 1744549 1744576) (-1034 "ROMAN.spad" 1740997 1741006 1741631 1741760) (-1033 "ROIRC.spad" 1740077 1740109 1740987 1740992) (-1032 "RNS.spad" 1738980 1738989 1739979 1740072) (-1031 "RNS.spad" 1737969 1737980 1738970 1738975) (-1030 "RNG.spad" 1737704 1737713 1737959 1737964) (-1029 "RMODULE.spad" 1737342 1737353 1737694 1737699) (-1028 "RMCAT2.spad" 1736750 1736807 1737332 1737337) (-1027 "RMATRIX.spad" 1735429 1735448 1735917 1735956) (-1026 "RMATCAT.spad" 1730950 1730981 1735373 1735424) (-1025 "RMATCAT.spad" 1726373 1726406 1730798 1730803) (-1024 "RINTERP.spad" 1726261 1726281 1726363 1726368) (-1023 "RING.spad" 1725618 1725627 1726241 1726256) (-1022 "RING.spad" 1724983 1724994 1725608 1725613) (-1021 "RIDIST.spad" 1724367 1724376 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"NSMP.spad" 1238900 1238919 1239208 1239335) (-757 "NREP.spad" 1237272 1237286 1238890 1238895) (-756 "NPCOEF.spad" 1236518 1236538 1237262 1237267) (-755 "NORMRETR.spad" 1236116 1236155 1236508 1236513) (-754 "NORMPK.spad" 1234018 1234037 1236106 1236111) (-753 "NORMMA.spad" 1233706 1233732 1234008 1234013) (-752 "NONE1.spad" 1233382 1233392 1233696 1233701) (-751 "NONE.spad" 1233123 1233131 1233372 1233377) (-750 "NODE1.spad" 1232592 1232608 1233113 1233118) (-749 "NNI.spad" 1231479 1231487 1232566 1232587) (-748 "NLINSOL.spad" 1230101 1230111 1231469 1231474) (-747 "NIPROB.spad" 1228584 1228592 1230091 1230096) (-746 "NFINTBAS.spad" 1226044 1226061 1228574 1228579) (-745 "NCODIV.spad" 1224242 1224258 1226034 1226039) (-744 "NCNTFRAC.spad" 1223884 1223898 1224232 1224237) (-743 "NCEP.spad" 1222044 1222058 1223874 1223879) (-742 "NASRING.spad" 1221640 1221648 1222034 1222039) (-741 "NASRING.spad" 1221234 1221244 1221630 1221635) (-740 "NARNG.spad" 1220578 1220586 1221224 1221229) (-739 "NARNG.spad" 1219920 1219930 1220568 1220573) (-738 "NAGSP.spad" 1218993 1219001 1219910 1219915) (-737 "NAGS.spad" 1208518 1208526 1218983 1218988) (-736 "NAGF07.spad" 1206911 1206919 1208508 1208513) (-735 "NAGF04.spad" 1201143 1201151 1206901 1206906) (-734 "NAGF02.spad" 1194952 1194960 1201133 1201138) (-733 "NAGF01.spad" 1190555 1190563 1194942 1194947) (-732 "NAGE04.spad" 1184015 1184023 1190545 1190550) (-731 "NAGE02.spad" 1174357 1174365 1184005 1184010) (-730 "NAGE01.spad" 1170241 1170249 1174347 1174352) (-729 "NAGD03.spad" 1168161 1168169 1170231 1170236) (-728 "NAGD02.spad" 1160692 1160700 1168151 1168156) (-727 "NAGD01.spad" 1154805 1154813 1160682 1160687) (-726 "NAGC06.spad" 1150592 1150600 1154795 1154800) (-725 "NAGC05.spad" 1149061 1149069 1150582 1150587) (-724 "NAGC02.spad" 1148316 1148324 1149051 1149056) (-723 "NAALG.spad" 1147851 1147861 1148284 1148311) (-722 "NAALG.spad" 1147406 1147418 1147841 1147846) (-721 "MULTSQFR.spad" 1144364 1144381 1147396 1147401) (-720 "MULTFACT.spad" 1143747 1143764 1144354 1144359) (-719 "MTSCAT.spad" 1141781 1141802 1143645 1143742) (-718 "MTHING.spad" 1141438 1141448 1141771 1141776) (-717 "MSYSCMD.spad" 1140872 1140880 1141428 1141433) (-716 "MSETAGG.spad" 1140705 1140715 1140828 1140867) (-715 "MSET.spad" 1138647 1138657 1140411 1140450) (-714 "MRING.spad" 1135618 1135630 1138355 1138422) (-713 "MRF2.spad" 1135186 1135200 1135608 1135613) (-712 "MRATFAC.spad" 1134732 1134749 1135176 1135181) (-711 "MPRFF.spad" 1132762 1132781 1134722 1134727) (-710 "MPOLY.spad" 1130197 1130212 1130556 1130683) (-709 "MPCPF.spad" 1129461 1129480 1130187 1130192) (-708 "MPC3.spad" 1129276 1129316 1129451 1129456) (-707 "MPC2.spad" 1128918 1128951 1129266 1129271) (-706 "MONOTOOL.spad" 1127253 1127270 1128908 1128913) (-705 "MONOID.spad" 1126572 1126580 1127243 1127248) (-704 "MONOID.spad" 1125889 1125899 1126562 1126567) (-703 "MONOGEN.spad" 1124635 1124648 1125749 1125884) (-702 "MONOGEN.spad" 1123403 1123418 1124519 1124524) (-701 "MONADWU.spad" 1121417 1121425 1123393 1123398) (-700 "MONADWU.spad" 1119429 1119439 1121407 1121412) (-699 "MONAD.spad" 1118573 1118581 1119419 1119424) (-698 "MONAD.spad" 1117715 1117725 1118563 1118568) (-697 "MOEBIUS.spad" 1116401 1116415 1117695 1117710) (-696 "MODULE.spad" 1116271 1116281 1116369 1116396) (-695 "MODULE.spad" 1116161 1116173 1116261 1116266) (-694 "MODRING.spad" 1115492 1115531 1116141 1116156) (-693 "MODOP.spad" 1114151 1114163 1115314 1115381) (-692 "MODMONOM.spad" 1113683 1113701 1114141 1114146) (-691 "MODMON.spad" 1110385 1110401 1111161 1111314) (-690 "MODFIELD.spad" 1109743 1109782 1110287 1110380) (-689 "MMLFORM.spad" 1108603 1108611 1109733 1109738) (-688 "MMAP.spad" 1108343 1108377 1108593 1108598) (-687 "MLO.spad" 1106770 1106780 1108299 1108338) (-686 "MLIFT.spad" 1105342 1105359 1106760 1106765) (-685 "MKUCFUNC.spad" 1104875 1104893 1105332 1105337) (-684 "MKRECORD.spad" 1104477 1104490 1104865 1104870) (-683 "MKFUNC.spad" 1103858 1103868 1104467 1104472) (-682 "MKFLCFN.spad" 1102814 1102824 1103848 1103853) (-681 "MKCHSET.spad" 1102590 1102600 1102804 1102809) (-680 "MKBCFUNC.spad" 1102075 1102093 1102580 1102585) (-679 "MINT.spad" 1101514 1101522 1101977 1102070) (-678 "MHROWRED.spad" 1100015 1100025 1101504 1101509) (-677 "MFLOAT.spad" 1098531 1098539 1099905 1100010) (-676 "MFINFACT.spad" 1097931 1097953 1098521 1098526) (-675 "MESH.spad" 1095668 1095676 1097921 1097926) (-674 "MDDFACT.spad" 1093861 1093871 1095658 1095663) (-673 "MDAGG.spad" 1093136 1093146 1093829 1093856) (-672 "MCMPLX.spad" 1089111 1089119 1089725 1089926) (-671 "MCDEN.spad" 1088319 1088331 1089101 1089106) (-670 "MCALCFN.spad" 1085421 1085447 1088309 1088314) (-669 "MAYBE.spad" 1084670 1084681 1085411 1085416) (-668 "MATSTOR.spad" 1081946 1081956 1084660 1084665) (-667 "MATRIX.spad" 1080650 1080660 1081134 1081161) (-666 "MATLIN.spad" 1077976 1078000 1080534 1080539) (-665 "MATCAT2.spad" 1077244 1077292 1077966 1077971) (-664 "MATCAT.spad" 1068817 1068839 1077200 1077239) (-663 "MATCAT.spad" 1060274 1060298 1068659 1068664) (-662 "MAPPKG3.spad" 1059173 1059187 1060264 1060269) (-661 "MAPPKG2.spad" 1058507 1058519 1059163 1059168) (-660 "MAPPKG1.spad" 1057325 1057335 1058497 1058502) (-659 "MAPPAST.spad" 1056638 1056646 1057315 1057320) (-658 "MAPHACK3.spad" 1056446 1056460 1056628 1056633) (-657 "MAPHACK2.spad" 1056211 1056223 1056436 1056441) (-656 "MAPHACK1.spad" 1055841 1055851 1056201 1056206) (-655 "MAGMA.spad" 1053631 1053648 1055831 1055836) (-654 "MACROAST.spad" 1053210 1053218 1053621 1053626) (-653 "M3D.spad" 1050906 1050916 1052588 1052593) (-652 "LZSTAGG.spad" 1048124 1048134 1050886 1050901) (-651 "LZSTAGG.spad" 1045350 1045362 1048114 1048119) (-650 "LWORD.spad" 1042055 1042072 1045340 1045345) (-649 "LSTAST.spad" 1041839 1041847 1042045 1042050) (-648 "LSQM.spad" 1040062 1040076 1040460 1040511) (-647 "LSPP.spad" 1039595 1039612 1040052 1040057) (-646 "LSMP1.spad" 1037416 1037430 1039585 1039590) (-645 "LSMP.spad" 1036263 1036291 1037406 1037411) (-644 "LSAGG.spad" 1035920 1035930 1036219 1036258) (-643 "LSAGG.spad" 1035609 1035621 1035910 1035915) (-642 "LPOLY.spad" 1034563 1034582 1035465 1035534) (-641 "LPEFRAC.spad" 1033820 1033830 1034553 1034558) (-640 "LOGIC.spad" 1033422 1033430 1033810 1033815) (-639 "LOGIC.spad" 1033022 1033032 1033412 1033417) (-638 "LODOOPS.spad" 1031940 1031952 1033012 1033017) (-637 "LODOF.spad" 1030984 1031001 1031897 1031902) (-636 "LODOCAT.spad" 1029642 1029652 1030940 1030979) (-635 "LODOCAT.spad" 1028298 1028310 1029598 1029603) (-634 "LODO2.spad" 1027571 1027583 1027978 1028017) (-633 "LODO1.spad" 1026971 1026981 1027251 1027290) (-632 "LODO.spad" 1026355 1026371 1026651 1026690) (-631 "LODEEF.spad" 1025127 1025145 1026345 1026350) (-630 "LO.spad" 1024528 1024542 1025061 1025088) (-629 "LNAGG.spad" 1020320 1020330 1024508 1024523) (-628 "LNAGG.spad" 1016086 1016098 1020276 1020281) (-627 "LMOPS.spad" 1012822 1012839 1016076 1016081) (-626 "LMODULE.spad" 1012464 1012474 1012812 1012817) (-625 "LMDICT.spad" 1011747 1011757 1012015 1012042) (-624 "LITERAL.spad" 1011653 1011664 1011737 1011742) (-623 "LIST3.spad" 1010944 1010958 1011643 1011648) (-622 "LIST2MAP.spad" 1007821 1007833 1010934 1010939) (-621 "LIST2.spad" 1006461 1006473 1007811 1007816) (-620 "LIST.spad" 1004179 1004189 1005608 1005635) (-619 "LINEXP.spad" 1003611 1003621 1004159 1004174) (-618 "LINDEP.spad" 1002388 1002400 1003523 1003528) (-617 "LIMITRF.spad" 1000321 1000331 1002378 1002383) (-616 "LIMITPS.spad" 999211 999224 1000311 1000316) (-615 "LIECAT.spad" 998687 998697 999137 999206) (-614 "LIECAT.spad" 998191 998203 998643 998648) (-613 "LIE.spad" 996205 996217 997481 997626) (-612 "LIB.spad" 994253 994261 994864 994879) (-611 "LGROBP.spad" 991606 991625 994243 994248) (-610 "LFCAT.spad" 990625 990633 991596 991601) (-609 "LF.spad" 989544 989560 990615 990620) (-608 "LEXTRIPK.spad" 985047 985062 989534 989539) (-607 "LEXP.spad" 983050 983077 985027 985042) (-606 "LETAST.spad" 982749 982757 983040 983045) (-605 "LEADCDET.spad" 981133 981150 982739 982744) (-604 "LAZM3PK.spad" 979837 979859 981123 981128) (-603 "LAUPOL.spad" 978526 978539 979430 979499) (-602 "LAPLACE.spad" 978099 978115 978516 978521) (-601 "LALG.spad" 977875 977885 978079 978094) (-600 "LALG.spad" 977659 977671 977865 977870) (-599 "LA.spad" 977099 977113 977581 977620) (-598 "KTVLOGIC.spad" 976522 976530 977089 977094) (-597 "KOVACIC.spad" 975235 975252 976512 976517) (-596 "KONVERT.spad" 974957 974967 975225 975230) (-595 "KOERCE.spad" 974694 974704 974947 974952) (-594 "KERNEL2.spad" 974397 974409 974684 974689) (-593 "KERNEL.spad" 972932 972942 974181 974186) (-592 "KDAGG.spad" 972023 972045 972900 972927) (-591 "KDAGG.spad" 971134 971158 972013 972018) (-590 "KAFILE.spad" 970097 970113 970332 970359) (-589 "JORDAN.spad" 967924 967936 969387 969532) (-588 "JOINAST.spad" 967618 967626 967914 967919) (-587 "JAVACODE.spad" 967384 967392 967608 967613) (-586 "IXAGG.spad" 965497 965521 967364 967379) (-585 "IXAGG.spad" 963475 963501 965344 965349) (-584 "IVECTOR.spad" 962246 962261 962401 962428) (-583 "ITUPLE.spad" 961391 961401 962236 962241) (-582 "ITRIGMNP.spad" 960202 960221 961381 961386) (-581 "ITFUN3.spad" 959696 959710 960192 960197) (-580 "ITFUN2.spad" 959426 959438 959686 959691) (-579 "ITAYLOR.spad" 957218 957233 959262 959387) (-578 "ISUPS.spad" 949629 949644 956192 956289) (-577 "ISUMP.spad" 949126 949142 949619 949624) (-576 "ISTRING.spad" 948129 948142 948295 948322) (-575 "ISAST.spad" 947848 947856 948119 948124) (-574 "IRURPK.spad" 946561 946580 947838 947843) (-573 "IRSN.spad" 944521 944529 946551 946556) (-572 "IRRF2F.spad" 942996 943006 944477 944482) (-571 "IRREDFFX.spad" 942597 942608 942986 942991) (-570 "IROOT.spad" 940928 940938 942587 942592) (-569 "IR2F.spad" 940128 940144 940918 940923) (-568 "IR2.spad" 939148 939164 940118 940123) (-567 "IR.spad" 936937 936951 939003 939030) (-566 "IPRNTPK.spad" 936697 936705 936927 936932) (-565 "IPF.spad" 936262 936274 936502 936595) (-564 "IPADIC.spad" 936023 936049 936188 936257) (-563 "IOMODE.spad" 935644 935652 936013 936018) (-562 "IOBCON.spad" 935509 935517 935634 935639) (-561 "INVLAPLA.spad" 935154 935170 935499 935504) (-560 "INTTR.spad" 928412 928429 935144 935149) (-559 "INTTOOLS.spad" 926123 926139 927986 927991) (-558 "INTSLPE.spad" 925429 925437 926113 926118) (-557 "INTRVL.spad" 924995 925005 925343 925424) (-556 "INTRF.spad" 923359 923373 924985 924990) (-555 "INTRET.spad" 922791 922801 923349 923354) (-554 "INTRAT.spad" 921466 921483 922781 922786) (-553 "INTPM.spad" 919829 919845 921109 921114) (-552 "INTPAF.spad" 917604 917622 919761 919766) (-551 "INTPACK.spad" 907914 907922 917594 917599) (-550 "INTHERTR.spad" 907180 907197 907904 907909) (-549 "INTHERAL.spad" 906846 906870 907170 907175) (-548 "INTHEORY.spad" 903259 903267 906836 906841) (-547 "INTG0.spad" 896740 896758 903191 903196) (-546 "INTFTBL.spad" 892194 892202 896730 896735) (-545 "INTFACT.spad" 891253 891263 892184 892189) (-544 "INTEF.spad" 889570 889586 891243 891248) (-543 "INTDOM.spad" 888185 888193 889496 889565) (-542 "INTDOM.spad" 886862 886872 888175 888180) (-541 "INTCAT.spad" 885115 885125 886776 886857) (-540 "INTBIT.spad" 884618 884626 885105 885110) (-539 "INTALG.spad" 883800 883827 884608 884613) (-538 "INTAF.spad" 883292 883308 883790 883795) (-537 "INTABL.spad" 881810 881841 881973 882000) (-536 "INT.spad" 881171 881179 881664 881805) (-535 "INS.spad" 878638 878646 881073 881166) (-534 "INS.spad" 876191 876201 878628 878633) (-533 "INPSIGN.spad" 875647 875660 876181 876186) (-532 "INPRODPF.spad" 874713 874732 875637 875642) (-531 "INPRODFF.spad" 873771 873795 874703 874708) (-530 "INNMFACT.spad" 872742 872759 873761 873766) (-529 "INMODGCD.spad" 872226 872256 872732 872737) (-528 "INFSP.spad" 870511 870533 872216 872221) (-527 "INFPROD0.spad" 869561 869580 870501 870506) (-526 "INFORM1.spad" 869186 869196 869551 869556) (-525 "INFORM.spad" 866347 866355 869176 869181) (-524 "INFINITY.spad" 865899 865907 866337 866342) (-523 "INEP.spad" 864431 864453 865889 865894) (-522 "INDE.spad" 864160 864177 864421 864426) (-521 "INCRMAPS.spad" 863581 863591 864150 864155) (-520 "INBFILE.spad" 862910 862918 863571 863576) (-519 "INBFF.spad" 858680 858691 862900 862905) (-518 "INBCON.spad" 857980 857988 858670 858675) (-517 "INBCON.spad" 857278 857288 857970 857975) (-516 "INAST.spad" 856943 856951 857268 857273) (-515 "IMPTAST.spad" 856651 856659 856933 856938) (-514 "IMATRIX.spad" 855596 855622 856108 856135) (-513 "IMATQF.spad" 854690 854734 855552 855557) (-512 "IMATLIN.spad" 853295 853319 854646 854651) (-511 "ILIST.spad" 851951 851966 852478 852505) (-510 "IIARRAY2.spad" 851339 851377 851558 851585) (-509 "IFF.spad" 850749 850765 851020 851113) (-508 "IFAST.spad" 850363 850371 850739 850744) (-507 "IFARRAY.spad" 847850 847865 849546 849573) (-506 "IFAMON.spad" 847712 847729 847806 847811) (-505 "IEVALAB.spad" 847101 847113 847702 847707) (-504 "IEVALAB.spad" 846488 846502 847091 847096) (-503 "IDPOAMS.spad" 846244 846256 846478 846483) (-502 "IDPOAM.spad" 845964 845976 846234 846239) (-501 "IDPO.spad" 845762 845774 845954 845959) (-500 "IDPC.spad" 844696 844708 845752 845757) (-499 "IDPAM.spad" 844441 844453 844686 844691) (-498 "IDPAG.spad" 844188 844200 844431 844436) (-497 "IDENT.spad" 844105 844113 844178 844183) (-496 "IDECOMP.spad" 841342 841360 844095 844100) (-495 "IDEAL.spad" 836265 836304 841277 841282) (-494 "ICDEN.spad" 835416 835432 836255 836260) (-493 "ICARD.spad" 834605 834613 835406 835411) (-492 "IBPTOOLS.spad" 833198 833215 834595 834600) (-491 "IBITS.spad" 832397 832410 832834 832861) (-490 "IBATOOL.spad" 829272 829291 832387 832392) (-489 "IBACHIN.spad" 827759 827774 829262 829267) (-488 "IARRAY2.spad" 826747 826773 827366 827393) (-487 "IARRAY1.spad" 825792 825807 825930 825957) (-486 "IAN.spad" 824005 824013 825608 825701) (-485 "IALGFACT.spad" 823606 823639 823995 824000) (-484 "HYPCAT.spad" 823030 823038 823596 823601) (-483 "HYPCAT.spad" 822452 822462 823020 823025) (-482 "HOSTNAME.spad" 822260 822268 822442 822447) (-481 "HOAGG.spad" 819518 819528 822240 822255) (-480 "HOAGG.spad" 816561 816573 819285 819290) (-479 "HEXADEC.spad" 814431 814439 815029 815122) (-478 "HEUGCD.spad" 813446 813457 814421 814426) (-477 "HELLFDIV.spad" 813036 813060 813436 813441) (-476 "HEAP.spad" 812428 812438 812643 812670) (-475 "HEADAST.spad" 811959 811967 812418 812423) (-474 "HDP.spad" 803076 803092 803453 803584) (-473 "HDMP.spad" 800252 800267 800870 800997) (-472 "HB.spad" 798489 798497 800242 800247) (-471 "HASHTBL.spad" 796959 796990 797170 797197) (-470 "HASAST.spad" 796675 796683 796949 796954) (-469 "HACKPI.spad" 796158 796166 796577 796670) (-468 "GTSET.spad" 795097 795113 795804 795831) (-467 "GSTBL.spad" 793616 793651 793790 793805) (-466 "GSERIES.spad" 790783 790810 791748 791897) (-465 "GROUP.spad" 790052 790060 790763 790778) (-464 "GROUP.spad" 789329 789339 790042 790047) (-463 "GROEBSOL.spad" 787817 787838 789319 789324) (-462 "GRMOD.spad" 786388 786400 787807 787812) (-461 "GRMOD.spad" 784957 784971 786378 786383) (-460 "GRIMAGE.spad" 777562 777570 784947 784952) (-459 "GRDEF.spad" 775941 775949 777552 777557) (-458 "GRAY.spad" 774400 774408 775931 775936) (-457 "GRALG.spad" 773447 773459 774390 774395) (-456 "GRALG.spad" 772492 772506 773437 773442) (-455 "GPOLSET.spad" 771946 771969 772174 772201) (-454 "GOSPER.spad" 771211 771229 771936 771941) (-453 "GMODPOL.spad" 770349 770376 771179 771206) (-452 "GHENSEL.spad" 769418 769432 770339 770344) (-451 "GENUPS.spad" 765519 765532 769408 769413) (-450 "GENUFACT.spad" 765096 765106 765509 765514) (-449 "GENPGCD.spad" 764680 764697 765086 765091) (-448 "GENMFACT.spad" 764132 764151 764670 764675) (-447 "GENEEZ.spad" 762071 762084 764122 764127) (-446 "GDMP.spad" 759089 759106 759865 759992) (-445 "GCNAALG.spad" 752984 753011 758883 758950) (-444 "GCDDOM.spad" 752156 752164 752910 752979) (-443 "GCDDOM.spad" 751390 751400 752146 752151) (-442 "GBINTERN.spad" 747410 747448 751380 751385) (-441 "GBF.spad" 743167 743205 747400 747405) (-440 "GBEUCLID.spad" 741041 741079 743157 743162) (-439 "GB.spad" 738559 738597 740997 741002) (-438 "GAUSSFAC.spad" 737856 737864 738549 738554) (-437 "GALUTIL.spad" 736178 736188 737812 737817) (-436 "GALPOLYU.spad" 734624 734637 736168 736173) (-435 "GALFACTU.spad" 732789 732808 734614 734619) (-434 "GALFACT.spad" 722922 722933 732779 732784) (-433 "FVFUN.spad" 719935 719943 722902 722917) (-432 "FVC.spad" 718977 718985 719915 719930) (-431 "FUNCTION.spad" 718826 718838 718967 718972) (-430 "FTEM.spad" 717989 717997 718816 718821) (-429 "FT.spad" 716204 716212 717979 717984) (-428 "FSUPFACT.spad" 715104 715123 716140 716145) (-427 "FST.spad" 713190 713198 715094 715099) (-426 "FSRED.spad" 712668 712684 713180 713185) (-425 "FSPRMELT.spad" 711492 711508 712625 712630) (-424 "FSPECF.spad" 709569 709585 711482 711487) (-423 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134304) (-117 "BPADICRT.spad" 131213 131225 131468 131561) (-116 "BPADIC.spad" 130877 130889 131139 131208) (-115 "BOUNDZRO.spad" 130533 130550 130867 130872) (-114 "BOP1.spad" 127919 127929 130489 130494) (-113 "BOP.spad" 123383 123391 127909 127914) (-112 "BOOLEAN.spad" 122707 122715 123373 123378) (-111 "BMODULE.spad" 122419 122431 122675 122702) (-110 "BITS.spad" 121838 121846 122055 122082) (-109 "BINFILE.spad" 121181 121189 121828 121833) (-108 "BINDING.spad" 120600 120608 121171 121176) (-107 "BINARY.spad" 118491 118499 119068 119161) (-106 "BGAGG.spad" 117676 117686 118459 118486) (-105 "BGAGG.spad" 116881 116893 117666 117671) (-104 "BFUNCT.spad" 116445 116453 116861 116876) (-103 "BEZOUT.spad" 115579 115606 116395 116400) (-102 "BBTREE.spad" 112398 112408 115186 115213) (-101 "BASTYPE.spad" 112070 112078 112388 112393) (-100 "BASTYPE.spad" 111740 111750 112060 112065) (-99 "BALFACT.spad" 111180 111192 111730 111735) (-98 "AUTOMOR.spad" 110627 110636 111160 111175) (-97 "ATTREG.spad" 107346 107353 110379 110622) (-96 "ATTRBUT.spad" 103369 103376 107326 107341) (-95 "ATTRAST.spad" 103086 103093 103359 103364) (-94 "ATRIG.spad" 102556 102563 103076 103081) (-93 "ATRIG.spad" 102024 102033 102546 102551) (-92 "ASTCAT.spad" 101928 101935 102014 102019) (-91 "ASTCAT.spad" 101830 101839 101918 101923) (-90 "ASTACK.spad" 101163 101172 101437 101464) (-89 "ASSOCEQ.spad" 99963 99974 101119 101124) (-88 "ASP9.spad" 99044 99057 99953 99958) (-87 "ASP80.spad" 98366 98379 99034 99039) (-86 "ASP8.spad" 97409 97422 98356 98361) (-85 "ASP78.spad" 96860 96873 97399 97404) (-84 "ASP77.spad" 96229 96242 96850 96855) (-83 "ASP74.spad" 95321 95334 96219 96224) (-82 "ASP73.spad" 94592 94605 95311 95316) (-81 "ASP7.spad" 93752 93765 94582 94587) (-80 "ASP6.spad" 92384 92397 93742 93747) (-79 "ASP55.spad" 90893 90906 92374 92379) (-78 "ASP50.spad" 88710 88723 90883 90888) (-77 "ASP49.spad" 87709 87722 88700 88705) (-76 "ASP42.spad" 86116 86155 87699 87704) (-75 "ASP41.spad" 84695 84734 86106 86111) (-74 "ASP4.spad" 83990 84003 84685 84690) (-73 "ASP35.spad" 82978 82991 83980 83985) (-72 "ASP34.spad" 82279 82292 82968 82973) (-71 "ASP33.spad" 81839 81852 82269 82274) (-70 "ASP31.spad" 80979 80992 81829 81834) (-69 "ASP30.spad" 79871 79884 80969 80974) (-68 "ASP29.spad" 79337 79350 79861 79866) (-67 "ASP28.spad" 70610 70623 79327 79332) (-66 "ASP27.spad" 69507 69520 70600 70605) (-65 "ASP24.spad" 68594 68607 69497 69502) (-64 "ASP20.spad" 67810 67823 68584 68589) (-63 "ASP19.spad" 62496 62509 67800 67805) (-62 "ASP12.spad" 61910 61923 62486 62491) (-61 "ASP10.spad" 61181 61194 61900 61905) (-60 "ASP1.spad" 60562 60575 61171 61176) (-59 "ARRAY2.spad" 59922 59931 60169 60196) (-58 "ARRAY12.spad" 58591 58602 59912 59917) (-57 "ARRAY1.spad" 57426 57435 57774 57801) (-56 "ARR2CAT.spad" 53076 53097 57382 57421) (-55 "ARR2CAT.spad" 48758 48781 53066 53071) (-54 "APPRULE.spad" 48002 48024 48748 48753) (-53 "APPLYORE.spad" 47617 47630 47992 47997) (-52 "ANY1.spad" 46688 46697 47607 47612) (-51 "ANY.spad" 45030 45037 46678 46683) (-50 "ANTISYM.spad" 43469 43485 45010 45025) (-49 "ANON.spad" 43166 43173 43459 43464) (-48 "AN.spad" 41467 41474 42982 43075) (-47 "AMR.spad" 39646 39657 41365 41462) (-46 "AMR.spad" 37662 37675 39383 39388) (-45 "ALIST.spad" 35074 35095 35424 35451) (-44 "ALGSC.spad" 34197 34223 34946 34999) (-43 "ALGPKG.spad" 29906 29917 34153 34158) (-42 "ALGMFACT.spad" 29095 29109 29896 29901) (-41 "ALGMANIP.spad" 26515 26530 28892 28897) (-40 "ALGFF.spad" 24830 24857 25047 25203) (-39 "ALGFACT.spad" 23951 23961 24820 24825) (-38 "ALGEBRA.spad" 23682 23691 23907 23946) (-37 "ALGEBRA.spad" 23445 23456 23672 23677) (-36 "ALAGG.spad" 22943 22964 23401 23440) (-35 "AHYP.spad" 22324 22331 22933 22938) (-34 "AGG.spad" 20623 20630 22304 22319) (-33 "AGG.spad" 18896 18905 20579 20584) (-32 "AF.spad" 17321 17336 18831 18836) (-31 "ADDAST.spad" 16999 17006 17311 17316) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865)) \ No newline at end of file
+((-3 NIL 2267916 2267921 2267926 2267931) (-2 NIL 2267896 2267901 2267906 2267911) (-1 NIL 2267876 2267881 2267886 2267891) (0 NIL 2267856 2267861 2267866 2267871) (-1260 "ZMOD.spad" 2267665 2267678 2267794 2267851) (-1259 "ZLINDEP.spad" 2266709 2266720 2267655 2267660) (-1258 "ZDSOLVE.spad" 2256558 2256580 2266699 2266704) (-1257 "YSTREAM.spad" 2256051 2256062 2256548 2256553) (-1256 "XRPOLY.spad" 2255271 2255291 2255907 2255976) (-1255 "XPR.spad" 2253000 2253013 2254989 2255088) (-1254 "XPOLYC.spad" 2252317 2252333 2252926 2252995) (-1253 "XPOLY.spad" 2251872 2251883 2252173 2252242) (-1252 "XPBWPOLY.spad" 2250309 2250329 2251652 2251721) (-1251 "XFALG.spad" 2247333 2247349 2250235 2250304) (-1250 "XF.spad" 2245794 2245809 2247235 2247328) (-1249 "XF.spad" 2244235 2244252 2245678 2245683) (-1248 "XEXPPKG.spad" 2243486 2243512 2244225 2244230) (-1247 "XDPOLY.spad" 2243100 2243116 2243342 2243411) (-1246 "XALG.spad" 2242698 2242709 2243056 2243095) (-1245 "WUTSET.spad" 2238537 2238554 2242344 2242371) (-1244 "WP.spad" 2237551 2237595 2238395 2238462) (-1243 "WHILEAST.spad" 2237349 2237358 2237541 2237546) (-1242 "WHEREAST.spad" 2237020 2237029 2237339 2237344) (-1241 "WFFINTBS.spad" 2234583 2234605 2237010 2237015) (-1240 "WEIER.spad" 2232797 2232808 2234573 2234578) (-1239 "VSPACE.spad" 2232470 2232481 2232765 2232792) (-1238 "VSPACE.spad" 2232163 2232176 2232460 2232465) (-1237 "VOID.spad" 2231753 2231762 2232153 2232158) (-1236 "VIEWDEF.spad" 2226950 2226959 2231743 2231748) (-1235 "VIEW3D.spad" 2210785 2210794 2226940 2226945) (-1234 "VIEW2D.spad" 2198522 2198531 2210775 2210780) (-1233 "VIEW.spad" 2196144 2196153 2198512 2198517) (-1232 "VECTOR2.spad" 2194771 2194784 2196134 2196139) (-1231 "VECTOR.spad" 2193446 2193457 2193697 2193724) (-1230 "VECTCAT.spad" 2191334 2191345 2193402 2193441) (-1229 "VECTCAT.spad" 2189042 2189055 2191112 2191117) (-1228 "VARIABLE.spad" 2188822 2188837 2189032 2189037) (-1227 "UTYPE.spad" 2188456 2188465 2188802 2188817) (-1226 "UTSODETL.spad" 2187749 2187773 2188412 2188417) (-1225 "UTSODE.spad" 2185937 2185957 2187739 2187744) (-1224 "UTSCAT.spad" 2183388 2183404 2185835 2185932) (-1223 "UTSCAT.spad" 2180483 2180501 2182932 2182937) (-1222 "UTS2.spad" 2180076 2180111 2180473 2180478) (-1221 "UTS.spad" 2174865 2174893 2178543 2178640) (-1220 "URAGG.spad" 2169487 2169498 2174845 2174860) (-1219 "URAGG.spad" 2164083 2164096 2169443 2169448) (-1218 "UPXSSING.spad" 2161726 2161752 2163164 2163297) (-1217 "UPXSCONS.spad" 2159483 2159503 2159858 2160007) (-1216 "UPXSCCA.spad" 2157941 2157961 2159329 2159478) (-1215 "UPXSCCA.spad" 2156541 2156563 2157931 2157936) (-1214 "UPXSCAT.spad" 2155122 2155138 2156387 2156536) (-1213 "UPXS2.spad" 2154663 2154716 2155112 2155117) (-1212 "UPXS.spad" 2151690 2151718 2152795 2152944) (-1211 "UPSQFREE.spad" 2150103 2150117 2151680 2151685) (-1210 "UPSCAT.spad" 2147696 2147720 2150001 2150098) (-1209 "UPSCAT.spad" 2144995 2145021 2147302 2147307) (-1208 "UPOLYC2.spad" 2144464 2144483 2144985 2144990) (-1207 "UPOLYC.spad" 2139442 2139453 2144306 2144459) (-1206 "UPOLYC.spad" 2134312 2134325 2139178 2139183) (-1205 "UPMP.spad" 2133202 2133215 2134302 2134307) (-1204 "UPDIVP.spad" 2132765 2132779 2133192 2133197) (-1203 "UPDECOMP.spad" 2131002 2131016 2132755 2132760) (-1202 "UPCDEN.spad" 2130209 2130225 2130992 2130997) (-1201 "UP2.spad" 2129571 2129592 2130199 2130204) (-1200 "UP.spad" 2126613 2126628 2127121 2127274) (-1199 "UNISEG2.spad" 2126106 2126119 2126569 2126574) (-1198 "UNISEG.spad" 2125459 2125470 2126025 2126030) (-1197 "UNIFACT.spad" 2124560 2124572 2125449 2125454) (-1196 "ULSCONS.spad" 2118599 2118619 2118971 2119120) (-1195 "ULSCCAT.spad" 2116196 2116216 2118419 2118594) (-1194 "ULSCCAT.spad" 2113927 2113949 2116152 2116157) (-1193 "ULSCAT.spad" 2112143 2112159 2113773 2113922) (-1192 "ULS2.spad" 2111655 2111708 2112133 2112138) (-1191 "ULS.spad" 2102209 2102237 2103302 2103731) (-1190 "UFD.spad" 2101274 2101283 2102135 2102204) (-1189 "UFD.spad" 2100401 2100412 2101264 2101269) (-1188 "UDVO.spad" 2099248 2099257 2100391 2100396) (-1187 "UDPO.spad" 2096675 2096686 2099204 2099209) (-1186 "TYPEAST.spad" 2096594 2096603 2096665 2096670) (-1185 "TYPE.spad" 2096516 2096525 2096574 2096589) (-1184 "TWOFACT.spad" 2095166 2095181 2096506 2096511) (-1183 "TUPLE.spad" 2094552 2094563 2095065 2095070) (-1182 "TUBETOOL.spad" 2091389 2091398 2094542 2094547) (-1181 "TUBE.spad" 2090030 2090047 2091379 2091384) (-1180 "TSETCAT.spad" 2077145 2077162 2089986 2090025) (-1179 "TSETCAT.spad" 2064258 2064277 2077101 2077106) (-1178 "TS.spad" 2062847 2062863 2063823 2063920) (-1177 "TRMANIP.spad" 2057213 2057230 2062553 2062558) (-1176 "TRIMAT.spad" 2056172 2056197 2057203 2057208) (-1175 "TRIGMNIP.spad" 2054689 2054706 2056162 2056167) (-1174 "TRIGCAT.spad" 2054201 2054210 2054679 2054684) (-1173 "TRIGCAT.spad" 2053711 2053722 2054191 2054196) (-1172 "TREE.spad" 2052282 2052293 2053318 2053345) (-1171 "TRANFUN.spad" 2052113 2052122 2052272 2052277) (-1170 "TRANFUN.spad" 2051942 2051953 2052103 2052108) (-1169 "TOPSP.spad" 2051616 2051625 2051932 2051937) (-1168 "TOOLSIGN.spad" 2051279 2051290 2051606 2051611) (-1167 "TEXTFILE.spad" 2049836 2049845 2051269 2051274) (-1166 "TEX1.spad" 2049392 2049403 2049826 2049831) (-1165 "TEX.spad" 2046409 2046418 2049382 2049387) (-1164 "TEMUTL.spad" 2045964 2045973 2046399 2046404) (-1163 "TBCMPPK.spad" 2044057 2044080 2045954 2045959) (-1162 "TBAGG.spad" 2043081 2043104 2044025 2044052) (-1161 "TBAGG.spad" 2042125 2042150 2043071 2043076) (-1160 "TANEXP.spad" 2041501 2041512 2042115 2042120) (-1159 "TABLEAU.spad" 2040982 2040993 2041491 2041496) (-1158 "TABLE.spad" 2039393 2039416 2039663 2039690) (-1157 "TABLBUMP.spad" 2036176 2036187 2039383 2039388) (-1156 "SYSTEM.spad" 2035450 2035459 2036166 2036171) (-1155 "SYSSOLP.spad" 2032923 2032934 2035440 2035445) (-1154 "SYNTAX.spad" 2029115 2029124 2032913 2032918) (-1153 "SYMTAB.spad" 2027171 2027180 2029105 2029110) (-1152 "SYMS.spad" 2023162 2023171 2027161 2027166) (-1151 "SYMPOLY.spad" 2022169 2022180 2022251 2022378) (-1150 "SYMFUNC.spad" 2021644 2021655 2022159 2022164) (-1149 "SYMBOL.spad" 2018980 2018989 2021634 2021639) (-1148 "SWITCH.spad" 2015737 2015746 2018970 2018975) (-1147 "SUTS.spad" 2012636 2012664 2014204 2014301) (-1146 "SUPXS.spad" 2009650 2009678 2010768 2010917) (-1145 "SUPFRACF.spad" 2008755 2008773 2009640 2009645) (-1144 "SUP2.spad" 2008145 2008158 2008745 2008750) (-1143 "SUP.spad" 2004914 2004925 2005695 2005848) (-1142 "SUMRF.spad" 2003880 2003891 2004904 2004909) (-1141 "SUMFS.spad" 2003513 2003530 2003870 2003875) (-1140 "SULS.spad" 1994054 1994082 1995160 1995589) (-1139 "SUCHTAST.spad" 1993823 1993832 1994044 1994049) (-1138 "SUCH.spad" 1993503 1993518 1993813 1993818) (-1137 "SUBSPACE.spad" 1985510 1985525 1993493 1993498) (-1136 "SUBRESP.spad" 1984670 1984684 1985466 1985471) (-1135 "STTFNC.spad" 1981138 1981154 1984660 1984665) (-1134 "STTF.spad" 1977237 1977253 1981128 1981133) (-1133 "STTAYLOR.spad" 1969635 1969646 1977118 1977123) (-1132 "STRTBL.spad" 1968140 1968157 1968289 1968316) (-1131 "STRING.spad" 1967549 1967558 1967563 1967590) (-1130 "STRICAT.spad" 1967325 1967334 1967505 1967544) (-1129 "STREAM3.spad" 1966870 1966885 1967315 1967320) (-1128 "STREAM2.spad" 1965938 1965951 1966860 1966865) (-1127 "STREAM1.spad" 1965642 1965653 1965928 1965933) (-1126 "STREAM.spad" 1962410 1962421 1965167 1965182) (-1125 "STINPROD.spad" 1961316 1961332 1962400 1962405) (-1124 "STEP.spad" 1960517 1960526 1961306 1961311) (-1123 "STBL.spad" 1959043 1959071 1959210 1959225) (-1122 "STAGG.spad" 1958108 1958119 1959023 1959038) (-1121 "STAGG.spad" 1957181 1957194 1958098 1958103) (-1120 "STACK.spad" 1956532 1956543 1956788 1956815) (-1119 "SREGSET.spad" 1954236 1954253 1956178 1956205) (-1118 "SRDCMPK.spad" 1952781 1952801 1954226 1954231) (-1117 "SRAGG.spad" 1947866 1947875 1952737 1952776) (-1116 "SRAGG.spad" 1942983 1942994 1947856 1947861) (-1115 "SQMATRIX.spad" 1940599 1940617 1941515 1941602) (-1114 "SPLTREE.spad" 1935151 1935164 1940035 1940062) (-1113 "SPLNODE.spad" 1931739 1931752 1935141 1935146) (-1112 "SPFCAT.spad" 1930516 1930525 1931729 1931734) (-1111 "SPECOUT.spad" 1929066 1929075 1930506 1930511) (-1110 "SPADXPT.spad" 1921195 1921204 1929046 1929061) (-1109 "spad-parser.spad" 1920660 1920669 1921185 1921190) (-1108 "SPADAST.spad" 1920361 1920370 1920650 1920655) (-1107 "SPACEC.spad" 1904374 1904385 1920351 1920356) (-1106 "SPACE3.spad" 1904150 1904161 1904364 1904369) (-1105 "SORTPAK.spad" 1903695 1903708 1904106 1904111) (-1104 "SOLVETRA.spad" 1901452 1901463 1903685 1903690) (-1103 "SOLVESER.spad" 1899972 1899983 1901442 1901447) (-1102 "SOLVERAD.spad" 1895982 1895993 1899962 1899967) (-1101 "SOLVEFOR.spad" 1894402 1894420 1895972 1895977) (-1100 "SNTSCAT.spad" 1893990 1894007 1894358 1894397) (-1099 "SMTS.spad" 1892250 1892276 1893555 1893652) (-1098 "SMP.spad" 1889689 1889709 1890079 1890206) (-1097 "SMITH.spad" 1888532 1888557 1889679 1889684) (-1096 "SMATCAT.spad" 1886630 1886660 1888464 1888527) (-1095 "SMATCAT.spad" 1884672 1884704 1886508 1886513) (-1094 "SKAGG.spad" 1883621 1883632 1884628 1884667) (-1093 "SINT.spad" 1881929 1881938 1883487 1883616) (-1092 "SIMPAN.spad" 1881657 1881666 1881919 1881924) (-1091 "SIGNRF.spad" 1880772 1880783 1881647 1881652) (-1090 "SIGNEF.spad" 1880048 1880065 1880762 1880767) (-1089 "SIGAST.spad" 1879429 1879438 1880038 1880043) (-1088 "SIG.spad" 1878757 1878766 1879419 1879424) (-1087 "SHP.spad" 1876675 1876690 1878713 1878718) (-1086 "SHDP.spad" 1867660 1867687 1868169 1868300) (-1085 "SGROUP.spad" 1867268 1867277 1867650 1867655) (-1084 "SGROUP.spad" 1866874 1866885 1867258 1867263) (-1083 "SGCF.spad" 1859755 1859764 1866864 1866869) (-1082 "SFRTCAT.spad" 1858671 1858688 1859711 1859750) (-1081 "SFRGCD.spad" 1857734 1857754 1858661 1858666) (-1080 "SFQCMPK.spad" 1852371 1852391 1857724 1857729) (-1079 "SFORT.spad" 1851806 1851820 1852361 1852366) (-1078 "SEXOF.spad" 1851649 1851689 1851796 1851801) (-1077 "SEXCAT.spad" 1848753 1848793 1851639 1851644) (-1076 "SEX.spad" 1848645 1848654 1848743 1848748) (-1075 "SETMN.spad" 1847081 1847098 1848635 1848640) (-1074 "SETCAT.spad" 1846566 1846575 1847071 1847076) (-1073 "SETCAT.spad" 1846049 1846060 1846556 1846561) (-1072 "SETAGG.spad" 1842558 1842569 1846017 1846044) (-1071 "SETAGG.spad" 1839087 1839100 1842548 1842553) (-1070 "SET.spad" 1837387 1837398 1838508 1838547) (-1069 "SEQAST.spad" 1837090 1837099 1837377 1837382) (-1068 "SEGXCAT.spad" 1836202 1836215 1837070 1837085) (-1067 "SEGCAT.spad" 1835021 1835032 1836182 1836197) (-1066 "SEGBIND2.spad" 1834717 1834730 1835011 1835016) (-1065 "SEGBIND.spad" 1833789 1833800 1834672 1834677) (-1064 "SEGAST.spad" 1833503 1833512 1833779 1833784) (-1063 "SEG2.spad" 1832928 1832941 1833459 1833464) (-1062 "SEG.spad" 1832741 1832752 1832847 1832852) (-1061 "SDVAR.spad" 1832017 1832028 1832731 1832736) (-1060 "SDPOL.spad" 1829407 1829418 1829698 1829825) (-1059 "SCPKG.spad" 1827486 1827497 1829397 1829402) (-1058 "SCOPE.spad" 1826631 1826640 1827476 1827481) (-1057 "SCACHE.spad" 1825313 1825324 1826621 1826626) (-1056 "SASTCAT.spad" 1825222 1825231 1825303 1825308) (-1055 "SAOS.spad" 1825094 1825103 1825212 1825217) (-1054 "SAERFFC.spad" 1824807 1824827 1825084 1825089) (-1053 "SAEFACT.spad" 1824508 1824528 1824797 1824802) (-1052 "SAE.spad" 1822683 1822699 1823294 1823429) (-1051 "RURPK.spad" 1820324 1820340 1822673 1822678) (-1050 "RULESET.spad" 1819765 1819789 1820314 1820319) (-1049 "RULECOLD.spad" 1819617 1819630 1819755 1819760) (-1048 "RULE.spad" 1817821 1817845 1819607 1819612) (-1047 "RSTRCAST.spad" 1817538 1817547 1817811 1817816) (-1046 "RSETGCD.spad" 1813916 1813936 1817528 1817533) (-1045 "RSETCAT.spad" 1803688 1803705 1813872 1813911) (-1044 "RSETCAT.spad" 1793492 1793511 1803678 1803683) (-1043 "RSDCMPK.spad" 1791944 1791964 1793482 1793487) (-1042 "RRCC.spad" 1790328 1790358 1791934 1791939) (-1041 "RRCC.spad" 1788710 1788742 1790318 1790323) (-1040 "RPTAST.spad" 1788412 1788421 1788700 1788705) (-1039 "RPOLCAT.spad" 1767772 1767787 1788280 1788407) (-1038 "RPOLCAT.spad" 1746846 1746863 1767356 1767361) (-1037 "ROUTINE.spad" 1742709 1742718 1745493 1745520) (-1036 "ROMAN.spad" 1741941 1741950 1742575 1742704) (-1035 "ROIRC.spad" 1741021 1741053 1741931 1741936) (-1034 "RNS.spad" 1739924 1739933 1740923 1741016) (-1033 "RNS.spad" 1738913 1738924 1739914 1739919) (-1032 "RNG.spad" 1738648 1738657 1738903 1738908) (-1031 "RMODULE.spad" 1738286 1738297 1738638 1738643) (-1030 "RMCAT2.spad" 1737694 1737751 1738276 1738281) (-1029 "RMATRIX.spad" 1736373 1736392 1736861 1736900) (-1028 "RMATCAT.spad" 1731894 1731925 1736317 1736368) (-1027 "RMATCAT.spad" 1727317 1727350 1731742 1731747) (-1026 "RINTERP.spad" 1727205 1727225 1727307 1727312) (-1025 "RING.spad" 1726562 1726571 1727185 1727200) (-1024 "RING.spad" 1725927 1725938 1726552 1726557) (-1023 "RIDIST.spad" 1725311 1725320 1725917 1725922) (-1022 "RGCHAIN.spad" 1723890 1723906 1724796 1724823) (-1021 "RGBCSPC.spad" 1723671 1723683 1723880 1723885) (-1020 "RGBCMDL.spad" 1723201 1723213 1723661 1723666) (-1019 "RFFACTOR.spad" 1722663 1722674 1723191 1723196) (-1018 "RFFACT.spad" 1722398 1722410 1722653 1722658) (-1017 "RFDIST.spad" 1721386 1721395 1722388 1722393) (-1016 "RF.spad" 1719000 1719011 1721376 1721381) (-1015 "RETSOL.spad" 1718417 1718430 1718990 1718995) (-1014 "RETRACT.spad" 1717766 1717777 1718407 1718412) (-1013 "RETRACT.spad" 1717113 1717126 1717756 1717761) (-1012 "RETAST.spad" 1716925 1716934 1717103 1717108) (-1011 "RESULT.spad" 1714985 1714994 1715572 1715599) (-1010 "RESRING.spad" 1714332 1714379 1714923 1714980) (-1009 "RESLATC.spad" 1713656 1713667 1714322 1714327) (-1008 "REPSQ.spad" 1713385 1713396 1713646 1713651) (-1007 "REPDB.spad" 1713090 1713101 1713375 1713380) (-1006 "REP2.spad" 1702662 1702673 1712932 1712937) (-1005 "REP1.spad" 1696652 1696663 1702612 1702617) (-1004 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1403767) (-835 "OSI.spad" 1402331 1402339 1402846 1402851) (-834 "OSGROUP.spad" 1402249 1402257 1402321 1402326) (-833 "ORTHPOL.spad" 1400710 1400720 1402166 1402171) (-832 "OREUP.spad" 1400068 1400096 1400390 1400429) (-831 "ORESUP.spad" 1399367 1399391 1399748 1399787) (-830 "OREPCTO.spad" 1397186 1397198 1399287 1399292) (-829 "OREPCAT.spad" 1391243 1391253 1397142 1397181) (-828 "OREPCAT.spad" 1385190 1385202 1391091 1391096) (-827 "ORDSET.spad" 1384356 1384364 1385180 1385185) (-826 "ORDSET.spad" 1383520 1383530 1384346 1384351) (-825 "ORDRING.spad" 1382910 1382918 1383500 1383515) (-824 "ORDRING.spad" 1382308 1382318 1382900 1382905) (-823 "ORDMON.spad" 1382163 1382171 1382298 1382303) (-822 "ORDFUNS.spad" 1381289 1381305 1382153 1382158) (-821 "ORDFIN.spad" 1381223 1381231 1381279 1381284) (-820 "ORDCOMP2.spad" 1380508 1380520 1381213 1381218) (-819 "ORDCOMP.spad" 1378973 1378983 1380055 1380084) (-818 "OPTPROB.spad" 1377553 1377561 1378963 1378968) (-817 "OPTPACK.spad" 1369938 1369946 1377543 1377548) (-816 "OPTCAT.spad" 1367613 1367621 1369928 1369933) (-815 "OPQUERY.spad" 1367162 1367170 1367603 1367608) (-814 "OP.spad" 1366904 1366914 1366984 1367051) (-813 "ONECOMP2.spad" 1366322 1366334 1366894 1366899) (-812 "ONECOMP.spad" 1365067 1365077 1365869 1365898) (-811 "OMSERVER.spad" 1364069 1364077 1365057 1365062) (-810 "OMSAGG.spad" 1363845 1363855 1364013 1364064) (-809 "OMPKG.spad" 1362457 1362465 1363835 1363840) (-808 "OMLO.spad" 1361882 1361894 1362343 1362382) (-807 "OMEXPR.spad" 1361716 1361726 1361872 1361877) (-806 "OMERRK.spad" 1360750 1360758 1361706 1361711) (-805 "OMERR.spad" 1360293 1360301 1360740 1360745) (-804 "OMENC.spad" 1359637 1359645 1360283 1360288) (-803 "OMDEV.spad" 1353926 1353934 1359627 1359632) (-802 "OMCONN.spad" 1353335 1353343 1353916 1353921) (-801 "OM.spad" 1352300 1352308 1353325 1353330) (-800 "OINTDOM.spad" 1352063 1352071 1352226 1352295) (-799 "OFMONOID.spad" 1348250 1348260 1352053 1352058) (-798 "ODVAR.spad" 1347511 1347521 1348240 1348245) (-797 "ODR.spad" 1346959 1346985 1347323 1347472) (-796 "ODPOL.spad" 1344305 1344315 1344645 1344772) (-795 "ODP.spad" 1335426 1335446 1335799 1335930) (-794 "ODETOOLS.spad" 1334009 1334028 1335416 1335421) (-793 "ODESYS.spad" 1331659 1331676 1333999 1334004) (-792 "ODERTRIC.spad" 1327600 1327617 1331616 1331621) (-791 "ODERED.spad" 1326987 1327011 1327590 1327595) (-790 "ODERAT.spad" 1324540 1324557 1326977 1326982) (-789 "ODEPRRIC.spad" 1321431 1321453 1324530 1324535) (-788 "ODEPROB.spad" 1320630 1320638 1321421 1321426) (-787 "ODEPRIM.spad" 1317904 1317926 1320620 1320625) (-786 "ODEPAL.spad" 1317280 1317304 1317894 1317899) (-785 "ODEPACK.spad" 1303882 1303890 1317270 1317275) (-784 "ODEINT.spad" 1303313 1303329 1303872 1303877) (-783 "ODEIFTBL.spad" 1300708 1300716 1303303 1303308) (-782 "ODEEF.spad" 1296079 1296095 1300698 1300703) (-781 "ODECONST.spad" 1295598 1295616 1296069 1296074) (-780 "ODECAT.spad" 1294194 1294202 1295588 1295593) (-779 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(-363 "FINITE.spad" 598379 598387 599217 599222) (-362 "FINAALG.spad" 587360 587370 598321 598374) (-361 "FINAALG.spad" 576353 576365 587316 587321) (-360 "FILECAT.spad" 574871 574888 576343 576348) (-359 "FILE.spad" 574454 574464 574861 574866) (-358 "FIELD.spad" 573860 573868 574356 574449) (-357 "FIELD.spad" 573352 573362 573850 573855) (-356 "FGROUP.spad" 571961 571971 573332 573347) (-355 "FGLMICPK.spad" 570748 570763 571951 571956) (-354 "FFX.spad" 570123 570138 570464 570557) (-353 "FFSLPE.spad" 569612 569633 570113 570118) (-352 "FFPOLY2.spad" 568672 568689 569602 569607) (-351 "FFPOLY.spad" 559924 559935 568662 568667) (-350 "FFP.spad" 559321 559341 559640 559733) (-349 "FFNBX.spad" 557833 557853 559037 559130) (-348 "FFNBP.spad" 556346 556363 557549 557642) (-347 "FFNB.spad" 554811 554832 556027 556120) (-346 "FFINTBAS.spad" 552225 552244 554801 554806) (-345 "FFIELDC.spad" 549800 549808 552127 552220) (-344 "FFIELDC.spad" 547461 547471 549790 549795) (-343 "FFHOM.spad" 546209 546226 547451 547456) (-342 "FFF.spad" 543644 543655 546199 546204) (-341 "FFCGX.spad" 542491 542511 543360 543453) (-340 "FFCGP.spad" 541380 541400 542207 542300) (-339 "FFCG.spad" 540172 540193 541061 541154) (-338 "FFCAT2.spad" 539917 539957 540162 540167) (-337 "FFCAT.spad" 532944 532966 539756 539912) (-336 "FFCAT.spad" 526050 526074 532864 532869) (-335 "FF.spad" 525498 525514 525731 525824) (-334 "FEXPR.spad" 517207 517253 525254 525293) (-333 "FEVALAB.spad" 516913 516923 517197 517202) (-332 "FEVALAB.spad" 516404 516416 516690 516695) (-331 "FDIVCAT.spad" 514446 514470 516394 516399) (-330 "FDIVCAT.spad" 512486 512512 514436 514441) (-329 "FDIV2.spad" 512140 512180 512476 512481) (-328 "FDIV.spad" 511582 511606 512130 512135) (-327 "FCPAK1.spad" 510135 510143 511572 511577) (-326 "FCOMP.spad" 509514 509524 510125 510130) (-325 "FC.spad" 499339 499347 509504 509509) (-324 "FAXF.spad" 492274 492288 499241 499334) (-323 "FAXF.spad" 485261 485277 492230 492235) (-322 "FARRAY.spad" 483407 483417 484444 484471) (-321 "FAMR.spad" 481527 481539 483305 483402) (-320 "FAMR.spad" 479631 479645 481411 481416) (-319 "FAMONOID.spad" 479281 479291 479585 479590) (-318 "FAMONC.spad" 477503 477515 479271 479276) (-317 "FAGROUP.spad" 477109 477119 477399 477426) (-316 "FACUTIL.spad" 475305 475322 477099 477104) (-315 "FACTFUNC.spad" 474481 474491 475295 475300) (-314 "EXPUPXS.spad" 471314 471337 472613 472762) (-313 "EXPRTUBE.spad" 468542 468550 471304 471309) (-312 "EXPRODE.spad" 465414 465430 468532 468537) (-311 "EXPR2UPS.spad" 461506 461519 465404 465409) (-310 "EXPR2.spad" 461209 461221 461496 461501) (-309 "EXPR.spad" 456484 456494 457198 457605) (-308 "EXPEXPAN.spad" 453423 453448 454057 454150) (-307 "EXITAST.spad" 453159 453167 453413 453418) (-306 "EXIT.spad" 452830 452838 453149 453154) (-305 "EVALCYC.spad" 452288 452302 452820 452825) (-304 "EVALAB.spad" 451852 451862 452278 452283) (-303 "EVALAB.spad" 451414 451426 451842 451847) (-302 "EUCDOM.spad" 448956 448964 451340 451409) (-301 "EUCDOM.spad" 446560 446570 448946 448951) (-300 "ESTOOLS2.spad" 446161 446175 446550 446555) (-299 "ESTOOLS1.spad" 445846 445857 446151 446156) (-298 "ESTOOLS.spad" 437686 437694 445836 445841) (-297 "ESCONT1.spad" 437435 437447 437676 437681) (-296 "ESCONT.spad" 434208 434216 437425 437430) (-295 "ES2.spad" 433703 433719 434198 434203) (-294 "ES1.spad" 433269 433285 433693 433698) (-293 "ES.spad" 425816 425824 433259 433264) (-292 "ES.spad" 418269 418279 425714 425719) (-291 "ERROR.spad" 415590 415598 418259 418264) (-290 "EQTBL.spad" 414062 414084 414271 414298) (-289 "EQ2.spad" 413778 413790 414052 414057) (-288 "EQ.spad" 408652 408662 411451 411563) (-287 "EP.spad" 404966 404976 408642 408647) (-286 "ENV.spad" 403668 403676 404956 404961) (-285 "ENTIRER.spad" 403336 403344 403612 403663) (-284 "EMR.spad" 402537 402578 403262 403331) (-283 "ELTAGG.spad" 400777 400796 402527 402532) (-282 "ELTAGG.spad" 398981 399002 400733 400738) (-281 "ELTAB.spad" 398428 398446 398971 398976) (-280 "ELFUTS.spad" 397807 397826 398418 398423) (-279 "ELEMFUN.spad" 397496 397504 397797 397802) (-278 "ELEMFUN.spad" 397183 397193 397486 397491) (-277 "ELAGG.spad" 395114 395124 397151 397178) (-276 "ELAGG.spad" 392994 393006 395033 395038) (-275 "ELABEXPR.spad" 391925 391933 392984 392989) (-274 "EFUPXS.spad" 388701 388731 391881 391886) (-273 "EFULS.spad" 385537 385560 388657 388662) (-272 "EFSTRUC.spad" 383492 383508 385527 385532) (-271 "EF.spad" 378258 378274 383482 383487) (-270 "EAB.spad" 376534 376542 378248 378253) (-269 "E04UCFA.spad" 376070 376078 376524 376529) (-268 "E04NAFA.spad" 375647 375655 376060 376065) (-267 "E04MBFA.spad" 375227 375235 375637 375642) (-266 "E04JAFA.spad" 374763 374771 375217 375222) (-265 "E04GCFA.spad" 374299 374307 374753 374758) (-264 "E04FDFA.spad" 373835 373843 374289 374294) (-263 "E04DGFA.spad" 373371 373379 373825 373830) (-262 "E04AGNT.spad" 369213 369221 373361 373366) (-261 "DVARCAT.spad" 365898 365908 369203 369208) (-260 "DVARCAT.spad" 362581 362593 365888 365893) (-259 "DSMP.spad" 360012 360026 360317 360444) (-258 "DROPT1.spad" 359675 359685 360002 360007) (-257 "DROPT0.spad" 354502 354510 359665 359670) (-256 "DROPT.spad" 348447 348455 354492 354497) (-255 "DRAWPT.spad" 346602 346610 348437 348442) (-254 "DRAWHACK.spad" 345910 345920 346592 346597) (-253 "DRAWCX.spad" 343352 343360 345900 345905) (-252 "DRAWCURV.spad" 342889 342904 343342 343347) (-251 "DRAWCFUN.spad" 332061 332069 342879 342884) (-250 "DRAW.spad" 324661 324674 332051 332056) (-249 "DQAGG.spad" 322817 322827 324617 324656) (-248 "DPOLCAT.spad" 318158 318174 322685 322812) (-247 "DPOLCAT.spad" 313585 313603 318114 318119) (-246 "DPMO.spad" 306888 306904 307026 307327) (-245 "DPMM.spad" 300204 300222 300329 300630) (-244 "DOMAIN.spad" 299475 299483 300194 300199) (-243 "DMP.spad" 296697 296712 297269 297396) (-242 "DLP.spad" 296045 296055 296687 296692) (-241 "DLIST.spad" 294457 294467 295228 295255) (-240 "DLAGG.spad" 292858 292868 294437 294452) (-239 "DIVRING.spad" 292400 292408 292802 292853) (-238 "DIVRING.spad" 291986 291996 292390 292395) (-237 "DISPLAY.spad" 290166 290174 291976 291981) (-236 "DIRPROD2.spad" 288974 288992 290156 290161) (-235 "DIRPROD.spad" 279828 279844 280468 280599) (-234 "DIRPCAT.spad" 278758 278774 279680 279823) (-233 "DIRPCAT.spad" 277429 277447 278353 278358) (-232 "DIOSP.spad" 276254 276262 277419 277424) (-231 "DIOPS.spad" 275226 275236 276222 276249) (-230 "DIOPS.spad" 274184 274196 275182 275187) (-229 "DIFRING.spad" 273476 273484 274164 274179) (-228 "DIFRING.spad" 272776 272786 273466 273471) (-227 "DIFEXT.spad" 271935 271945 272756 272771) (-226 "DIFEXT.spad" 271011 271023 271834 271839) (-225 "DIAGG.spad" 270629 270639 270979 271006) (-224 "DIAGG.spad" 270267 270279 270619 270624) (-223 "DHMATRIX.spad" 268571 268581 269724 269751) (-222 "DFSFUN.spad" 261979 261987 268561 268566) (-221 "DFLOAT.spad" 258700 258708 261869 261974) (-220 "DFINTTLS.spad" 256909 256925 258690 258695) (-219 "DERHAM.spad" 254819 254851 256889 256904) (-218 "DEQUEUE.spad" 254137 254147 254426 254453) (-217 "DEGRED.spad" 253752 253766 254127 254132) (-216 "DEFINTRF.spad" 251322 251332 253742 253747) (-215 "DEFINTEF.spad" 249846 249862 251312 251317) (-214 "DEFAST.spad" 249214 249222 249836 249841) (-213 "DECIMAL.spad" 247096 247104 247682 247775) (-212 "DDFACT.spad" 244895 244912 247086 247091) (-211 "DBLRESP.spad" 244493 244517 244885 244890) (-210 "DBASE.spad" 243065 243075 244483 244488) (-209 "DATABUF.spad" 242553 242566 243055 243060) (-208 "D03FAFA.spad" 242381 242389 242543 242548) (-207 "D03EEFA.spad" 242201 242209 242371 242376) (-206 "D03AGNT.spad" 241281 241289 242191 242196) (-205 "D02EJFA.spad" 240743 240751 241271 241276) (-204 "D02CJFA.spad" 240221 240229 240733 240738) (-203 "D02BHFA.spad" 239711 239719 240211 240216) (-202 "D02BBFA.spad" 239201 239209 239701 239706) (-201 "D02AGNT.spad" 234005 234013 239191 239196) (-200 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"CSTTOOLS.spad" 215469 215482 216216 216221) (-179 "CRFP.spad" 209173 209186 215459 215464) (-178 "CRCEAST.spad" 208893 208901 209163 209168) (-177 "CRAPACK.spad" 207936 207946 208883 208888) (-176 "CPMATCH.spad" 207436 207451 207861 207866) (-175 "CPIMA.spad" 207141 207160 207426 207431) (-174 "COORDSYS.spad" 202034 202044 207131 207136) (-173 "CONTOUR.spad" 201436 201444 202024 202029) (-172 "CONTFRAC.spad" 197048 197058 201338 201431) (-171 "CONDUIT.spad" 196806 196814 197038 197043) (-170 "COMRING.spad" 196480 196488 196744 196801) (-169 "COMPPROP.spad" 195994 196002 196470 196475) (-168 "COMPLPAT.spad" 195761 195776 195984 195989) (-167 "COMPLEX2.spad" 195474 195486 195751 195756) (-166 "COMPLEX.spad" 189500 189510 189744 190005) (-165 "COMPFACT.spad" 189102 189116 189490 189495) (-164 "COMPCAT.spad" 187158 187168 188824 189097) (-163 "COMPCAT.spad" 184920 184932 186588 186593) (-162 "COMMUPC.spad" 184666 184684 184910 184915) (-161 "COMMONOP.spad" 184199 184207 184656 184661) (-160 "COMMAAST.spad" 183962 183970 184189 184194) (-159 "COMM.spad" 183771 183779 183952 183957) (-158 "COMBOPC.spad" 182676 182684 183761 183766) (-157 "COMBINAT.spad" 181421 181431 182666 182671) (-156 "COMBF.spad" 178789 178805 181411 181416) (-155 "COLOR.spad" 177626 177634 178779 178784) (-154 "COLONAST.spad" 177292 177300 177616 177621) (-153 "CMPLXRT.spad" 177001 177018 177282 177287) (-152 "CLLCTAST.spad" 176663 176671 176991 176996) (-151 "CLIP.spad" 172755 172763 176653 176658) (-150 "CLIF.spad" 171394 171410 172711 172750) (-149 "CLAGG.spad" 167869 167879 171374 171389) (-148 "CLAGG.spad" 164225 164237 167732 167737) (-147 "CINTSLPE.spad" 163550 163563 164215 164220) (-146 "CHVAR.spad" 161628 161650 163540 163545) (-145 "CHARZ.spad" 161543 161551 161608 161623) (-144 "CHARPOL.spad" 161051 161061 161533 161538) (-143 "CHARNZ.spad" 160804 160812 161031 161046) (-142 "CHAR.spad" 158672 158680 160794 160799) (-141 "CFCAT.spad" 157988 157996 158662 158667) (-140 "CDEN.spad" 157146 157160 157978 157983) (-139 "CCLASS.spad" 155295 155303 156557 156596) (-138 "CATEGORY.spad" 155074 155082 155285 155290) (-137 "CATAST.spad" 154701 154709 155064 155069) (-136 "CASEAST.spad" 154415 154423 154691 154696) (-135 "CARTEN2.spad" 153801 153828 154405 154410) (-134 "CARTEN.spad" 148904 148928 153791 153796) (-133 "CARD.spad" 146193 146201 148878 148899) (-132 "CAPSLAST.spad" 145967 145975 146183 146188) (-131 "CACHSET.spad" 145589 145597 145957 145962) (-130 "CABMON.spad" 145142 145150 145579 145584) (-129 "BYTEARY.spad" 144217 144225 144311 144338) (-128 "BYTE.spad" 143391 143399 144207 144212) (-127 "BTREE.spad" 142460 142470 142998 143025) (-126 "BTOURN.spad" 141463 141473 142067 142094) (-125 "BTCAT.spad" 140839 140849 141419 141458) (-124 "BTCAT.spad" 140247 140259 140829 140834) (-123 "BTAGG.spad" 139357 139365 140203 140242) (-122 "BTAGG.spad" 138499 138509 139347 139352) (-121 "BSTREE.spad" 137234 137244 138106 138133) (-120 "BRILL.spad" 135429 135440 137224 137229) (-119 "BRAGG.spad" 134343 134353 135409 135424) (-118 "BRAGG.spad" 133231 133243 134299 134304) (-117 "BPADICRT.spad" 131213 131225 131468 131561) (-116 "BPADIC.spad" 130877 130889 131139 131208) (-115 "BOUNDZRO.spad" 130533 130550 130867 130872) (-114 "BOP1.spad" 127919 127929 130489 130494) (-113 "BOP.spad" 123383 123391 127909 127914) (-112 "BOOLEAN.spad" 122707 122715 123373 123378) (-111 "BMODULE.spad" 122419 122431 122675 122702) (-110 "BITS.spad" 121838 121846 122055 122082) (-109 "BINFILE.spad" 121181 121189 121828 121833) (-108 "BINDING.spad" 120600 120608 121171 121176) (-107 "BINARY.spad" 118491 118499 119068 119161) (-106 "BGAGG.spad" 117676 117686 118459 118486) (-105 "BGAGG.spad" 116881 116893 117666 117671) (-104 "BFUNCT.spad" 116445 116453 116861 116876) (-103 "BEZOUT.spad" 115579 115606 116395 116400) (-102 "BBTREE.spad" 112398 112408 115186 115213) (-101 "BASTYPE.spad" 112070 112078 112388 112393) (-100 "BASTYPE.spad" 111740 111750 112060 112065) (-99 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diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 34f7c1f3..a43fd8c7 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
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141079) ((-1216 . -1029) 140984) ((-1216 . -21) T) ((-1216 . -23) T) ((-1216 . -1072) T) ((-1216 . -595) 140966) ((-1216 . -101) T) ((-1216 . -25) T) ((-1216 . -130) T) ((-1216 . -696) 140858) ((-1216 . -143) 140819) ((-1216 . -145) 140780) ((-1216 . -170) T) ((-1216 . -543) T) ((-1216 . -283) T) ((-1216 . -47) 140724) ((-1215 . -1214) 140703) ((-1215 . -356) 140682) ((-1215 . -1188) 140661) ((-1215 . -895) 140640) ((-1215 . -543) 140591) ((-1215 . -170) 140522) ((-1215 . -696) 140363) ((-1215 . -38) 140204) ((-1215 . -444) 140183) ((-1215 . -300) 140162) ((-1215 . -626) 140059) ((-1215 . -705) T) ((-1215 . -1083) T) ((-1215 . -1030) T) ((-1215 . -1023) T) ((-1215 . -111) 139880) ((-1215 . -1029) 139715) ((-1215 . -21) T) ((-1215 . -23) T) ((-1215 . -1072) T) ((-1215 . -595) 139697) ((-1215 . -101) T) ((-1215 . -25) T) ((-1215 . -130) T) ((-1215 . -283) 139648) ((-1215 . -237) 139627) ((-1215 . -976) 139593) ((-1215 . -1169) 139559) ((-1215 . -1172) 139525) ((-1215 . -484) 139491) ((-1215 . -277) 139457) ((-1215 . -94) 139423) ((-1215 . -35) 139389) ((-1215 . -1208) 139359) ((-1215 . -47) 139329) ((-1215 . -145) 139308) ((-1215 . -143) 139287) ((-1215 . -947) 139249) ((-1215 . -874) 139155) ((-1215 . -279) 139140) ((-1215 . -227) 139092) ((-1215 . -1212) 139076) ((-1215 . -1012) 139060) ((-1210 . -1214) 139021) ((-1210 . -356) 139000) ((-1210 . -1188) 138979) ((-1210 . -895) 138958) ((-1210 . -543) 138909) ((-1210 . -170) 138840) ((-1210 . -696) 138681) ((-1210 . -38) 138522) ((-1210 . -444) 138501) ((-1210 . -300) 138480) ((-1210 . -626) 138377) ((-1210 . -705) T) ((-1210 . -1083) T) ((-1210 . -1030) T) ((-1210 . -1023) T) ((-1210 . -111) 138198) ((-1210 . -1029) 138033) ((-1210 . -21) T) ((-1210 . -23) T) ((-1210 . -1072) T) ((-1210 . -595) 138015) ((-1210 . -101) T) ((-1210 . -25) T) ((-1210 . -130) T) ((-1210 . -283) 137966) ((-1210 . -237) 137945) ((-1210 . -976) 137911) ((-1210 . -1169) 137877) ((-1210 . -1172) 137843) ((-1210 . -484) 137809) ((-1210 . -277) 137775) ((-1210 . -94) 137741) ((-1210 . -35) 137707) ((-1210 . -1208) 137677) ((-1210 . -47) 137647) ((-1210 . -145) 137626) ((-1210 . -143) 137605) ((-1210 . -947) 137567) ((-1210 . -874) 137473) ((-1210 . -279) 137458) ((-1210 . -227) 137410) ((-1210 . -1212) 137394) ((-1210 . -1012) 137329) ((-1198 . -1205) 137313) ((-1198 . -1122) 137291) ((-1198 . -596) NIL) ((-1198 . -302) 137278) ((-1198 . -505) 137225) ((-1198 . -319) 137202) ((-1198 . -1012) 137082) ((-1198 . -405) 137066) ((-1198 . -38) 136895) ((-1198 . -111) 136704) ((-1198 . -1029) 136527) ((-1198 . -626) 136452) ((-1198 . -696) 136281) ((-1198 . -143) 136260) ((-1198 . -145) 136239) ((-1198 . -47) 136216) ((-1198 . -370) 136200) ((-1198 . -619) 136148) ((-1198 . -825) 136127) ((-1198 . -874) 136070) ((-1198 . -860) NIL) ((-1198 . -884) 136049) ((-1198 . -1188) 136028) ((-1198 . -924) 135997) ((-1198 . -895) 135976) ((-1198 . -543) 135887) ((-1198 . -283) 135798) ((-1198 . -170) 135689) ((-1198 . -444) 135620) ((-1198 . -300) 135599) ((-1198 . -279) 135526) ((-1198 . -227) T) ((-1198 . -130) T) ((-1198 . -25) T) ((-1198 . -101) T) ((-1198 . -595) 135508) ((-1198 . -1072) T) ((-1198 . -23) T) ((-1198 . -21) T) ((-1198 . -705) T) ((-1198 . -1083) T) ((-1198 . -1030) T) ((-1198 . -1023) T) ((-1198 . -225) 135492) ((-1196 . -1065) 135476) ((-1196 . -1183) T) ((-1196 . -1072) 135454) ((-1196 . -595) 135421) ((-1196 . -101) 135399) ((-1196 . -1066) 135356) ((-1194 . -1193) 135335) ((-1194 . -976) 135301) ((-1194 . -1169) 135267) ((-1194 . -1172) 135233) ((-1194 . -484) 135199) ((-1194 . -277) 135165) ((-1194 . -94) 135131) ((-1194 . -35) 135097) ((-1194 . -1208) 135074) ((-1194 . -47) 135051) ((-1194 . -696) 134865) ((-1194 . -626) 134735) ((-1194 . -1029) 134543) ((-1194 . -111) 134332) ((-1194 . -38) 134146) ((-1194 . -947) 134115) ((-1194 . -279) 134035) ((-1194 . -1191) 134019) ((-1194 . -705) T) ((-1194 . -1083) T) ((-1194 . -1030) T) ((-1194 . -1023) T) ((-1194 . -21) T) ((-1194 . -23) T) ((-1194 . -1072) T) ((-1194 . -595) 134001) ((-1194 . -101) T) ((-1194 . -25) T) ((-1194 . -130) T) ((-1194 . -143) 133926) ((-1194 . -145) 133851) ((-1194 . -596) 133524) ((-1194 . -225) 133494) ((-1194 . -874) 133345) ((-1194 . -227) 133250) ((-1194 . -356) 133229) ((-1194 . -1188) 133208) ((-1194 . -895) 133187) ((-1194 . -543) 133138) ((-1194 . -170) 133069) ((-1194 . -444) 133048) ((-1194 . -300) 133027) ((-1194 . -283) 132978) ((-1194 . -237) 132957) ((-1194 . -331) 132927) ((-1194 . -505) 132787) ((-1194 . -302) 132726) ((-1194 . -370) 132696) ((-1194 . -619) 132604) ((-1194 . -393) 132574) ((-1194 . -1183) 132553) ((-1194 . -860) 132426) ((-1194 . -798) 132379) ((-1194 . -769) 132332) ((-1194 . -770) 132285) ((-1194 . -825) 132184) ((-1194 . -772) 132137) ((-1194 . -775) 132090) ((-1194 . -823) 132043) ((-1194 . -858) 132013) ((-1194 . -884) 131966) ((-1194 . -994) 131919) ((-1194 . -1012) 131705) ((-1194 . -1122) 131657) ((-1194 . -965) 131627) ((-1189 . -1193) 131588) ((-1189 . -976) 131554) ((-1189 . -1169) 131520) ((-1189 . -1172) 131486) ((-1189 . -484) 131452) ((-1189 . -277) 131418) ((-1189 . -94) 131384) ((-1189 . -35) 131350) ((-1189 . -1208) 131327) ((-1189 . -47) 131304) ((-1189 . -696) 131100) ((-1189 . -626) 130952) ((-1189 . -1029) 130742) ((-1189 . -111) 130511) ((-1189 . -38) 130307) ((-1189 . -947) 130276) ((-1189 . -279) 130124) ((-1189 . -1191) 130108) ((-1189 . -705) T) ((-1189 . -1083) T) ((-1189 . -1030) T) ((-1189 . -1023) T) ((-1189 . -21) T) ((-1189 . -23) T) ((-1189 . -1072) T) ((-1189 . -595) 130090) ((-1189 . -101) T) ((-1189 . -25) T) ((-1189 . -130) T) ((-1189 . -143) 129997) ((-1189 . -145) 129904) ((-1189 . -596) NIL) ((-1189 . -225) 129856) ((-1189 . -874) 129689) ((-1189 . -227) 129576) ((-1189 . -356) 129555) ((-1189 . -1188) 129534) ((-1189 . -895) 129513) ((-1189 . -543) 129464) ((-1189 . -170) 129395) ((-1189 . -444) 129374) ((-1189 . -300) 129353) ((-1189 . -283) 129304) ((-1189 . -237) 129283) ((-1189 . -331) 129235) ((-1189 . -505) 129004) ((-1189 . -302) 128889) ((-1189 . -370) 128841) ((-1189 . -619) 128793) ((-1189 . -393) 128745) ((-1189 . -1183) 128724) ((-1189 . -860) NIL) ((-1189 . -798) NIL) ((-1189 . -769) NIL) ((-1189 . -770) NIL) ((-1189 . -825) NIL) ((-1189 . -772) NIL) ((-1189 . -775) NIL) ((-1189 . -823) NIL) ((-1189 . -858) 128676) ((-1189 . -884) NIL) ((-1189 . -994) NIL) ((-1189 . -1012) 128642) ((-1189 . -1122) NIL) ((-1189 . -965) 128594) ((-1184 . -1054) T) ((-1184 . -595) 128560) ((-1184 . -1072) T) ((-1184 . -101) T) ((-1184 . -92) T) ((-1181 . -595) 128472) ((-1181 . -1072) 128450) ((-1181 . -101) 128428) ((-1176 . -719) 128404) ((-1176 . -35) 128370) ((-1176 . -94) 128336) ((-1176 . -277) 128302) ((-1176 . -484) 128268) ((-1176 . -1172) 128234) ((-1176 . -1169) 128200) ((-1176 . -976) 128166) ((-1176 . -47) 128135) ((-1176 . -38) 128032) ((-1176 . -696) 127929) ((-1176 . -283) 127908) ((-1176 . -543) 127887) ((-1176 . -111) 127756) ((-1176 . -1029) 127639) ((-1176 . -170) 127590) ((-1176 . -145) 127569) ((-1176 . -143) 127548) ((-1176 . -626) 127473) ((-1176 . -947) 127435) ((-1176 . -1023) T) ((-1176 . -1030) T) ((-1176 . -1083) T) ((-1176 . -705) T) ((-1176 . -21) T) ((-1176 . -23) T) ((-1176 . -1072) T) ((-1176 . -595) 127417) ((-1176 . -101) T) ((-1176 . -25) T) ((-1176 . -130) T) ((-1176 . -874) 127398) ((-1176 . -505) 127365) ((-1176 . -302) 127352) ((-1170 . -984) 127336) ((-1170 . -34) T) ((-1170 . -1183) T) ((-1170 . -595) 127268) ((-1170 . -302) 127206) ((-1170 . -505) 127139) ((-1170 . -1072) 127117) ((-1170 . -101) 127095) ((-1170 . -481) 127079) ((-1165 . -358) 127053) ((-1165 . -101) T) ((-1165 . -595) 127035) ((-1165 . -1072) T) ((-1163 . -1072) T) ((-1163 . -595) 127017) ((-1163 . -101) T) ((-1156 . -1160) 126996) ((-1156 . -223) 126946) ((-1156 . -106) 126896) ((-1156 . -302) 126700) ((-1156 . -505) 126492) ((-1156 . -481) 126429) ((-1156 . -149) 126379) ((-1156 . -596) NIL) ((-1156 . -229) 126329) ((-1156 . -592) 126308) ((-1156 . -281) 126287) ((-1156 . -279) 126266) ((-1156 . -101) T) ((-1156 . -1072) T) ((-1156 . -595) 126248) ((-1156 . -1183) T) ((-1156 . -34) T) ((-1156 . -586) 126227) ((-1152 . -1225) T) ((-1152 . -1072) T) ((-1152 . -595) 126209) ((-1152 . -101) T) ((-1151 . -595) 126191) ((-1150 . -595) 126173) ((-1149 . -319) 126150) ((-1149 . -1012) 126046) ((-1149 . -405) 126030) ((-1149 . -38) 125927) ((-1149 . -626) 125852) ((-1149 . -705) T) ((-1149 . -1083) T) ((-1149 . -1030) T) ((-1149 . -1023) T) ((-1149 . -111) 125721) ((-1149 . -1029) 125604) ((-1149 . -21) T) ((-1149 . -23) T) ((-1149 . -1072) T) ((-1149 . -595) 125586) ((-1149 . -101) T) ((-1149 . -25) T) ((-1149 . -130) T) ((-1149 . -696) 125483) ((-1149 . -143) 125462) ((-1149 . -145) 125441) ((-1149 . -170) 125392) ((-1149 . -543) 125371) ((-1149 . -283) 125350) ((-1149 . -47) 125327) ((-1147 . -825) T) ((-1147 . -101) T) ((-1147 . -595) 125309) ((-1147 . -1072) T) ((-1147 . -596) 125231) ((-1147 . -799) T) ((-1147 . -860) 125198) ((-1146 . -595) 125180) ((-1145 . -1222) 125164) ((-1145 . -227) 125123) ((-1145 . -626) 125048) ((-1145 . -130) T) ((-1145 . -25) T) ((-1145 . -101) T) ((-1145 . -595) 125030) ((-1145 . -1072) T) ((-1145 . -23) T) ((-1145 . -21) T) ((-1145 . -705) T) ((-1145 . -1083) T) ((-1145 . -1030) T) ((-1145 . -1023) T) ((-1145 . -279) 125015) ((-1145 . -874) 124928) ((-1145 . -947) 124897) ((-1145 . -38) 124794) ((-1145 . -111) 124663) ((-1145 . -1029) 124546) ((-1145 . -696) 124443) ((-1145 . -143) 124422) ((-1145 . -145) 124401) ((-1145 . -170) 124352) ((-1145 . -543) 124331) ((-1145 . -283) 124310) ((-1145 . -47) 124287) ((-1145 . -1208) 124264) ((-1145 . -35) 124230) ((-1145 . -94) 124196) ((-1145 . -277) 124162) ((-1145 . -484) 124128) ((-1145 . -1172) 124094) ((-1145 . -1169) 124060) ((-1145 . -976) 124026) ((-1144 . -1214) 123987) ((-1144 . -356) 123966) ((-1144 . -1188) 123945) ((-1144 . -895) 123924) ((-1144 . -543) 123875) ((-1144 . -170) 123806) ((-1144 . -696) 123647) ((-1144 . -38) 123488) ((-1144 . -444) 123467) ((-1144 . -300) 123446) ((-1144 . -626) 123343) ((-1144 . -705) T) ((-1144 . -1083) T) ((-1144 . -1030) T) ((-1144 . -1023) T) ((-1144 . -111) 123164) ((-1144 . -1029) 122999) ((-1144 . -21) T) ((-1144 . -23) T) ((-1144 . -1072) T) ((-1144 . -595) 122981) ((-1144 . -101) T) ((-1144 . -25) T) ((-1144 . -130) T) ((-1144 . -283) 122932) ((-1144 . -237) 122911) ((-1144 . -976) 122877) ((-1144 . -1169) 122843) ((-1144 . -1172) 122809) ((-1144 . -484) 122775) ((-1144 . -277) 122741) ((-1144 . -94) 122707) ((-1144 . -35) 122673) ((-1144 . -1208) 122643) ((-1144 . -47) 122613) ((-1144 . -145) 122592) ((-1144 . -143) 122571) ((-1144 . -947) 122533) ((-1144 . -874) 122439) ((-1144 . -279) 122424) ((-1144 . -227) 122376) ((-1144 . -1212) 122360) ((-1144 . -1012) 122295) ((-1141 . -1205) 122279) ((-1141 . -1122) 122257) ((-1141 . -596) NIL) ((-1141 . -302) 122244) ((-1141 . -505) 122191) ((-1141 . -319) 122168) ((-1141 . -1012) 122048) ((-1141 . -405) 122032) ((-1141 . -38) 121861) ((-1141 . -111) 121670) ((-1141 . -1029) 121493) ((-1141 . -626) 121418) ((-1141 . -696) 121247) ((-1141 . -143) 121226) ((-1141 . -145) 121205) ((-1141 . -47) 121182) ((-1141 . -370) 121166) ((-1141 . -619) 121114) ((-1141 . -825) 121093) ((-1141 . -874) 121036) ((-1141 . -860) NIL) ((-1141 . -884) 121015) ((-1141 . -1188) 120994) ((-1141 . -924) 120963) ((-1141 . -895) 120942) ((-1141 . -543) 120853) ((-1141 . -283) 120764) ((-1141 . -170) 120655) ((-1141 . -444) 120586) ((-1141 . -300) 120565) ((-1141 . -279) 120492) ((-1141 . -227) T) ((-1141 . -130) T) ((-1141 . -25) T) ((-1141 . -101) T) ((-1141 . -595) 120474) ((-1141 . -1072) T) ((-1141 . -23) T) ((-1141 . -21) T) ((-1141 . -705) T) ((-1141 . -1083) T) ((-1141 . -1030) T) ((-1141 . -1023) T) ((-1141 . -225) 120458) ((-1138 . -1193) 120419) ((-1138 . -976) 120385) ((-1138 . -1169) 120351) ((-1138 . -1172) 120317) ((-1138 . -484) 120283) ((-1138 . -277) 120249) ((-1138 . -94) 120215) ((-1138 . -35) 120181) ((-1138 . -1208) 120158) ((-1138 . -47) 120135) ((-1138 . -696) 119931) ((-1138 . -626) 119783) ((-1138 . -1029) 119573) ((-1138 . -111) 119342) ((-1138 . -38) 119138) ((-1138 . -947) 119107) ((-1138 . -279) 118955) ((-1138 . -1191) 118939) ((-1138 . -705) T) ((-1138 . -1083) T) ((-1138 . -1030) T) ((-1138 . -1023) T) ((-1138 . -21) T) ((-1138 . -23) T) ((-1138 . -1072) T) ((-1138 . -595) 118921) ((-1138 . -101) T) ((-1138 . -25) T) ((-1138 . -130) T) ((-1138 . -143) 118828) ((-1138 . -145) 118735) ((-1138 . -596) NIL) ((-1138 . -225) 118687) ((-1138 . -874) 118520) ((-1138 . -227) 118407) ((-1138 . -356) 118386) ((-1138 . -1188) 118365) ((-1138 . -895) 118344) ((-1138 . -543) 118295) ((-1138 . -170) 118226) ((-1138 . -444) 118205) ((-1138 . -300) 118184) ((-1138 . -283) 118135) ((-1138 . -237) 118114) ((-1138 . -331) 118066) ((-1138 . -505) 117835) ((-1138 . -302) 117720) ((-1138 . -370) 117672) ((-1138 . -619) 117624) ((-1138 . -393) 117576) ((-1138 . -1183) 117555) ((-1138 . -860) NIL) ((-1138 . -798) NIL) ((-1138 . -769) NIL) ((-1138 . -770) NIL) ((-1138 . -825) NIL) ((-1138 . -772) NIL) ((-1138 . -775) NIL) ((-1138 . -823) NIL) ((-1138 . -858) 117507) ((-1138 . -884) NIL) ((-1138 . -994) NIL) ((-1138 . -1012) 117473) ((-1138 . -1122) NIL) ((-1138 . -965) 117425) ((-1137 . -1054) T) ((-1137 . -595) 117391) ((-1137 . -1072) T) ((-1137 . -101) T) ((-1137 . -92) T) ((-1136 . -1072) T) ((-1136 . -595) 117373) ((-1136 . -101) T) ((-1135 . -1072) T) ((-1135 . -595) 117355) ((-1135 . -101) T) ((-1130 . -1160) 117331) ((-1130 . -223) 117278) ((-1130 . -106) 117225) ((-1130 . -302) 117020) ((-1130 . -505) 116803) ((-1130 . -481) 116737) ((-1130 . -149) 116684) ((-1130 . -596) NIL) ((-1130 . -229) 116631) ((-1130 . -592) 116607) ((-1130 . -281) 116583) ((-1130 . -279) 116559) ((-1130 . -101) T) ((-1130 . -1072) T) ((-1130 . -595) 116541) ((-1130 . -1183) T) ((-1130 . -34) T) ((-1130 . -586) 116517) ((-1129 . -1128) T) ((-1129 . -19) 116499) ((-1129 . -629) 116481) ((-1129 . -281) 116456) ((-1129 . -279) 116431) ((-1129 . -586) 116406) ((-1129 . -596) NIL) ((-1129 . -481) 116388) ((-1129 . -505) NIL) ((-1129 . -302) NIL) ((-1129 . -1183) T) ((-1129 . -34) T) ((-1129 . -149) 116370) ((-1129 . -825) T) ((-1129 . -365) 116352) ((-1129 . -1115) T) ((-1129 . -101) T) ((-1129 . -595) 116334) ((-1129 . -1072) T) ((-1129 . -799) T) ((-1124 . -652) 116318) ((-1124 . -629) 116302) ((-1124 . -281) 116279) ((-1124 . -279) 116256) ((-1124 . -586) 116233) ((-1124 . -596) 116194) ((-1124 . -481) 116178) ((-1124 . -101) 116156) ((-1124 . -1072) 116134) ((-1124 . -505) 116067) ((-1124 . -302) 116005) ((-1124 . -595) 115937) ((-1124 . -1183) T) ((-1124 . -34) T) ((-1124 . -149) 115921) ((-1124 . -1218) 115905) ((-1124 . -984) 115889) ((-1124 . -1120) 115873) ((-1121 . -1160) 115852) ((-1121 . -223) 115802) ((-1121 . -106) 115752) ((-1121 . -302) 115556) ((-1121 . -505) 115348) ((-1121 . -481) 115285) ((-1121 . -149) 115235) ((-1121 . -596) NIL) ((-1121 . -229) 115185) ((-1121 . -592) 115164) ((-1121 . -281) 115143) ((-1121 . -279) 115122) ((-1121 . -101) T) ((-1121 . -1072) T) ((-1121 . -595) 115104) ((-1121 . -1183) T) ((-1121 . -34) T) ((-1121 . -586) 115083) ((-1118 . -1092) 115067) ((-1118 . -481) 115051) ((-1118 . -101) 115029) ((-1118 . -1072) 115007) ((-1118 . -505) 114940) ((-1118 . -302) 114878) ((-1118 . -595) 114810) ((-1118 . -1183) T) ((-1118 . -34) T) ((-1118 . -106) 114794) ((-1117 . -1080) 114763) ((-1117 . -1178) 114732) ((-1117 . -595) 114694) ((-1117 . -149) 114678) ((-1117 . -34) T) ((-1117 . -1183) T) ((-1117 . -302) 114616) ((-1117 . -505) 114549) ((-1117 . -1072) T) ((-1117 . -101) T) ((-1117 . -481) 114533) ((-1117 . -596) 114494) ((-1117 . -950) 114463) ((-1117 . -1043) 114432) ((-1113 . -1094) 114377) ((-1113 . -481) 114361) ((-1113 . -505) 114294) ((-1113 . -302) 114232) ((-1113 . -1183) T) ((-1113 . -34) T) ((-1113 . -1026) 114172) ((-1113 . -1012) 114068) ((-1113 . -405) 114052) ((-1113 . -619) 114000) ((-1113 . -370) 113984) ((-1113 . -227) 113963) ((-1113 . -874) 113922) ((-1113 . -225) 113906) ((-1113 . -696) 113838) ((-1113 . -626) 113812) ((-1113 . -130) T) ((-1113 . -25) T) ((-1113 . -101) T) ((-1113 . -595) 113774) ((-1113 . -1072) T) ((-1113 . -23) T) ((-1113 . -21) T) ((-1113 . -1029) 113758) ((-1113 . -111) 113737) ((-1113 . -1023) T) ((-1113 . -1030) T) ((-1113 . -1083) T) ((-1113 . -705) T) ((-1113 . -38) 113697) ((-1113 . -596) 113658) ((-1112 . -984) 113629) ((-1112 . -34) T) ((-1112 . -1183) T) ((-1112 . -595) 113611) ((-1112 . -302) 113537) ((-1112 . -505) 113456) ((-1112 . -1072) T) ((-1112 . -101) T) ((-1112 . -481) 113427) ((-1111 . -1072) T) ((-1111 . -595) 113409) ((-1111 . -101) T) ((-1106 . -1108) T) ((-1106 . -1225) T) ((-1106 . -92) T) ((-1106 . -101) T) ((-1106 . -595) 113375) ((-1106 . -1072) T) ((-1106 . -1054) T) ((-1104 . -1105) 113359) ((-1104 . -101) T) ((-1104 . -595) 113341) ((-1104 . -1072) T) ((-1097 . -719) 113320) ((-1097 . -35) 113286) ((-1097 . -94) 113252) ((-1097 . -277) 113218) ((-1097 . -484) 113184) ((-1097 . -1172) 113150) ((-1097 . -1169) 113116) ((-1097 . -976) 113082) ((-1097 . -47) 113054) ((-1097 . -38) 112951) ((-1097 . -696) 112848) ((-1097 . -283) 112827) ((-1097 . -543) 112806) ((-1097 . -111) 112675) ((-1097 . -1029) 112558) ((-1097 . -170) 112509) ((-1097 . -145) 112488) ((-1097 . -143) 112467) ((-1097 . -626) 112392) ((-1097 . -947) 112359) ((-1097 . -1023) T) ((-1097 . -1030) T) ((-1097 . -1083) T) ((-1097 . -705) T) ((-1097 . -21) T) ((-1097 . -23) T) ((-1097 . -1072) T) ((-1097 . -595) 112341) ((-1097 . -101) T) ((-1097 . -25) T) ((-1097 . -130) T) ((-1097 . -874) 112325) ((-1097 . -505) 112295) ((-1097 . -302) 112282) ((-1096 . -924) 112249) ((-1096 . -1012) 112132) ((-1096 . -1188) 112111) ((-1096 . -884) 112090) ((-1096 . -860) 111949) ((-1096 . -874) 111933) ((-1096 . -825) 111912) ((-1096 . -505) 111864) ((-1096 . -444) 111815) ((-1096 . -619) 111763) ((-1096 . -370) 111747) ((-1096 . -47) 111719) ((-1096 . -38) 111568) ((-1096 . -696) 111417) ((-1096 . -283) 111348) ((-1096 . -543) 111279) ((-1096 . -111) 111108) ((-1096 . -1029) 110951) ((-1096 . -170) 110862) ((-1096 . -145) 110841) ((-1096 . -143) 110820) ((-1096 . -626) 110745) ((-1096 . -130) T) ((-1096 . -25) T) ((-1096 . -101) T) ((-1096 . -595) 110727) ((-1096 . -1072) T) ((-1096 . -23) T) ((-1096 . -21) T) ((-1096 . -1023) T) ((-1096 . -1030) T) ((-1096 . -1083) T) ((-1096 . -705) T) ((-1096 . -405) 110711) ((-1096 . -319) 110683) ((-1096 . -302) 110670) ((-1096 . -596) 110418) ((-1091 . -535) T) ((-1091 . -1188) T) ((-1091 . -1122) T) ((-1091 . -1012) 110400) ((-1091 . -596) 110315) ((-1091 . -994) T) ((-1091 . -860) 110297) ((-1091 . -823) T) ((-1091 . -775) T) ((-1091 . -772) T) ((-1091 . -825) T) ((-1091 . -770) T) ((-1091 . -769) T) ((-1091 . -798) T) ((-1091 . -619) 110279) ((-1091 . -895) T) ((-1091 . -543) T) ((-1091 . -283) T) ((-1091 . -170) T) ((-1091 . -696) 110266) ((-1091 . -1029) 110253) ((-1091 . -111) 110238) ((-1091 . -38) 110225) ((-1091 . -444) T) ((-1091 . -300) T) ((-1091 . -227) T) ((-1091 . -141) T) ((-1091 . -1023) T) ((-1091 . -1030) T) ((-1091 . -1083) T) ((-1091 . -705) T) ((-1091 . -21) T) ((-1091 . -23) T) ((-1091 . -1072) T) ((-1091 . -595) 110207) ((-1091 . -101) T) ((-1091 . -25) T) ((-1091 . -130) T) ((-1091 . -626) 110194) ((-1091 . -145) T) ((-1091 . -640) T) ((-1091 . -799) T) ((-1087 . -1054) T) ((-1087 . -595) 110160) ((-1087 . -1072) T) ((-1087 . -101) T) ((-1087 . -92) T) ((-1086 . -1072) T) ((-1086 . -595) 110142) ((-1086 . -101) T) ((-1084 . -232) 110121) ((-1084 . -1237) 110091) ((-1084 . -769) 110070) ((-1084 . -823) 110049) ((-1084 . -775) 110000) ((-1084 . -772) 109951) ((-1084 . -825) 109902) ((-1084 . -770) 109853) ((-1084 . -771) 109832) ((-1084 . -281) 109809) ((-1084 . -279) 109786) ((-1084 . -481) 109770) ((-1084 . -505) 109703) ((-1084 . -302) 109641) ((-1084 . -1183) T) ((-1084 . -34) T) ((-1084 . -586) 109618) ((-1084 . -1012) 109445) ((-1084 . -405) 109414) ((-1084 . -619) 109320) ((-1084 . -370) 109289) ((-1084 . -361) 109268) ((-1084 . -227) 109220) ((-1084 . -874) 109152) ((-1084 . -225) 109121) ((-1084 . -111) 109011) ((-1084 . -1029) 108908) ((-1084 . -170) 108887) ((-1084 . -595) 108618) ((-1084 . -696) 108560) ((-1084 . -626) 108408) ((-1084 . -130) 108278) ((-1084 . -23) 108148) ((-1084 . -21) 108058) ((-1084 . -1023) 107988) ((-1084 . -1030) 107918) ((-1084 . -1083) 107828) ((-1084 . -705) 107738) ((-1084 . -38) 107708) ((-1084 . -1072) 107498) ((-1084 . -101) 107288) ((-1084 . -25) 107139) ((-1077 . -389) T) ((-1077 . -1183) T) ((-1077 . -595) 107121) ((-1076 . -1075) 107085) ((-1076 . -101) T) ((-1076 . -595) 107067) ((-1076 . -1072) T) ((-1074 . -1075) 107019) ((-1074 . -101) T) ((-1074 . -595) 107001) ((-1074 . -1072) T) ((-1073 . -361) T) ((-1073 . -101) T) ((-1073 . -595) 106983) ((-1073 . -1072) T) ((-1068 . -419) 106967) ((-1068 . -1070) 106951) ((-1068 . -361) 106930) ((-1068 . -229) 106914) ((-1068 . -596) 106875) ((-1068 . -149) 106859) ((-1068 . -481) 106843) ((-1068 . -101) T) ((-1068 . -1072) T) ((-1068 . -505) 106776) ((-1068 . -302) 106714) ((-1068 . -595) 106696) ((-1068 . -1183) T) ((-1068 . -34) T) ((-1068 . -106) 106680) ((-1068 . -223) 106664) ((-1067 . -1054) T) ((-1067 . -595) 106630) ((-1067 . -1072) T) ((-1067 . -101) T) ((-1067 . -92) T) ((-1063 . -1183) T) ((-1063 . -1072) 106608) ((-1063 . -595) 106575) ((-1063 . -101) 106553) ((-1062 . -1054) T) ((-1062 . -595) 106519) ((-1062 . -1072) T) ((-1062 . -101) T) ((-1062 . -92) T) ((-1060 . -1065) 106503) ((-1060 . -1183) T) ((-1060 . -1072) 106481) ((-1060 . -595) 106448) ((-1060 . -101) 106426) ((-1060 . -1066) 106384) ((-1059 . -259) 106368) ((-1059 . -1012) 106352) ((-1059 . -1072) T) ((-1059 . -595) 106334) ((-1059 . -101) T) ((-1059 . -825) T) ((-1058 . -246) 106271) ((-1058 . -1012) 106098) ((-1058 . -596) NIL) ((-1058 . -319) 106059) ((-1058 . -405) 106043) ((-1058 . -38) 105892) ((-1058 . -111) 105721) ((-1058 . -1029) 105564) ((-1058 . -626) 105489) ((-1058 . -696) 105338) ((-1058 . -143) 105317) ((-1058 . -145) 105296) ((-1058 . -170) 105207) ((-1058 . -543) 105138) ((-1058 . -283) 105069) ((-1058 . -47) 105030) ((-1058 . -370) 105014) ((-1058 . -619) 104962) ((-1058 . -444) 104913) ((-1058 . -505) 104780) ((-1058 . -825) 104759) ((-1058 . -874) 104694) ((-1058 . -860) NIL) ((-1058 . -884) 104673) ((-1058 . -1188) 104652) ((-1058 . -924) 104597) ((-1058 . -302) 104584) ((-1058 . -227) 104563) ((-1058 . -130) T) ((-1058 . -25) T) ((-1058 . -101) T) ((-1058 . -595) 104545) ((-1058 . -1072) T) ((-1058 . -23) T) ((-1058 . -21) T) ((-1058 . -705) T) ((-1058 . -1083) T) ((-1058 . -1030) T) ((-1058 . -1023) T) ((-1058 . -225) 104529) ((-1056 . -595) 104511) ((-1053 . -825) T) ((-1053 . -101) T) ((-1053 . -595) 104493) ((-1053 . -1072) T) ((-1050 . -703) 104472) ((-1050 . -1012) 104368) ((-1050 . -405) 104352) ((-1050 . -619) 104300) ((-1050 . -370) 104284) ((-1050 . -363) 104263) ((-1050 . -145) 104242) ((-1050 . -696) 104110) ((-1050 . -626) 104020) ((-1050 . -1029) 103930) ((-1050 . -111) 103826) ((-1050 . -38) 103694) ((-1050 . -403) 103673) ((-1050 . -395) 103652) ((-1050 . -143) 103603) ((-1050 . -1122) 103582) ((-1050 . -343) 103561) ((-1050 . -361) 103512) ((-1050 . -237) 103463) ((-1050 . -283) 103414) ((-1050 . -300) 103365) ((-1050 . -444) 103316) ((-1050 . -543) 103267) ((-1050 . -895) 103218) ((-1050 . -1188) 103169) ((-1050 . -356) 103120) ((-1050 . -227) 103045) ((-1050 . -874) 102978) ((-1050 . -225) 102948) ((-1050 . -596) 102932) ((-1050 . -21) T) ((-1050 . -23) T) ((-1050 . -1072) T) ((-1050 . -595) 102914) ((-1050 . -101) T) ((-1050 . -25) T) ((-1050 . -130) T) ((-1050 . -1023) T) ((-1050 . -1030) T) ((-1050 . -1083) T) ((-1050 . -705) T) ((-1050 . -170) T) ((-1048 . -1072) T) ((-1048 . -595) 102896) ((-1048 . -101) T) ((-1048 . -279) 102875) ((-1047 . -1072) T) ((-1047 . -595) 102857) ((-1047 . -101) T) ((-1046 . -1072) T) ((-1046 . -595) 102839) ((-1046 . -101) T) ((-1046 . -279) 102818) ((-1046 . -1012) 102795) ((-1045 . -1054) T) ((-1045 . -595) 102761) ((-1045 . -1072) T) ((-1045 . -101) T) ((-1045 . -92) T) ((-1038 . -1054) T) ((-1038 . -595) 102727) ((-1038 . -1072) T) ((-1038 . -101) T) ((-1038 . -92) T) ((-1035 . -1160) 102702) ((-1035 . -223) 102648) ((-1035 . -106) 102594) ((-1035 . -302) 102445) ((-1035 . -505) 102289) ((-1035 . -481) 102220) ((-1035 . -149) 102166) ((-1035 . -596) NIL) ((-1035 . -229) 102112) ((-1035 . -592) 102087) ((-1035 . -281) 102062) ((-1035 . -279) 102037) ((-1035 . -101) T) ((-1035 . -1072) T) ((-1035 . -595) 102019) ((-1035 . -1183) T) ((-1035 . -34) T) ((-1035 . -586) 101994) ((-1034 . -535) T) ((-1034 . -1188) T) ((-1034 . -1122) T) ((-1034 . -1012) 101976) ((-1034 . -596) 101891) ((-1034 . -994) T) ((-1034 . -860) 101873) ((-1034 . -823) T) ((-1034 . -775) T) ((-1034 . -772) T) ((-1034 . -825) T) ((-1034 . -770) T) ((-1034 . -769) T) ((-1034 . -798) T) ((-1034 . -619) 101855) ((-1034 . -895) T) ((-1034 . -543) T) ((-1034 . -283) T) ((-1034 . -170) T) ((-1034 . -696) 101842) ((-1034 . -1029) 101829) ((-1034 . -111) 101814) ((-1034 . -38) 101801) ((-1034 . -444) T) ((-1034 . -300) T) ((-1034 . -227) T) ((-1034 . -141) T) ((-1034 . -1023) T) ((-1034 . -1030) T) ((-1034 . -1083) T) ((-1034 . -705) T) ((-1034 . -21) T) ((-1034 . -23) T) ((-1034 . -1072) T) ((-1034 . -595) 101783) ((-1034 . -101) T) ((-1034 . -25) T) ((-1034 . -130) T) ((-1034 . -626) 101770) ((-1034 . -145) T) ((-1033 . -1040) 101749) ((-1033 . -101) T) ((-1033 . -595) 101731) ((-1033 . -1072) T) ((-1027 . -1026) 101671) ((-1027 . -696) 101613) ((-1027 . -34) T) ((-1027 . -1183) T) ((-1027 . -302) 101551) ((-1027 . -505) 101484) ((-1027 . -481) 101468) ((-1027 . -626) 101452) ((-1027 . -130) T) ((-1027 . -25) T) ((-1027 . -101) T) ((-1027 . -595) 101414) ((-1027 . -1072) T) ((-1027 . -23) T) ((-1027 . -21) T) ((-1027 . -1029) 101398) ((-1027 . -111) 101377) ((-1027 . -1237) 101347) ((-1027 . -596) 101308) ((-1020 . -1043) 101237) ((-1020 . -950) 101166) ((-1020 . -596) 101108) ((-1020 . -481) 101073) ((-1020 . -101) T) ((-1020 . -1072) T) ((-1020 . -505) 100974) ((-1020 . -302) 100882) ((-1020 . -595) 100825) ((-1020 . -1183) T) ((-1020 . -34) T) ((-1020 . -149) 100790) ((-1020 . -1178) 100719) ((-1010 . -1054) T) ((-1010 . -595) 100685) ((-1010 . -1072) T) ((-1010 . -101) T) ((-1010 . -92) T) ((-1009 . -1160) 100660) ((-1009 . -223) 100606) ((-1009 . -106) 100552) ((-1009 . -302) 100403) ((-1009 . -505) 100247) ((-1009 . -481) 100178) ((-1009 . -149) 100124) ((-1009 . -596) NIL) ((-1009 . -229) 100070) ((-1009 . -592) 100045) ((-1009 . -281) 100020) ((-1009 . -279) 99995) ((-1009 . -101) T) ((-1009 . -1072) T) ((-1009 . -595) 99977) ((-1009 . -1183) T) ((-1009 . -34) T) ((-1009 . -586) 99952) ((-1008 . -170) T) ((-1008 . -705) T) ((-1008 . -1083) T) ((-1008 . -1030) T) ((-1008 . -1023) T) ((-1008 . -626) 99926) ((-1008 . -130) T) ((-1008 . -25) T) ((-1008 . -101) T) ((-1008 . -595) 99908) ((-1008 . -1072) T) ((-1008 . -23) T) ((-1008 . -21) T) ((-1008 . -1029) 99882) ((-1008 . -111) 99849) ((-1008 . -38) 99833) ((-1008 . -696) 99817) ((-1001 . -1043) 99786) ((-1001 . -950) 99755) ((-1001 . -596) 99716) ((-1001 . -481) 99700) ((-1001 . -101) T) ((-1001 . -1072) T) ((-1001 . -505) 99633) ((-1001 . -302) 99571) ((-1001 . -595) 99533) ((-1001 . -1183) T) ((-1001 . -34) T) ((-1001 . -149) 99517) ((-1001 . -1178) 99486) ((-1000 . -1183) T) ((-1000 . -1072) 99464) ((-1000 . -595) 99431) ((-1000 . -101) 99409) ((-998 . -986) T) ((-998 . -976) T) ((-998 . -769) T) ((-998 . -770) T) ((-998 . -825) T) ((-998 . -772) T) ((-998 . -775) T) ((-998 . -823) T) ((-998 . -1012) 99289) ((-998 . -405) 99251) ((-998 . -237) T) ((-998 . -283) T) ((-998 . -300) T) ((-998 . -444) T) ((-998 . -38) 99188) ((-998 . -696) 99125) ((-998 . -543) T) ((-998 . -895) T) ((-998 . -1188) T) ((-998 . -356) T) ((-998 . -111) 99041) ((-998 . -1029) 98978) ((-998 . -170) T) ((-998 . -145) T) ((-998 . -626) 98915) ((-998 . -130) T) ((-998 . -25) T) ((-998 . -101) T) ((-998 . -595) 98897) ((-998 . -1072) T) ((-998 . -23) T) ((-998 . -21) T) ((-998 . -1023) T) ((-998 . -1030) T) ((-998 . -1083) T) ((-998 . -705) T) ((-993 . -1054) T) ((-993 . -595) 98863) ((-993 . -1072) T) ((-993 . -101) T) ((-993 . -92) T) ((-978 . -965) 98845) ((-978 . -1122) T) ((-978 . -1012) 98805) ((-978 . -596) 98735) ((-978 . -994) T) ((-978 . -884) NIL) ((-978 . -858) 98717) ((-978 . -823) T) ((-978 . -775) T) ((-978 . -772) T) ((-978 . -825) T) ((-978 . -770) T) ((-978 . -769) T) ((-978 . -798) T) ((-978 . -860) 98699) ((-978 . -1183) T) ((-978 . -393) 98681) ((-978 . -619) 98663) ((-978 . -370) 98645) ((-978 . -279) NIL) ((-978 . -302) NIL) ((-978 . -505) NIL) ((-978 . -331) 98627) ((-978 . -237) T) ((-978 . -111) 98561) ((-978 . -1029) 98511) ((-978 . -283) T) ((-978 . -696) 98461) ((-978 . -626) 98411) ((-978 . -38) 98361) ((-978 . -300) T) ((-978 . -444) T) ((-978 . -170) T) ((-978 . -543) T) ((-978 . -895) T) ((-978 . -1188) T) ((-978 . -356) T) ((-978 . -227) T) ((-978 . -874) NIL) ((-978 . -225) 98343) ((-978 . -145) T) ((-978 . -143) NIL) ((-978 . -130) T) ((-978 . -25) T) ((-978 . -101) T) ((-978 . -595) 98325) ((-978 . -1072) T) ((-978 . -23) T) ((-978 . -21) T) ((-978 . -1023) T) ((-978 . -1030) T) ((-978 . -1083) T) ((-978 . -705) T) ((-977 . -335) 98299) ((-977 . -170) T) ((-977 . -705) T) ((-977 . -1083) T) ((-977 . -1030) T) ((-977 . -1023) T) ((-977 . -626) 98244) ((-977 . -130) T) ((-977 . -25) T) ((-977 . -101) T) ((-977 . -595) 98226) ((-977 . -1072) T) ((-977 . -23) T) ((-977 . -21) T) ((-977 . -1029) 98171) ((-977 . -111) 98100) ((-977 . -596) 98084) ((-977 . -225) 98061) ((-977 . -874) 98013) ((-977 . -227) 97985) ((-977 . -356) T) ((-977 . -1188) T) ((-977 . -895) T) ((-977 . -543) T) ((-977 . -696) 97930) ((-977 . -38) 97875) ((-977 . -444) T) ((-977 . -300) T) ((-977 . -283) T) ((-977 . -237) T) ((-977 . -361) NIL) ((-977 . -343) NIL) ((-977 . -1122) NIL) ((-977 . 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. -770) NIL) ((-845 . -769) NIL) ((-845 . -798) NIL) ((-845 . -860) NIL) ((-845 . -1183) T) ((-845 . -393) 88330) ((-845 . -619) 88307) ((-845 . -370) 88284) ((-845 . -279) 88235) ((-845 . -302) 88192) ((-845 . -505) 88100) ((-845 . -331) 88077) ((-845 . -237) T) ((-845 . -111) 88006) ((-845 . -1029) 87951) ((-845 . -283) T) ((-845 . -696) 87896) ((-845 . -626) 87841) ((-845 . -38) 87786) ((-845 . -300) T) ((-845 . -444) T) ((-845 . -170) T) ((-845 . -543) T) ((-845 . -895) T) ((-845 . -1188) T) ((-845 . -356) T) ((-845 . -227) NIL) ((-845 . -874) NIL) ((-845 . -225) 87763) ((-845 . -145) T) ((-845 . -143) NIL) ((-845 . -130) T) ((-845 . -25) T) ((-845 . -101) T) ((-845 . -595) 87745) ((-845 . -1072) T) ((-845 . -23) T) ((-845 . -21) T) ((-845 . -1023) T) ((-845 . -1030) T) ((-845 . -1083) T) ((-845 . -705) T) ((-843 . -844) 87729) ((-843 . -895) T) ((-843 . -543) T) ((-843 . -283) T) ((-843 . -170) T) ((-843 . -696) 87716) ((-843 . -1029) 87703) ((-843 . -111) 87688) ((-843 . -38) 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. -601) 12887) ((-217 . -626) 12854) ((-217 . -705) T) ((-217 . -1083) T) ((-217 . -1030) T) ((-217 . -1023) T) ((-217 . -21) T) ((-217 . -23) T) ((-217 . -1072) T) ((-217 . -595) 12836) ((-217 . -101) T) ((-217 . -25) T) ((-217 . -130) T) ((-217 . -1012) 12813) ((-216 . -247) 12797) ((-216 . -1092) 12781) ((-216 . -106) 12765) ((-216 . -34) T) ((-216 . -1183) T) ((-216 . -595) 12697) ((-216 . -302) 12635) ((-216 . -505) 12568) ((-216 . -1072) 12546) ((-216 . -101) 12524) ((-216 . -481) 12508) ((-216 . -969) 12492) ((-212 . -1054) T) ((-212 . -595) 12458) ((-212 . -1072) T) ((-212 . -101) T) ((-212 . -92) T) ((-211 . -965) 12440) ((-211 . -1122) T) ((-211 . -1012) 12400) ((-211 . -596) 12330) ((-211 . -994) T) ((-211 . -884) NIL) ((-211 . -858) 12312) ((-211 . -823) T) ((-211 . -775) T) ((-211 . -772) T) ((-211 . -825) T) ((-211 . -770) T) ((-211 . -769) T) ((-211 . -798) T) ((-211 . -860) 12294) ((-211 . -1183) T) ((-211 . -393) 12276) ((-211 . -619) 12258) ((-211 . -370) 12240) 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-1031) 144217) ((-1252 . -111) 144196) ((-1252 . -38) 144166) ((-1252 . -1251) 144145) ((-1252 . -379) 144117) ((-1247 . -379) 144089) ((-1247 . -1014) 144066) ((-1247 . -698) 144036) ((-1247 . -628) 144010) ((-1247 . -130) T) ((-1247 . -25) T) ((-1247 . -101) T) ((-1247 . -597) 143992) ((-1247 . -1074) T) ((-1247 . -23) T) ((-1247 . -21) T) ((-1247 . -1031) 143976) ((-1247 . -111) 143955) ((-1247 . -1254) 143934) ((-1247 . -1025) T) ((-1247 . -1032) T) ((-1247 . -1085) T) ((-1247 . -707) T) ((-1247 . -1246) 143918) ((-1247 . -38) 143888) ((-1247 . -1251) 143867) ((-1245 . -1180) 143836) ((-1245 . -597) 143798) ((-1245 . -149) 143782) ((-1245 . -34) T) ((-1245 . -1185) T) ((-1245 . -304) 143720) ((-1245 . -507) 143653) ((-1245 . -1074) T) ((-1245 . -101) T) ((-1245 . -483) 143637) ((-1245 . -598) 143598) ((-1245 . -952) 143567) ((-1244 . -1025) T) ((-1244 . -1032) T) ((-1244 . -1085) T) ((-1244 . -707) T) ((-1244 . -21) T) ((-1244 . -23) T) ((-1244 . -1074) T) ((-1244 . -597) 143549) 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-1224) 142688) ((-1221 . -229) 142647) ((-1221 . -628) 142572) ((-1221 . -130) T) ((-1221 . -25) T) ((-1221 . -101) T) ((-1221 . -597) 142554) ((-1221 . -1074) T) ((-1221 . -23) T) ((-1221 . -21) T) ((-1221 . -707) T) ((-1221 . -1085) T) ((-1221 . -1032) T) ((-1221 . -1025) T) ((-1221 . -281) 142539) ((-1221 . -876) 142452) ((-1221 . -949) 142421) ((-1221 . -38) 142318) ((-1221 . -111) 142187) ((-1221 . -1031) 142070) ((-1221 . -698) 141967) ((-1221 . -143) 141946) ((-1221 . -145) 141925) ((-1221 . -170) 141876) ((-1221 . -545) 141855) ((-1221 . -285) 141834) ((-1221 . -47) 141811) ((-1221 . -1210) 141788) ((-1221 . -35) 141754) ((-1221 . -94) 141720) ((-1221 . -279) 141686) ((-1221 . -486) 141652) ((-1221 . -1174) 141618) ((-1221 . -1171) 141584) ((-1221 . -978) 141550) ((-1218 . -321) 141494) ((-1218 . -1014) 141460) ((-1218 . -407) 141426) ((-1218 . -38) 141318) ((-1218 . -628) 141223) ((-1218 . -707) T) ((-1218 . -1085) T) ((-1218 . -1032) T) ((-1218 . -1025) T) ((-1218 . -111) 141115) ((-1218 . -1031) 141020) ((-1218 . -21) T) ((-1218 . -23) T) ((-1218 . -1074) T) ((-1218 . -597) 141002) ((-1218 . -101) T) ((-1218 . -25) T) ((-1218 . -130) T) ((-1218 . -698) 140894) ((-1218 . -143) 140855) ((-1218 . -145) 140816) ((-1218 . -170) T) ((-1218 . -545) T) ((-1218 . -285) T) ((-1218 . -47) 140760) ((-1217 . -1216) 140739) ((-1217 . -358) 140718) ((-1217 . -1190) 140697) ((-1217 . -897) 140676) ((-1217 . -545) 140627) ((-1217 . -170) 140558) ((-1217 . -698) 140399) ((-1217 . -38) 140240) ((-1217 . -446) 140219) ((-1217 . -302) 140198) ((-1217 . -628) 140095) ((-1217 . -707) T) ((-1217 . -1085) T) ((-1217 . -1032) T) ((-1217 . -1025) T) ((-1217 . -111) 139916) ((-1217 . -1031) 139751) ((-1217 . -21) T) ((-1217 . -23) T) ((-1217 . -1074) T) ((-1217 . -597) 139733) ((-1217 . -101) T) ((-1217 . -25) T) ((-1217 . -130) T) ((-1217 . -285) 139684) ((-1217 . -239) 139663) ((-1217 . -978) 139629) ((-1217 . -1171) 139595) ((-1217 . -1174) 139561) ((-1217 . -486) 139527) ((-1217 . -279) 139493) ((-1217 . -94) 139459) ((-1217 . -35) 139425) ((-1217 . -1210) 139395) ((-1217 . -47) 139365) ((-1217 . -145) 139344) ((-1217 . -143) 139323) ((-1217 . -949) 139285) ((-1217 . -876) 139191) ((-1217 . -281) 139176) ((-1217 . -229) 139128) ((-1217 . -1214) 139112) ((-1217 . -1014) 139096) ((-1212 . -1216) 139057) ((-1212 . -358) 139036) ((-1212 . -1190) 139015) ((-1212 . -897) 138994) ((-1212 . -545) 138945) ((-1212 . -170) 138876) ((-1212 . -698) 138717) ((-1212 . -38) 138558) ((-1212 . -446) 138537) ((-1212 . -302) 138516) ((-1212 . -628) 138413) ((-1212 . -707) T) ((-1212 . -1085) T) ((-1212 . -1032) T) ((-1212 . -1025) T) ((-1212 . -111) 138234) ((-1212 . -1031) 138069) ((-1212 . -21) T) ((-1212 . -23) T) ((-1212 . -1074) T) ((-1212 . -597) 138051) ((-1212 . -101) T) ((-1212 . -25) T) ((-1212 . -130) T) ((-1212 . -285) 138002) ((-1212 . -239) 137981) ((-1212 . -978) 137947) ((-1212 . -1171) 137913) ((-1212 . -1174) 137879) ((-1212 . -486) 137845) ((-1212 . -279) 137811) ((-1212 . -94) 137777) ((-1212 . -35) 137743) ((-1212 . -1210) 137713) ((-1212 . -47) 137683) ((-1212 . -145) 137662) ((-1212 . -143) 137641) ((-1212 . -949) 137603) ((-1212 . -876) 137509) ((-1212 . -281) 137494) ((-1212 . -229) 137446) ((-1212 . -1214) 137430) ((-1212 . -1014) 137365) ((-1200 . -1207) 137349) ((-1200 . -1124) 137327) ((-1200 . -598) NIL) ((-1200 . -304) 137314) ((-1200 . -507) 137261) ((-1200 . -321) 137238) ((-1200 . -1014) 137118) ((-1200 . -407) 137102) ((-1200 . -38) 136931) ((-1200 . -111) 136740) ((-1200 . -1031) 136563) ((-1200 . -628) 136488) ((-1200 . -698) 136317) ((-1200 . -143) 136296) ((-1200 . -145) 136275) ((-1200 . -47) 136252) ((-1200 . -372) 136236) ((-1200 . -621) 136184) ((-1200 . -827) 136163) ((-1200 . -876) 136106) ((-1200 . -862) NIL) ((-1200 . -886) 136085) ((-1200 . -1190) 136064) ((-1200 . -926) 136033) ((-1200 . -897) 136012) ((-1200 . -545) 135923) ((-1200 . -285) 135834) ((-1200 . -170) 135725) ((-1200 . -446) 135656) ((-1200 . -302) 135635) ((-1200 . -281) 135562) ((-1200 . -229) T) ((-1200 . -130) T) ((-1200 . -25) T) ((-1200 . -101) T) ((-1200 . -597) 135544) ((-1200 . -1074) T) ((-1200 . -23) T) ((-1200 . -21) T) ((-1200 . -707) T) ((-1200 . -1085) T) ((-1200 . -1032) T) ((-1200 . -1025) T) ((-1200 . -227) 135528) ((-1198 . -1067) 135512) ((-1198 . -1185) T) ((-1198 . -1074) 135490) ((-1198 . -597) 135457) ((-1198 . -101) 135435) ((-1198 . -1068) 135392) ((-1196 . -1195) 135371) ((-1196 . -978) 135337) ((-1196 . -1171) 135303) ((-1196 . -1174) 135269) ((-1196 . -486) 135235) ((-1196 . -279) 135201) ((-1196 . -94) 135167) ((-1196 . -35) 135133) ((-1196 . -1210) 135110) ((-1196 . -47) 135087) ((-1196 . -698) 134901) ((-1196 . -628) 134771) ((-1196 . -1031) 134579) ((-1196 . -111) 134368) ((-1196 . -38) 134182) ((-1196 . -949) 134151) ((-1196 . -281) 134071) ((-1196 . -1193) 134055) ((-1196 . -707) T) ((-1196 . -1085) T) ((-1196 . -1032) T) ((-1196 . -1025) T) ((-1196 . -21) T) ((-1196 . -23) T) ((-1196 . -1074) T) ((-1196 . -597) 134037) ((-1196 . -101) T) ((-1196 . -25) T) ((-1196 . -130) T) ((-1196 . -143) 133962) ((-1196 . -145) 133887) ((-1196 . -598) 133560) ((-1196 . -227) 133530) ((-1196 . -876) 133381) ((-1196 . -229) 133286) ((-1196 . -358) 133265) ((-1196 . -1190) 133244) ((-1196 . -897) 133223) ((-1196 . -545) 133174) ((-1196 . -170) 133105) ((-1196 . -446) 133084) ((-1196 . -302) 133063) ((-1196 . -285) 133014) ((-1196 . -239) 132993) ((-1196 . -333) 132963) ((-1196 . -507) 132823) ((-1196 . -304) 132762) ((-1196 . -372) 132732) ((-1196 . -621) 132640) ((-1196 . -395) 132610) ((-1196 . -1185) 132589) ((-1196 . -862) 132462) ((-1196 . -800) 132415) ((-1196 . -771) 132368) ((-1196 . -772) 132321) ((-1196 . -827) 132220) ((-1196 . -774) 132173) ((-1196 . -777) 132126) ((-1196 . -825) 132079) ((-1196 . -860) 132049) ((-1196 . -886) 132002) ((-1196 . -996) 131955) ((-1196 . -1014) 131741) ((-1196 . -1124) 131693) ((-1196 . -967) 131663) ((-1191 . -1195) 131624) ((-1191 . -978) 131590) ((-1191 . -1171) 131556) ((-1191 . -1174) 131522) ((-1191 . -486) 131488) ((-1191 . -279) 131454) ((-1191 . -94) 131420) ((-1191 . -35) 131386) ((-1191 . -1210) 131363) ((-1191 . -47) 131340) ((-1191 . -698) 131136) ((-1191 . -628) 130988) ((-1191 . -1031) 130778) ((-1191 . -111) 130547) ((-1191 . -38) 130343) ((-1191 . -949) 130312) ((-1191 . -281) 130160) ((-1191 . -1193) 130144) ((-1191 . -707) T) ((-1191 . -1085) T) ((-1191 . -1032) T) ((-1191 . -1025) T) ((-1191 . -21) T) ((-1191 . -23) T) ((-1191 . -1074) T) ((-1191 . -597) 130126) ((-1191 . -101) T) ((-1191 . -25) T) ((-1191 . -130) T) ((-1191 . -143) 130033) ((-1191 . -145) 129940) ((-1191 . -598) NIL) ((-1191 . -227) 129892) ((-1191 . -876) 129725) ((-1191 . -229) 129612) ((-1191 . -358) 129591) ((-1191 . -1190) 129570) ((-1191 . -897) 129549) ((-1191 . -545) 129500) ((-1191 . -170) 129431) ((-1191 . -446) 129410) ((-1191 . -302) 129389) ((-1191 . -285) 129340) ((-1191 . -239) 129319) ((-1191 . -333) 129271) ((-1191 . -507) 129040) ((-1191 . -304) 128925) ((-1191 . -372) 128877) ((-1191 . -621) 128829) ((-1191 . -395) 128781) ((-1191 . -1185) 128760) ((-1191 . -862) NIL) ((-1191 . -800) NIL) ((-1191 . -771) NIL) ((-1191 . -772) NIL) ((-1191 . -827) NIL) ((-1191 . -774) NIL) ((-1191 . -777) NIL) ((-1191 . -825) NIL) ((-1191 . -860) 128712) ((-1191 . -886) NIL) ((-1191 . -996) NIL) ((-1191 . -1014) 128678) ((-1191 . -1124) NIL) ((-1191 . -967) 128630) ((-1186 . -1056) T) ((-1186 . -597) 128596) ((-1186 . -1074) T) ((-1186 . -101) T) ((-1186 . -92) T) ((-1183 . -597) 128508) ((-1183 . -1074) 128486) ((-1183 . -101) 128464) ((-1178 . -721) 128440) ((-1178 . -35) 128406) ((-1178 . -94) 128372) ((-1178 . -279) 128338) ((-1178 . -486) 128304) ((-1178 . -1174) 128270) ((-1178 . -1171) 128236) ((-1178 . -978) 128202) ((-1178 . -47) 128171) ((-1178 . -38) 128068) ((-1178 . -698) 127965) ((-1178 . -285) 127944) ((-1178 . -545) 127923) ((-1178 . -111) 127792) ((-1178 . -1031) 127675) ((-1178 . -170) 127626) ((-1178 . -145) 127605) ((-1178 . -143) 127584) ((-1178 . -628) 127509) ((-1178 . -949) 127471) ((-1178 . -1025) T) ((-1178 . -1032) T) ((-1178 . -1085) T) ((-1178 . -707) T) ((-1178 . -21) T) ((-1178 . -23) T) ((-1178 . -1074) T) ((-1178 . -597) 127453) ((-1178 . -101) T) ((-1178 . -25) T) ((-1178 . -130) T) ((-1178 . -876) 127434) ((-1178 . -507) 127401) ((-1178 . -304) 127388) ((-1172 . -986) 127372) ((-1172 . -34) T) ((-1172 . -1185) T) ((-1172 . -597) 127304) ((-1172 . -304) 127242) ((-1172 . -507) 127175) ((-1172 . -1074) 127153) ((-1172 . -101) 127131) ((-1172 . -483) 127115) ((-1167 . -360) 127089) ((-1167 . -101) T) ((-1167 . -597) 127071) ((-1167 . -1074) T) ((-1165 . -1074) T) ((-1165 . -597) 127053) ((-1165 . -101) T) ((-1158 . -1162) 127032) ((-1158 . -225) 126982) ((-1158 . -106) 126932) ((-1158 . -304) 126736) ((-1158 . -507) 126528) ((-1158 . -483) 126465) ((-1158 . -149) 126415) ((-1158 . -598) NIL) ((-1158 . -231) 126365) ((-1158 . -594) 126344) ((-1158 . -283) 126323) ((-1158 . -281) 126302) ((-1158 . -101) T) ((-1158 . -1074) T) ((-1158 . -597) 126284) ((-1158 . -1185) T) ((-1158 . -34) T) ((-1158 . -588) 126263) ((-1154 . -1227) T) ((-1154 . -1074) T) ((-1154 . -597) 126245) ((-1154 . -101) T) ((-1153 . -597) 126227) ((-1152 . -597) 126209) ((-1151 . -321) 126186) ((-1151 . -1014) 126082) ((-1151 . -407) 126066) ((-1151 . -38) 125963) ((-1151 . -628) 125888) ((-1151 . -707) T) ((-1151 . -1085) T) ((-1151 . -1032) T) ((-1151 . -1025) T) ((-1151 . -111) 125757) ((-1151 . -1031) 125640) ((-1151 . -21) T) ((-1151 . -23) T) ((-1151 . -1074) T) ((-1151 . -597) 125622) ((-1151 . -101) T) ((-1151 . -25) T) ((-1151 . -130) T) ((-1151 . -698) 125519) ((-1151 . -143) 125498) ((-1151 . -145) 125477) ((-1151 . -170) 125428) ((-1151 . -545) 125407) ((-1151 . -285) 125386) ((-1151 . -47) 125363) ((-1149 . -827) T) ((-1149 . -101) T) ((-1149 . -597) 125345) ((-1149 . -1074) T) ((-1149 . -598) 125267) ((-1149 . -801) T) ((-1149 . -862) 125234) ((-1148 . -597) 125216) ((-1147 . -1224) 125200) ((-1147 . -229) 125159) ((-1147 . -628) 125084) ((-1147 . -130) T) ((-1147 . -25) T) ((-1147 . -101) T) ((-1147 . -597) 125066) ((-1147 . -1074) T) ((-1147 . -23) T) ((-1147 . -21) T) ((-1147 . -707) T) ((-1147 . -1085) T) ((-1147 . -1032) T) ((-1147 . -1025) T) ((-1147 . -281) 125051) ((-1147 . -876) 124964) ((-1147 . -949) 124933) ((-1147 . -38) 124830) ((-1147 . -111) 124699) ((-1147 . -1031) 124582) ((-1147 . -698) 124479) ((-1147 . -143) 124458) ((-1147 . -145) 124437) ((-1147 . -170) 124388) ((-1147 . -545) 124367) ((-1147 . -285) 124346) ((-1147 . -47) 124323) ((-1147 . -1210) 124300) ((-1147 . -35) 124266) ((-1147 . -94) 124232) ((-1147 . -279) 124198) ((-1147 . -486) 124164) ((-1147 . -1174) 124130) ((-1147 . -1171) 124096) ((-1147 . -978) 124062) ((-1146 . -1216) 124023) ((-1146 . -358) 124002) ((-1146 . -1190) 123981) ((-1146 . -897) 123960) ((-1146 . -545) 123911) ((-1146 . -170) 123842) ((-1146 . -698) 123683) ((-1146 . -38) 123524) ((-1146 . -446) 123503) ((-1146 . -302) 123482) ((-1146 . -628) 123379) ((-1146 . -707) T) ((-1146 . -1085) T) ((-1146 . -1032) T) ((-1146 . -1025) T) ((-1146 . -111) 123200) ((-1146 . -1031) 123035) ((-1146 . -21) T) ((-1146 . -23) T) ((-1146 . -1074) T) ((-1146 . -597) 123017) ((-1146 . -101) T) ((-1146 . -25) T) ((-1146 . -130) T) ((-1146 . -285) 122968) ((-1146 . -239) 122947) ((-1146 . -978) 122913) ((-1146 . -1171) 122879) ((-1146 . -1174) 122845) ((-1146 . -486) 122811) ((-1146 . -279) 122777) ((-1146 . -94) 122743) ((-1146 . -35) 122709) ((-1146 . -1210) 122679) ((-1146 . -47) 122649) ((-1146 . -145) 122628) ((-1146 . -143) 122607) ((-1146 . -949) 122569) ((-1146 . -876) 122475) ((-1146 . -281) 122460) ((-1146 . -229) 122412) ((-1146 . -1214) 122396) ((-1146 . -1014) 122331) ((-1143 . -1207) 122315) ((-1143 . -1124) 122293) ((-1143 . -598) NIL) ((-1143 . -304) 122280) ((-1143 . -507) 122227) ((-1143 . -321) 122204) ((-1143 . -1014) 122084) ((-1143 . -407) 122068) ((-1143 . -38) 121897) ((-1143 . -111) 121706) ((-1143 . -1031) 121529) ((-1143 . -628) 121454) ((-1143 . -698) 121283) ((-1143 . -143) 121262) ((-1143 . -145) 121241) ((-1143 . -47) 121218) ((-1143 . -372) 121202) ((-1143 . -621) 121150) ((-1143 . -827) 121129) ((-1143 . -876) 121072) ((-1143 . -862) NIL) ((-1143 . -886) 121051) ((-1143 . -1190) 121030) ((-1143 . -926) 120999) ((-1143 . -897) 120978) ((-1143 . -545) 120889) ((-1143 . -285) 120800) ((-1143 . -170) 120691) ((-1143 . -446) 120622) ((-1143 . -302) 120601) ((-1143 . -281) 120528) ((-1143 . -229) T) ((-1143 . -130) T) ((-1143 . -25) T) ((-1143 . -101) T) ((-1143 . -597) 120510) ((-1143 . -1074) T) ((-1143 . -23) T) ((-1143 . -21) T) ((-1143 . -707) T) ((-1143 . -1085) T) ((-1143 . -1032) T) ((-1143 . -1025) T) ((-1143 . -227) 120494) ((-1140 . -1195) 120455) ((-1140 . -978) 120421) ((-1140 . -1171) 120387) ((-1140 . -1174) 120353) ((-1140 . -486) 120319) ((-1140 . -279) 120285) ((-1140 . -94) 120251) ((-1140 . -35) 120217) ((-1140 . -1210) 120194) ((-1140 . -47) 120171) ((-1140 . -698) 119967) ((-1140 . -628) 119819) ((-1140 . -1031) 119609) ((-1140 . -111) 119378) ((-1140 . -38) 119174) ((-1140 . -949) 119143) ((-1140 . -281) 118991) ((-1140 . -1193) 118975) ((-1140 . -707) T) ((-1140 . -1085) T) ((-1140 . -1032) T) ((-1140 . -1025) T) ((-1140 . -21) T) ((-1140 . -23) T) ((-1140 . -1074) T) ((-1140 . -597) 118957) ((-1140 . -101) T) ((-1140 . -25) T) ((-1140 . -130) T) ((-1140 . -143) 118864) ((-1140 . -145) 118771) ((-1140 . -598) NIL) ((-1140 . -227) 118723) ((-1140 . -876) 118556) ((-1140 . -229) 118443) ((-1140 . -358) 118422) ((-1140 . -1190) 118401) ((-1140 . -897) 118380) ((-1140 . -545) 118331) ((-1140 . -170) 118262) ((-1140 . -446) 118241) ((-1140 . -302) 118220) ((-1140 . -285) 118171) ((-1140 . -239) 118150) ((-1140 . -333) 118102) ((-1140 . -507) 117871) ((-1140 . -304) 117756) ((-1140 . -372) 117708) ((-1140 . -621) 117660) ((-1140 . -395) 117612) ((-1140 . -1185) 117591) ((-1140 . -862) NIL) ((-1140 . -800) NIL) ((-1140 . -771) NIL) ((-1140 . -772) NIL) ((-1140 . -827) NIL) ((-1140 . -774) NIL) ((-1140 . -777) NIL) ((-1140 . -825) NIL) ((-1140 . -860) 117543) ((-1140 . -886) NIL) ((-1140 . -996) NIL) ((-1140 . -1014) 117509) ((-1140 . -1124) NIL) ((-1140 . -967) 117461) ((-1139 . -1056) T) ((-1139 . -597) 117427) ((-1139 . -1074) T) ((-1139 . -101) T) ((-1139 . -92) T) ((-1138 . -1074) T) ((-1138 . -597) 117409) ((-1138 . -101) T) ((-1137 . -1074) T) ((-1137 . -597) 117391) ((-1137 . -101) T) ((-1132 . -1162) 117367) ((-1132 . -225) 117314) ((-1132 . -106) 117261) ((-1132 . -304) 117056) ((-1132 . -507) 116839) ((-1132 . -483) 116773) ((-1132 . -149) 116720) ((-1132 . -598) NIL) ((-1132 . -231) 116667) ((-1132 . -594) 116643) ((-1132 . -283) 116619) ((-1132 . -281) 116595) ((-1132 . -101) T) ((-1132 . -1074) T) ((-1132 . -597) 116577) ((-1132 . -1185) T) ((-1132 . -34) T) ((-1132 . -588) 116553) ((-1131 . -1130) T) ((-1131 . -19) 116535) ((-1131 . -631) 116517) ((-1131 . -283) 116492) ((-1131 . -281) 116467) ((-1131 . -588) 116442) ((-1131 . -598) NIL) ((-1131 . -483) 116424) ((-1131 . -507) NIL) ((-1131 . -304) NIL) ((-1131 . -1185) T) ((-1131 . -34) T) ((-1131 . -149) 116406) ((-1131 . -827) T) ((-1131 . -367) 116388) ((-1131 . -1117) T) ((-1131 . -101) T) ((-1131 . -597) 116370) ((-1131 . -1074) T) ((-1131 . -801) T) ((-1126 . -654) 116354) ((-1126 . -631) 116338) ((-1126 . -283) 116315) ((-1126 . -281) 116292) ((-1126 . -588) 116269) ((-1126 . -598) 116230) ((-1126 . -483) 116214) ((-1126 . -101) 116192) ((-1126 . -1074) 116170) ((-1126 . -507) 116103) ((-1126 . -304) 116041) ((-1126 . -597) 115973) ((-1126 . -1185) T) ((-1126 . -34) T) ((-1126 . -149) 115957) ((-1126 . -1220) 115941) ((-1126 . -986) 115925) ((-1126 . -1122) 115909) ((-1123 . -1162) 115888) ((-1123 . -225) 115838) ((-1123 . -106) 115788) ((-1123 . -304) 115592) ((-1123 . -507) 115384) ((-1123 . -483) 115321) ((-1123 . -149) 115271) ((-1123 . -598) NIL) ((-1123 . -231) 115221) ((-1123 . -594) 115200) ((-1123 . -283) 115179) ((-1123 . -281) 115158) ((-1123 . -101) T) ((-1123 . -1074) T) ((-1123 . -597) 115140) ((-1123 . -1185) T) ((-1123 . -34) T) ((-1123 . -588) 115119) ((-1120 . -1094) 115103) ((-1120 . -483) 115087) ((-1120 . -101) 115065) ((-1120 . -1074) 115043) ((-1120 . -507) 114976) ((-1120 . -304) 114914) ((-1120 . -597) 114846) ((-1120 . -1185) T) ((-1120 . -34) T) ((-1120 . -106) 114830) ((-1119 . -1082) 114799) ((-1119 . -1180) 114768) ((-1119 . -597) 114730) ((-1119 . -149) 114714) ((-1119 . -34) T) ((-1119 . -1185) T) ((-1119 . -304) 114652) ((-1119 . -507) 114585) ((-1119 . -1074) T) ((-1119 . -101) T) ((-1119 . -483) 114569) ((-1119 . -598) 114530) ((-1119 . -952) 114499) ((-1119 . -1045) 114468) ((-1115 . -1096) 114413) ((-1115 . -483) 114397) ((-1115 . -507) 114330) ((-1115 . -304) 114268) ((-1115 . -1185) T) ((-1115 . -34) T) ((-1115 . -1028) 114208) ((-1115 . -1014) 114104) ((-1115 . -407) 114088) ((-1115 . -621) 114036) ((-1115 . -372) 114020) ((-1115 . -229) 113999) ((-1115 . -876) 113958) ((-1115 . -227) 113942) ((-1115 . -698) 113874) ((-1115 . -628) 113848) ((-1115 . -130) T) ((-1115 . -25) T) ((-1115 . -101) T) ((-1115 . -597) 113810) ((-1115 . -1074) T) ((-1115 . -23) T) ((-1115 . -21) T) ((-1115 . -1031) 113794) ((-1115 . -111) 113773) ((-1115 . -1025) T) ((-1115 . -1032) T) ((-1115 . -1085) T) ((-1115 . -707) T) ((-1115 . -38) 113733) ((-1115 . -598) 113694) ((-1114 . -986) 113665) ((-1114 . -34) T) ((-1114 . -1185) T) ((-1114 . -597) 113647) ((-1114 . -304) 113573) ((-1114 . -507) 113492) ((-1114 . -1074) T) ((-1114 . -101) T) ((-1114 . -483) 113463) ((-1113 . -1074) T) ((-1113 . -597) 113445) ((-1113 . -101) T) ((-1108 . -1110) T) ((-1108 . -1227) T) ((-1108 . -92) T) ((-1108 . -101) T) ((-1108 . -597) 113411) ((-1108 . -1074) T) ((-1108 . -1056) T) ((-1106 . -1107) 113395) ((-1106 . -101) T) ((-1106 . -597) 113377) ((-1106 . -1074) T) ((-1099 . -721) 113356) ((-1099 . -35) 113322) ((-1099 . -94) 113288) ((-1099 . -279) 113254) ((-1099 . -486) 113220) ((-1099 . -1174) 113186) ((-1099 . -1171) 113152) ((-1099 . -978) 113118) ((-1099 . -47) 113090) ((-1099 . -38) 112987) ((-1099 . -698) 112884) ((-1099 . -285) 112863) ((-1099 . -545) 112842) ((-1099 . -111) 112711) ((-1099 . -1031) 112594) ((-1099 . -170) 112545) ((-1099 . -145) 112524) ((-1099 . -143) 112503) ((-1099 . -628) 112428) ((-1099 . -949) 112395) ((-1099 . -1025) T) ((-1099 . -1032) T) ((-1099 . -1085) T) ((-1099 . -707) T) ((-1099 . -21) T) ((-1099 . -23) T) ((-1099 . -1074) T) ((-1099 . -597) 112377) ((-1099 . -101) T) ((-1099 . -25) T) ((-1099 . -130) T) ((-1099 . -876) 112361) ((-1099 . -507) 112331) ((-1099 . -304) 112318) ((-1098 . -926) 112285) ((-1098 . -1014) 112168) ((-1098 . -1190) 112147) ((-1098 . -886) 112126) ((-1098 . -862) 111985) ((-1098 . -876) 111969) ((-1098 . -827) 111948) ((-1098 . -507) 111900) ((-1098 . -446) 111851) ((-1098 . -621) 111799) ((-1098 . -372) 111783) ((-1098 . -47) 111755) ((-1098 . -38) 111604) ((-1098 . -698) 111453) ((-1098 . -285) 111384) ((-1098 . -545) 111315) ((-1098 . -111) 111144) ((-1098 . -1031) 110987) ((-1098 . -170) 110898) ((-1098 . -145) 110877) ((-1098 . -143) 110856) ((-1098 . -628) 110781) ((-1098 . -130) T) ((-1098 . -25) T) ((-1098 . -101) T) ((-1098 . -597) 110763) ((-1098 . -1074) T) ((-1098 . -23) T) ((-1098 . -21) T) ((-1098 . -1025) T) ((-1098 . -1032) T) ((-1098 . -1085) T) ((-1098 . -707) T) ((-1098 . -407) 110747) ((-1098 . -321) 110719) ((-1098 . -304) 110706) ((-1098 . -598) 110454) ((-1093 . -537) T) ((-1093 . -1190) T) ((-1093 . -1124) T) ((-1093 . -1014) 110436) ((-1093 . -598) 110351) ((-1093 . -996) T) ((-1093 . -862) 110333) ((-1093 . -825) T) ((-1093 . -777) T) ((-1093 . -774) T) ((-1093 . -827) T) ((-1093 . -772) T) ((-1093 . -771) T) ((-1093 . -800) T) ((-1093 . -621) 110315) ((-1093 . -897) T) ((-1093 . -545) T) ((-1093 . -285) T) ((-1093 . -170) T) ((-1093 . -698) 110302) ((-1093 . -1031) 110289) ((-1093 . -111) 110274) ((-1093 . -38) 110261) ((-1093 . -446) T) ((-1093 . -302) T) ((-1093 . -229) T) ((-1093 . -141) T) ((-1093 . -1025) T) ((-1093 . -1032) T) ((-1093 . -1085) T) ((-1093 . -707) T) ((-1093 . -21) T) ((-1093 . -23) T) ((-1093 . -1074) T) ((-1093 . -597) 110243) ((-1093 . -101) T) ((-1093 . -25) T) ((-1093 . -130) T) ((-1093 . -628) 110230) ((-1093 . -145) T) ((-1093 . -642) T) ((-1093 . -801) T) ((-1089 . -1056) T) ((-1089 . -597) 110196) ((-1089 . -1074) T) ((-1089 . -101) T) ((-1089 . -92) T) ((-1088 . -1074) T) ((-1088 . -597) 110178) ((-1088 . -101) T) ((-1086 . -234) 110157) ((-1086 . -1239) 110127) ((-1086 . -771) 110106) ((-1086 . -825) 110085) ((-1086 . -777) 110036) ((-1086 . -774) 109987) ((-1086 . -827) 109938) ((-1086 . -772) 109889) ((-1086 . -773) 109868) ((-1086 . -283) 109845) ((-1086 . -281) 109822) ((-1086 . -483) 109806) ((-1086 . -507) 109739) ((-1086 . -304) 109677) ((-1086 . -1185) T) ((-1086 . -34) T) ((-1086 . -588) 109654) ((-1086 . -1014) 109481) ((-1086 . -407) 109450) ((-1086 . -621) 109356) ((-1086 . -372) 109325) ((-1086 . -363) 109304) ((-1086 . -229) 109256) ((-1086 . -876) 109188) ((-1086 . -227) 109157) ((-1086 . -111) 109047) ((-1086 . -1031) 108944) ((-1086 . -170) 108923) ((-1086 . -597) 108654) ((-1086 . -698) 108596) ((-1086 . -628) 108444) ((-1086 . -130) 108314) ((-1086 . -23) 108184) ((-1086 . -21) 108094) ((-1086 . -1025) 108024) ((-1086 . -1032) 107954) ((-1086 . -1085) 107864) ((-1086 . -707) 107774) ((-1086 . -38) 107744) ((-1086 . -1074) 107534) ((-1086 . -101) 107324) ((-1086 . -25) 107175) ((-1079 . -391) T) ((-1079 . -1185) T) ((-1079 . -597) 107157) ((-1078 . -1077) 107121) ((-1078 . -101) T) ((-1078 . -597) 107103) ((-1078 . -1074) T) ((-1076 . -1077) 107055) ((-1076 . -101) T) ((-1076 . -597) 107037) ((-1076 . -1074) T) ((-1075 . -363) T) ((-1075 . -101) T) ((-1075 . -597) 107019) ((-1075 . -1074) T) ((-1070 . -421) 107003) ((-1070 . -1072) 106987) ((-1070 . -363) 106966) ((-1070 . -231) 106950) ((-1070 . -598) 106911) ((-1070 . -149) 106895) ((-1070 . -483) 106879) ((-1070 . -101) T) ((-1070 . -1074) T) ((-1070 . -507) 106812) ((-1070 . -304) 106750) ((-1070 . -597) 106732) ((-1070 . -1185) T) ((-1070 . -34) T) ((-1070 . -106) 106716) ((-1070 . -225) 106700) ((-1069 . -1056) T) ((-1069 . -597) 106666) ((-1069 . -1074) T) ((-1069 . -101) T) ((-1069 . -92) T) ((-1065 . -1185) T) ((-1065 . -1074) 106644) ((-1065 . -597) 106611) ((-1065 . -101) 106589) ((-1064 . -1056) T) ((-1064 . -597) 106555) ((-1064 . -1074) T) ((-1064 . -101) T) ((-1064 . -92) T) ((-1062 . -1067) 106539) ((-1062 . -1185) T) ((-1062 . -1074) 106517) ((-1062 . -597) 106484) ((-1062 . -101) 106462) ((-1062 . -1068) 106420) ((-1061 . -261) 106404) ((-1061 . -1014) 106388) ((-1061 . -1074) T) ((-1061 . -597) 106370) ((-1061 . -101) T) ((-1061 . -827) T) ((-1060 . -248) 106307) ((-1060 . -1014) 106134) ((-1060 . -598) NIL) ((-1060 . -321) 106095) ((-1060 . -407) 106079) ((-1060 . -38) 105928) ((-1060 . -111) 105757) ((-1060 . -1031) 105600) ((-1060 . -628) 105525) ((-1060 . -698) 105374) ((-1060 . -143) 105353) ((-1060 . -145) 105332) ((-1060 . -170) 105243) ((-1060 . -545) 105174) ((-1060 . -285) 105105) ((-1060 . -47) 105066) ((-1060 . -372) 105050) ((-1060 . -621) 104998) ((-1060 . -446) 104949) ((-1060 . -507) 104816) ((-1060 . -827) 104795) ((-1060 . -876) 104730) ((-1060 . -862) NIL) ((-1060 . -886) 104709) ((-1060 . -1190) 104688) ((-1060 . -926) 104633) ((-1060 . -304) 104620) ((-1060 . -229) 104599) ((-1060 . -130) T) ((-1060 . -25) T) ((-1060 . -101) T) ((-1060 . -597) 104581) ((-1060 . -1074) T) ((-1060 . -23) T) ((-1060 . -21) T) ((-1060 . -707) T) ((-1060 . -1085) T) ((-1060 . -1032) T) ((-1060 . -1025) T) ((-1060 . -227) 104565) ((-1058 . -597) 104547) ((-1055 . -827) T) ((-1055 . -101) T) ((-1055 . -597) 104529) ((-1055 . -1074) T) ((-1052 . -705) 104508) ((-1052 . -1014) 104404) ((-1052 . -407) 104388) ((-1052 . -621) 104336) ((-1052 . -372) 104320) ((-1052 . -365) 104299) ((-1052 . -145) 104278) ((-1052 . -698) 104146) ((-1052 . -628) 104056) ((-1052 . -1031) 103966) ((-1052 . -111) 103862) ((-1052 . -38) 103730) ((-1052 . -405) 103709) ((-1052 . -397) 103688) ((-1052 . -143) 103639) ((-1052 . -1124) 103618) ((-1052 . -345) 103597) ((-1052 . -363) 103548) ((-1052 . -239) 103499) ((-1052 . -285) 103450) ((-1052 . -302) 103401) ((-1052 . -446) 103352) ((-1052 . -545) 103303) ((-1052 . -897) 103254) ((-1052 . -1190) 103205) ((-1052 . -358) 103156) ((-1052 . -229) 103081) ((-1052 . -876) 103014) ((-1052 . -227) 102984) ((-1052 . -598) 102968) ((-1052 . -21) T) ((-1052 . -23) T) ((-1052 . -1074) T) ((-1052 . -597) 102950) ((-1052 . -101) T) ((-1052 . -25) T) ((-1052 . -130) T) ((-1052 . -1025) T) ((-1052 . -1032) T) ((-1052 . -1085) T) ((-1052 . -707) T) ((-1052 . -170) T) ((-1050 . -1074) T) ((-1050 . -597) 102932) ((-1050 . -101) T) ((-1050 . -281) 102911) ((-1049 . -1074) T) ((-1049 . -597) 102893) ((-1049 . -101) T) ((-1048 . -1074) T) ((-1048 . -597) 102875) ((-1048 . -101) T) ((-1048 . -281) 102854) ((-1048 . -1014) 102831) ((-1047 . -1056) T) ((-1047 . -597) 102797) ((-1047 . -1074) T) ((-1047 . -101) T) ((-1047 . -92) T) ((-1040 . -1056) T) ((-1040 . -597) 102763) ((-1040 . -1074) T) ((-1040 . -101) T) ((-1040 . -92) T) ((-1037 . -1162) 102738) ((-1037 . -225) 102684) ((-1037 . -106) 102630) ((-1037 . -304) 102481) ((-1037 . -507) 102325) ((-1037 . -483) 102256) ((-1037 . -149) 102202) ((-1037 . -598) NIL) ((-1037 . -231) 102148) ((-1037 . -594) 102123) ((-1037 . -283) 102098) ((-1037 . -281) 102073) ((-1037 . -101) T) ((-1037 . -1074) T) ((-1037 . -597) 102055) ((-1037 . -1185) T) ((-1037 . -34) T) ((-1037 . -588) 102030) ((-1036 . -537) T) ((-1036 . -1190) T) ((-1036 . -1124) T) ((-1036 . -1014) 102012) ((-1036 . -598) 101927) ((-1036 . -996) T) ((-1036 . -862) 101909) ((-1036 . -825) T) ((-1036 . -777) T) ((-1036 . -774) T) ((-1036 . -827) T) ((-1036 . -772) T) ((-1036 . -771) T) ((-1036 . -800) T) ((-1036 . -621) 101891) ((-1036 . -897) T) ((-1036 . -545) T) ((-1036 . -285) T) ((-1036 . -170) T) ((-1036 . -698) 101878) ((-1036 . -1031) 101865) ((-1036 . -111) 101850) ((-1036 . -38) 101837) ((-1036 . -446) T) ((-1036 . -302) T) ((-1036 . -229) T) ((-1036 . -141) T) ((-1036 . -1025) T) ((-1036 . -1032) T) ((-1036 . -1085) T) ((-1036 . -707) T) ((-1036 . -21) T) ((-1036 . -23) T) ((-1036 . -1074) T) ((-1036 . -597) 101819) ((-1036 . -101) T) ((-1036 . -25) T) ((-1036 . -130) T) ((-1036 . -628) 101806) ((-1036 . -145) T) ((-1035 . -1042) 101785) ((-1035 . -101) T) ((-1035 . -597) 101767) ((-1035 . -1074) T) ((-1029 . -1028) 101707) ((-1029 . -698) 101649) ((-1029 . -34) T) ((-1029 . -1185) T) ((-1029 . -304) 101587) ((-1029 . -507) 101520) ((-1029 . -483) 101504) ((-1029 . -628) 101488) ((-1029 . -130) T) ((-1029 . -25) T) ((-1029 . -101) T) ((-1029 . -597) 101450) ((-1029 . -1074) T) ((-1029 . -23) T) ((-1029 . -21) T) ((-1029 . -1031) 101434) ((-1029 . -111) 101413) ((-1029 . -1239) 101383) ((-1029 . -598) 101344) ((-1022 . -1045) 101273) ((-1022 . -952) 101202) ((-1022 . -598) 101144) ((-1022 . -483) 101109) ((-1022 . -101) T) ((-1022 . -1074) T) ((-1022 . -507) 101010) ((-1022 . -304) 100918) ((-1022 . -597) 100861) ((-1022 . -1185) T) ((-1022 . -34) T) ((-1022 . -149) 100826) ((-1022 . -1180) 100755) ((-1012 . -1056) T) ((-1012 . -597) 100721) ((-1012 . -1074) T) ((-1012 . -101) T) ((-1012 . -92) T) ((-1011 . -1162) 100696) ((-1011 . -225) 100642) ((-1011 . -106) 100588) ((-1011 . -304) 100439) ((-1011 . -507) 100283) ((-1011 . -483) 100214) ((-1011 . -149) 100160) ((-1011 . -598) NIL) ((-1011 . -231) 100106) ((-1011 . -594) 100081) ((-1011 . -283) 100056) ((-1011 . -281) 100031) ((-1011 . -101) T) ((-1011 . -1074) T) ((-1011 . -597) 100013) ((-1011 . -1185) T) ((-1011 . -34) T) ((-1011 . -588) 99988) ((-1010 . -170) T) ((-1010 . -707) T) ((-1010 . -1085) T) ((-1010 . -1032) T) ((-1010 . -1025) T) ((-1010 . -628) 99962) ((-1010 . -130) T) ((-1010 . -25) T) ((-1010 . -101) T) ((-1010 . -597) 99944) ((-1010 . -1074) T) ((-1010 . -23) T) ((-1010 . -21) T) ((-1010 . -1031) 99918) ((-1010 . -111) 99885) ((-1010 . -38) 99869) ((-1010 . -698) 99853) ((-1003 . -1045) 99822) ((-1003 . -952) 99791) ((-1003 . -598) 99752) ((-1003 . -483) 99736) ((-1003 . -101) T) ((-1003 . -1074) T) ((-1003 . -507) 99669) ((-1003 . -304) 99607) ((-1003 . -597) 99569) ((-1003 . -1185) T) ((-1003 . -34) T) ((-1003 . -149) 99553) ((-1003 . -1180) 99522) ((-1002 . -1185) T) ((-1002 . -1074) 99500) ((-1002 . -597) 99467) ((-1002 . -101) 99445) ((-1000 . -988) T) ((-1000 . -978) T) ((-1000 . -771) T) ((-1000 . -772) T) ((-1000 . -827) T) ((-1000 . -774) T) ((-1000 . -777) T) ((-1000 . -825) T) ((-1000 . -1014) 99325) ((-1000 . -407) 99287) ((-1000 . -239) T) ((-1000 . -285) T) ((-1000 . -302) T) ((-1000 . -446) T) ((-1000 . -38) 99224) ((-1000 . -698) 99161) ((-1000 . -545) T) ((-1000 . -897) T) ((-1000 . -1190) T) ((-1000 . -358) T) ((-1000 . -111) 99077) ((-1000 . -1031) 99014) ((-1000 . -170) T) ((-1000 . -145) T) ((-1000 . -628) 98951) ((-1000 . -130) T) ((-1000 . -25) T) ((-1000 . -101) T) ((-1000 . -597) 98933) ((-1000 . -1074) T) ((-1000 . -23) T) ((-1000 . -21) T) ((-1000 . -1025) T) ((-1000 . -1032) T) ((-1000 . -1085) T) ((-1000 . -707) T) ((-995 . -1056) T) ((-995 . -597) 98899) ((-995 . -1074) T) ((-995 . -101) T) ((-995 . -92) T) ((-980 . -967) 98881) ((-980 . -1124) T) ((-980 . -1014) 98841) ((-980 . -598) 98771) ((-980 . -996) T) ((-980 . -886) NIL) ((-980 . -860) 98753) ((-980 . -825) T) ((-980 . -777) T) ((-980 . -774) T) ((-980 . -827) T) ((-980 . -772) T) ((-980 . -771) T) ((-980 . -800) T) ((-980 . -862) 98735) ((-980 . -1185) T) ((-980 . -395) 98717) ((-980 . -621) 98699) ((-980 . -372) 98681) ((-980 . -281) NIL) ((-980 . -304) NIL) ((-980 . -507) NIL) ((-980 . -333) 98663) ((-980 . -239) T) ((-980 . -111) 98597) ((-980 . -1031) 98547) ((-980 . -285) T) ((-980 . -698) 98497) ((-980 . -628) 98447) ((-980 . -38) 98397) ((-980 . -302) T) ((-980 . -446) T) ((-980 . -170) T) ((-980 . -545) T) ((-980 . -897) T) ((-980 . -1190) T) ((-980 . -358) T) ((-980 . -229) T) ((-980 . -876) NIL) ((-980 . -227) 98379) ((-980 . -145) T) ((-980 . -143) NIL) ((-980 . -130) T) ((-980 . -25) T) ((-980 . -101) T) ((-980 . -597) 98361) ((-980 . -1074) T) ((-980 . -23) T) ((-980 . -21) T) ((-980 . -1025) T) ((-980 . -1032) T) ((-980 . -1085) T) ((-980 . -707) T) ((-979 . -337) 98335) ((-979 . -170) T) ((-979 . -707) T) ((-979 . -1085) T) ((-979 . -1032) T) ((-979 . -1025) T) ((-979 . -628) 98280) ((-979 . -130) T) ((-979 . -25) T) ((-979 . -101) T) ((-979 . -597) 98262) ((-979 . -1074) T) ((-979 . -23) T) ((-979 . -21) T) ((-979 . -1031) 98207) ((-979 . -111) 98136) ((-979 . -598) 98120) ((-979 . -227) 98097) ((-979 . -876) 98049) ((-979 . -229) 98021) ((-979 . -358) T) ((-979 . -1190) T) ((-979 . -897) T) ((-979 . -545) T) ((-979 . -698) 97966) ((-979 . -38) 97911) ((-979 . -446) T) ((-979 . -302) T) ((-979 . -285) T) ((-979 . -239) T) ((-979 . -363) NIL) ((-979 . -345) NIL) ((-979 . -1124) NIL) ((-979 . -143) 97883) ((-979 . -397) NIL) ((-979 . -405) 97855) ((-979 . -145) 97827) ((-979 . -365) 97799) ((-979 . -372) 97776) ((-979 . -621) 97715) ((-979 . -407) 97692) ((-979 . -1014) 97580) ((-979 . -705) 97552) ((-976 . -971) 97536) ((-976 . -483) 97520) ((-976 . -101) 97498) ((-976 . -1074) 97476) ((-976 . -507) 97409) ((-976 . -304) 97347) ((-976 . -597) 97279) ((-976 . -1185) T) ((-976 . -34) T) ((-976 . -106) 97263) ((-972 . -974) 97247) ((-972 . -827) 97226) ((-972 . -1014) 97122) ((-972 . -407) 97106) ((-972 . -621) 97054) ((-972 . -372) 97038) ((-972 . -281) 96996) ((-972 . -304) 96961) ((-972 . -507) 96873) ((-972 . -333) 96857) ((-972 . -38) 96805) ((-972 . -111) 96687) ((-972 . -1031) 96583) ((-972 . -628) 96521) ((-972 . -698) 96469) ((-972 . -285) 96420) ((-972 . -239) 96399) ((-972 . -229) 96378) ((-972 . -876) 96337) ((-972 . -227) 96321) ((-972 . -598) 96282) ((-972 . -145) 96261) ((-972 . -143) 96240) ((-972 . -130) T) ((-972 . -25) T) ((-972 . -101) T) ((-972 . -597) 96222) ((-972 . -1074) T) ((-972 . -23) T) ((-972 . -21) T) ((-972 . -1025) T) ((-972 . -1032) T) ((-972 . -1085) T) ((-972 . -707) T) ((-970 . -1056) T) ((-970 . -597) 96188) ((-970 . -1074) T) ((-970 . -101) T) ((-970 . -92) T) ((-969 . -21) T) ((-969 . -23) T) ((-969 . -1074) T) ((-969 . -597) 96170) ((-969 . -101) T) ((-969 . -25) T) ((-969 . -130) T) ((-965 . -597) 96152) ((-962 . -1074) T) ((-962 . -597) 96134) ((-962 . -101) T) ((-947 . -777) T) ((-947 . -774) T) ((-947 . -827) T) ((-947 . -772) T) ((-947 . -23) T) ((-947 . -1074) T) ((-947 . -597) 96116) ((-947 . -101) T) ((-947 . -25) T) ((-947 . -130) T) ((-947 . -598) 96091) ((-946 . -1056) T) ((-946 . -597) 96057) ((-946 . -1074) T) ((-946 . -101) T) ((-946 . -92) T) ((-942 . -943) T) ((-942 . -101) T) ((-942 . -597) 96039) ((-942 . -1074) T) ((-941 . -597) 96021) ((-940 . -1074) T) ((-940 . -597) 96003) ((-940 . -101) T) ((-940 . -363) 95956) ((-940 . -707) 95855) ((-940 . -1085) 95754) 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. -283) 91669) ((-919 . -281) 91646) ((-919 . -588) 91623) ((-919 . -598) 91584) ((-919 . -483) 91568) ((-919 . -101) 91518) ((-919 . -1074) 91468) ((-919 . -507) 91401) ((-919 . -304) 91339) ((-919 . -597) 91251) ((-919 . -1185) T) ((-919 . -34) T) ((-919 . -149) 91235) ((-919 . -827) 91214) ((-919 . -367) 91198) ((-919 . -1230) 91182) ((-903 . -950) T) ((-903 . -597) 91164) ((-901 . -931) T) ((-901 . -597) 91146) ((-895 . -774) T) ((-895 . -827) T) ((-895 . -1074) T) ((-895 . -597) 91128) ((-895 . -101) T) ((-895 . -25) T) ((-895 . -707) T) ((-895 . -1085) T) ((-890 . -358) T) ((-890 . -1190) T) ((-890 . -897) T) ((-890 . -545) T) ((-890 . -170) T) ((-890 . -698) 91080) ((-890 . -38) 91032) ((-890 . -446) T) ((-890 . -302) T) ((-890 . -628) 90984) ((-890 . -707) T) ((-890 . -1085) T) ((-890 . -1032) T) ((-890 . -1025) T) ((-890 . -111) 90922) ((-890 . -1031) 90874) ((-890 . -21) T) ((-890 . -23) T) ((-890 . -1074) T) ((-890 . -597) 90856) ((-890 . -101) T) ((-890 . -25) T) ((-890 . -130) T) ((-890 . -285) T) ((-890 . -239) T) ((-882 . -345) T) ((-882 . -1124) T) ((-882 . -363) T) ((-882 . -143) T) ((-882 . -358) T) ((-882 . -1190) T) ((-882 . -897) T) ((-882 . -545) T) ((-882 . -170) T) ((-882 . -698) 90821) ((-882 . -38) 90786) ((-882 . -446) T) ((-882 . -302) T) ((-882 . -111) 90742) ((-882 . -1031) 90707) ((-882 . -628) 90672) ((-882 . -285) T) ((-882 . -239) T) ((-882 . -397) T) ((-882 . -1025) T) ((-882 . -1032) T) ((-882 . -1085) T) ((-882 . -707) T) ((-882 . -21) T) ((-882 . -23) T) ((-882 . -1074) T) ((-882 . -597) 90654) ((-882 . -101) T) ((-882 . -25) T) ((-882 . -130) T) ((-882 . -229) T) ((-882 . -324) 90641) ((-882 . -145) 90623) ((-882 . -1014) 90610) ((-882 . -1239) 90597) ((-882 . -1250) 90584) ((-882 . -598) 90566) ((-881 . -1074) T) ((-881 . -597) 90548) ((-881 . -101) T) ((-878 . -880) 90532) ((-878 . -827) 90483) ((-878 . -707) T) ((-878 . -1074) T) ((-878 . -597) 90465) ((-878 . -101) T) ((-878 . -1085) T) ((-878 . -467) T) ((-877 . -119) 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NIL) ((-847 . -827) NIL) ((-847 . -772) NIL) ((-847 . -771) NIL) ((-847 . -800) NIL) ((-847 . -862) NIL) ((-847 . -1185) T) ((-847 . -395) 88366) ((-847 . -621) 88343) ((-847 . -372) 88320) ((-847 . -281) 88271) ((-847 . -304) 88228) ((-847 . -507) 88136) ((-847 . -333) 88113) ((-847 . -239) T) ((-847 . -111) 88042) ((-847 . -1031) 87987) ((-847 . -285) T) ((-847 . -698) 87932) ((-847 . -628) 87877) ((-847 . -38) 87822) ((-847 . -302) T) ((-847 . -446) T) ((-847 . -170) T) ((-847 . -545) T) ((-847 . -897) T) ((-847 . -1190) T) ((-847 . -358) T) ((-847 . -229) NIL) ((-847 . -876) NIL) ((-847 . -227) 87799) ((-847 . -145) T) ((-847 . -143) NIL) ((-847 . -130) T) ((-847 . -25) T) ((-847 . -101) T) ((-847 . -597) 87781) ((-847 . -1074) T) ((-847 . -23) T) ((-847 . -21) T) ((-847 . -1025) T) ((-847 . -1032) T) ((-847 . -1085) T) ((-847 . -707) T) ((-845 . -846) 87765) ((-845 . -897) T) ((-845 . -545) T) ((-845 . -285) T) ((-845 . -170) T) ((-845 . -698) 87752) ((-845 . -1031) 87739) ((-845 . -111) 87724) ((-845 . -38) 87711) ((-845 . -446) T) ((-845 . -302) T) ((-845 . -1025) T) ((-845 . -1032) T) ((-845 . -1085) T) ((-845 . -707) T) ((-845 . -21) T) ((-845 . -23) T) ((-845 . -1074) T) ((-845 . -597) 87693) ((-845 . -101) T) ((-845 . -25) T) ((-845 . -130) T) ((-845 . -628) 87680) ((-845 . -145) T) ((-842 . -1025) T) ((-842 . -1032) T) ((-842 . -1085) T) ((-842 . -707) T) ((-842 . -21) T) ((-842 . -23) T) ((-842 . -1074) T) ((-842 . -597) 87662) ((-842 . -101) T) ((-842 . -25) T) ((-842 . -130) T) ((-842 . -628) 87622) ((-842 . -38) 87592) ((-842 . -111) 87557) ((-842 . -1031) 87527) ((-842 . -698) 87497) ((-841 . -821) T) ((-841 . -827) T) ((-841 . -1074) T) ((-841 . -597) 87479) ((-841 . -101) T) ((-841 . -363) T) ((-841 . -598) 87401) ((-840 . -1074) T) ((-840 . -597) 87383) ((-840 . -101) T) ((-839 . -838) T) ((-839 . -171) T) ((-839 . -597) 87365) ((-835 . -827) T) ((-835 . -101) T) ((-835 . -597) 87347) ((-835 . -1074) T) ((-832 . -829) 87331) ((-832 . -1014) 87227) ((-832 . -407) 87211) ((-832 . -698) 87181) ((-832 . -628) 87155) ((-832 . -130) T) ((-832 . -25) T) ((-832 . -101) T) ((-832 . -597) 87137) ((-832 . -1074) T) ((-832 . -23) T) ((-832 . -21) T) ((-832 . -1031) 87121) ((-832 . -111) 87100) ((-832 . -1025) T) ((-832 . -1032) T) ((-832 . -1085) T) ((-832 . -707) T) ((-832 . -38) 87070) ((-831 . -829) 87054) ((-831 . -1014) 86950) ((-831 . -407) 86934) ((-831 . -698) 86904) ((-831 . -628) 86878) ((-831 . -130) T) ((-831 . -25) T) ((-831 . -101) T) ((-831 . -597) 86860) ((-831 . -1074) T) ((-831 . -23) T) ((-831 . -21) T) ((-831 . -1031) 86844) ((-831 . -111) 86823) ((-831 . -1025) T) ((-831 . -1032) T) ((-831 . -1085) T) ((-831 . -707) T) ((-831 . -38) 86793) ((-819 . -1074) T) ((-819 . -597) 86775) ((-819 . -101) T) ((-819 . -407) 86759) ((-819 . -1014) 86655) ((-819 . -21) 86607) ((-819 . -23) 86559) ((-819 . -25) 86511) ((-819 . -130) 86463) ((-819 . -825) 86442) ((-819 . -628) 86415) ((-819 . -1032) 86394) ((-819 . -1025) 86373) 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85406) ((-812 . -1085) 85385) ((-812 . -707) 85364) ((-808 . -689) 85348) ((-808 . -698) 85318) ((-808 . -628) 85292) ((-808 . -130) T) ((-808 . -25) T) ((-808 . -101) T) ((-808 . -597) 85274) ((-808 . -1074) T) ((-808 . -23) T) ((-808 . -21) T) ((-808 . -1031) 85258) ((-808 . -111) 85237) ((-808 . -1025) T) ((-808 . -1032) T) ((-808 . -1085) T) ((-808 . -707) T) ((-808 . -38) 85207) ((-808 . -229) 85186) ((-806 . -1074) T) ((-806 . -597) 85168) ((-806 . -101) T) ((-805 . -1074) T) ((-805 . -597) 85150) ((-805 . -101) T) ((-804 . -1074) T) ((-804 . -597) 85132) ((-804 . -101) T) ((-799 . -823) T) ((-799 . -827) T) ((-799 . -834) T) ((-799 . -1085) T) ((-799 . -101) T) ((-799 . -597) 85114) ((-799 . -1074) T) ((-799 . -707) T) ((-799 . -1014) 85098) ((-798 . -261) 85082) ((-798 . -1014) 85066) ((-798 . -1074) T) ((-798 . -597) 85048) ((-798 . -101) T) ((-798 . -827) T) ((-797 . -111) 84990) ((-797 . -1031) 84941) ((-797 . -21) T) ((-797 . -23) T) ((-797 . -1074) T) ((-797 . -597) 84923) ((-797 . -101) T) ((-797 . -25) T) ((-797 . -130) T) ((-797 . -628) 84874) ((-797 . -229) T) ((-797 . -707) T) ((-797 . -1085) T) ((-797 . -1032) T) ((-797 . -1025) T) ((-797 . -358) 84853) ((-797 . -1190) 84832) ((-797 . -897) 84811) ((-797 . -545) 84790) ((-797 . -170) 84769) ((-797 . -698) 84711) ((-797 . -38) 84653) ((-797 . -446) 84632) ((-797 . -302) 84611) ((-797 . -285) 84590) ((-797 . -239) 84569) ((-796 . -248) 84508) ((-796 . -1014) 84336) ((-796 . -598) NIL) ((-796 . -321) 84298) ((-796 . -407) 84282) ((-796 . -38) 84131) ((-796 . -111) 83960) ((-796 . -1031) 83803) ((-796 . -628) 83728) ((-796 . -698) 83577) ((-796 . -143) 83556) ((-796 . -145) 83535) ((-796 . -170) 83446) ((-796 . -545) 83377) ((-796 . -285) 83308) ((-796 . -47) 83270) ((-796 . -372) 83254) ((-796 . -621) 83202) ((-796 . -446) 83153) ((-796 . -507) 83021) ((-796 . -827) 83000) ((-796 . -876) 82936) ((-796 . -862) NIL) ((-796 . -886) 82915) ((-796 . -1190) 82894) ((-796 . -926) 82841) ((-796 . -304) 82828) 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72609) ((-695 . -145) 72588) ((-695 . -143) 72567) ((-695 . -38) 72537) ((-695 . -111) 72502) ((-695 . -1031) 72472) ((-695 . -698) 72442) ((-694 . -827) T) ((-694 . -101) T) ((-694 . -597) 72424) ((-694 . -1074) T) ((-693 . -1207) 72408) ((-693 . -1124) 72386) ((-693 . -598) NIL) ((-693 . -304) 72373) ((-693 . -507) 72320) ((-693 . -321) 72297) ((-693 . -1014) 72177) ((-693 . -407) 72161) ((-693 . -38) 71990) ((-693 . -111) 71799) ((-693 . -1031) 71622) ((-693 . -628) 71547) ((-693 . -698) 71376) ((-693 . -143) 71355) ((-693 . -145) 71334) ((-693 . -47) 71311) ((-693 . -372) 71295) ((-693 . -621) 71243) ((-693 . -827) 71222) ((-693 . -876) 71165) ((-693 . -862) NIL) ((-693 . -886) 71144) ((-693 . -1190) 71123) ((-693 . -926) 71092) ((-693 . -897) 71071) ((-693 . -545) 70982) ((-693 . -285) 70893) ((-693 . -170) 70784) ((-693 . -446) 70715) ((-693 . -302) 70694) ((-693 . -281) 70621) ((-693 . -229) T) ((-693 . -130) T) ((-693 . -25) T) ((-693 . -101) T) ((-693 . -597) 70603) ((-693 . 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. -21) T) ((-681 . -23) T) ((-681 . -1074) T) ((-681 . -597) 70238) ((-681 . -101) T) ((-681 . -25) T) ((-681 . -130) T) ((-681 . -628) 70225) ((-681 . -698) 70212) ((-681 . -170) T) ((-681 . -285) T) ((-681 . -545) T) ((-681 . -537) T) ((-681 . -1190) T) ((-681 . -1124) T) ((-681 . -598) 70127) ((-681 . -996) T) ((-681 . -862) 70109) ((-681 . -825) T) ((-681 . -777) T) ((-681 . -774) T) ((-681 . -772) T) ((-681 . -771) T) ((-681 . -800) T) ((-681 . -621) 70091) ((-681 . -897) T) ((-681 . -446) T) ((-681 . -302) T) ((-681 . -229) T) ((-681 . -141) T) ((-681 . -145) T) ((-679 . -399) T) ((-679 . -145) T) ((-679 . -628) 70056) ((-679 . -130) T) ((-679 . -25) T) ((-679 . -101) T) ((-679 . -597) 70038) ((-679 . -1074) T) ((-679 . -23) T) ((-679 . -21) T) ((-679 . -707) T) ((-679 . -1085) T) ((-679 . -1032) T) ((-679 . -1025) T) ((-679 . -598) 69983) ((-679 . -358) T) ((-679 . -1190) T) ((-679 . -897) T) ((-679 . -545) T) ((-679 . -170) T) ((-679 . -698) 69948) ((-679 . -38) 69913) ((-679 . 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NIL) ((-674 . -345) NIL) ((-674 . -1124) NIL) ((-674 . -397) NIL) ((-674 . -405) 69261) ((-674 . -365) 69228) ((-674 . -705) 69195) ((-674 . -407) 69177) ((-674 . -862) 69159) ((-674 . -1185) T) ((-674 . -395) 69141) ((-674 . -621) 69123) ((-674 . -372) 69105) ((-674 . -281) NIL) ((-674 . -304) NIL) ((-674 . -507) NIL) ((-674 . -333) 69087) ((-674 . -239) T) ((-674 . -1190) T) ((-674 . -358) T) ((-674 . -897) T) ((-674 . -446) T) ((-674 . -302) T) ((-674 . -229) NIL) ((-674 . -876) NIL) ((-674 . -227) 69069) ((-674 . -145) T) ((-674 . -143) NIL) ((-671 . -1227) T) ((-671 . -597) 69051) ((-669 . -666) 69009) ((-669 . -483) 68993) ((-669 . -101) 68971) ((-669 . -1074) 68949) ((-669 . -507) 68882) ((-669 . -304) 68820) ((-669 . -597) 68752) ((-669 . -1185) T) ((-669 . -34) T) ((-669 . -56) 68710) ((-669 . -598) 68671) ((-661 . -1056) T) ((-661 . -597) 68621) ((-661 . -1074) T) ((-661 . -101) T) ((-661 . -92) T) ((-657 . -827) T) ((-657 . -101) T) ((-657 . -597) 68603) ((-657 . -1074) T) 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67585) ((-650 . -1025) T) ((-650 . -1032) T) ((-650 . -1085) T) ((-650 . -707) T) ((-650 . -38) 67545) ((-650 . -413) 67529) ((-650 . -725) 67513) ((-650 . -701) T) ((-650 . -742) T) ((-650 . -362) 67497) ((-644 . -369) 67476) ((-644 . -698) 67460) ((-644 . -628) 67444) ((-644 . -130) T) ((-644 . -25) T) ((-644 . -101) T) ((-644 . -597) 67426) ((-644 . -1074) T) ((-644 . -23) T) ((-644 . -21) T) ((-644 . -1031) 67410) ((-644 . -111) 67389) ((-644 . -617) 67373) ((-644 . -379) 67345) ((-644 . -1014) 67322) ((-636 . -638) 67306) ((-636 . -38) 67276) ((-636 . -628) 67250) ((-636 . -707) T) ((-636 . -1085) T) ((-636 . -1032) T) ((-636 . -1025) T) ((-636 . -111) 67229) ((-636 . -1031) 67213) ((-636 . -21) T) ((-636 . -23) T) ((-636 . -1074) T) ((-636 . -597) 67195) ((-636 . -101) T) ((-636 . -25) T) ((-636 . -130) T) ((-636 . -698) 67165) ((-636 . -407) 67149) ((-636 . -1014) 67045) ((-636 . -829) 67029) ((-636 . -281) 66990) ((-635 . -638) 66974) ((-635 . -38) 66944) ((-635 . -628) 66918) 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. -285) T) ((-350 . -239) T) ((-350 . -397) 38072) ((-350 . -143) 38023) ((-350 . -1014) 38007) ((-350 . -1239) 37991) ((-350 . -1250) 37975) ((-349 . -324) 37959) ((-349 . -229) 37938) ((-349 . -363) 37917) ((-349 . -1124) 37896) ((-349 . -345) 37875) ((-349 . -145) 37854) ((-349 . -628) 37806) ((-349 . -130) T) ((-349 . -25) T) ((-349 . -101) T) ((-349 . -597) 37788) ((-349 . -1074) T) ((-349 . -23) T) ((-349 . -21) T) ((-349 . -707) T) ((-349 . -1085) T) ((-349 . -1032) T) ((-349 . -1025) T) ((-349 . -358) T) ((-349 . -1190) T) ((-349 . -897) T) ((-349 . -545) T) ((-349 . -170) T) ((-349 . -698) 37740) ((-349 . -38) 37705) ((-349 . -446) T) ((-349 . -302) T) ((-349 . -111) 37643) ((-349 . -1031) 37595) ((-349 . -285) T) ((-349 . -239) T) ((-349 . -397) 37546) ((-349 . -143) 37497) ((-349 . -1014) 37481) ((-349 . -1239) 37465) ((-349 . -1250) 37449) ((-348 . -324) 37433) ((-348 . -229) 37412) ((-348 . -363) 37391) ((-348 . -1124) 37370) ((-348 . -345) 37349) ((-348 . -145) 37328) 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-94) 11051) ((-166 . -279) 11029) ((-166 . -486) 11007) ((-166 . -1174) 10985) ((-166 . -1171) 10963) ((-166 . -978) 10915) ((-166 . -886) 10868) ((-166 . -598) 10630) ((-166 . -860) 10614) ((-166 . -827) 10593) ((-166 . -363) 10544) ((-166 . -345) 10523) ((-166 . -1124) 10502) ((-166 . -397) 10481) ((-166 . -405) 10452) ((-166 . -38) 10280) ((-166 . -111) 10176) ((-166 . -1031) 10086) ((-166 . -628) 9996) ((-166 . -698) 9824) ((-166 . -365) 9795) ((-166 . -705) 9766) ((-166 . -1014) 9662) ((-166 . -407) 9646) ((-166 . -862) 9571) ((-166 . -1185) T) ((-166 . -395) 9555) ((-166 . -621) 9503) ((-166 . -372) 9487) ((-166 . -281) 9445) ((-166 . -304) 9410) ((-166 . -507) 9322) ((-166 . -333) 9306) ((-166 . -239) 9257) ((-166 . -1190) 9162) ((-166 . -358) 9113) ((-166 . -897) 9044) ((-166 . -545) 8955) ((-166 . -285) 8866) ((-166 . -446) 8797) ((-166 . -302) 8728) ((-166 . -229) 8679) ((-166 . -876) 8638) ((-166 . -227) 8622) ((-166 . -170) T) ((-166 . -145) 8601) ((-166 . -1025) T) ((-166 . -1032) T) ((-166 . -1085) T) ((-166 . -707) T) ((-166 . -21) T) ((-166 . -23) T) ((-166 . -1074) T) ((-166 . -597) 8583) ((-166 . -101) T) ((-166 . -25) T) ((-166 . -130) T) ((-166 . -143) 8534) ((-166 . -801) 8513) ((-160 . -1056) T) ((-160 . -597) 8479) ((-160 . -1074) T) ((-160 . -101) T) ((-160 . -92) T) ((-159 . -1074) T) ((-159 . -597) 8461) ((-159 . -101) T) ((-155 . -25) T) ((-155 . -101) T) ((-155 . -597) 8443) ((-155 . -1074) T) ((-154 . -1056) T) ((-154 . -597) 8409) ((-154 . -1074) T) ((-154 . -101) T) ((-154 . -92) T) ((-152 . -1056) T) ((-152 . -597) 8375) ((-152 . -1074) T) ((-152 . -101) T) ((-152 . -92) T) ((-150 . -1025) T) ((-150 . -1032) T) ((-150 . -1085) T) ((-150 . -707) T) ((-150 . -21) T) ((-150 . -23) T) ((-150 . -1074) T) ((-150 . -597) 8357) ((-150 . -101) T) ((-150 . -25) T) ((-150 . -130) T) ((-150 . -628) 8331) ((-150 . -38) 8315) ((-150 . -111) 8294) ((-150 . -1031) 8278) ((-150 . -698) 8262) ((-150 . -1239) 8246) ((-142 . -821) T) ((-142 . -827) T) ((-142 . -1074) T) ((-142 . -597) 8228) ((-142 . -101) T) ((-142 . -363) T) ((-139 . -1074) T) ((-139 . -597) 8210) ((-139 . -101) T) ((-139 . -598) 8169) ((-139 . -421) 8151) ((-139 . -1072) 8133) ((-139 . -363) T) ((-139 . -231) 8115) ((-139 . -149) 8097) ((-139 . -483) 8079) ((-139 . -507) NIL) ((-139 . -304) NIL) ((-139 . -1185) T) ((-139 . -34) T) ((-139 . -106) 8061) ((-139 . -225) 8043) ((-138 . -597) 8025) ((-137 . -1056) T) ((-137 . -597) 7991) ((-137 . -1074) T) ((-137 . -101) T) ((-137 . -92) T) ((-136 . -1056) T) ((-136 . -597) 7957) ((-136 . -1074) T) ((-136 . -101) T) ((-136 . -92) T) ((-134 . -459) 7934) ((-134 . -1014) 7918) ((-134 . -1074) T) ((-134 . -597) 7900) ((-134 . -101) T) ((-134 . -464) 7855) ((-133 . -827) T) ((-133 . -101) T) ((-133 . -597) 7837) ((-133 . -1074) T) ((-133 . -23) T) ((-133 . -25) T) ((-133 . -707) T) ((-133 . -1085) T) ((-133 . -1014) 7819) ((-132 . -1056) T) ((-132 . -597) 7785) ((-132 . -1074) T) ((-132 . -101) T) ((-132 . -92) T) ((-129 . -19) 7767) ((-129 . -631) 7749) ((-129 . -283) 7724) ((-129 . -281) 7699) ((-129 . -588) 7674) ((-129 . -598) NIL) ((-129 . -483) 7656) ((-129 . -101) T) ((-129 . -1074) T) ((-129 . -507) NIL) ((-129 . -304) NIL) ((-129 . -597) 7638) ((-129 . -1185) T) ((-129 . -34) T) ((-129 . -149) 7620) ((-129 . -827) T) ((-129 . -367) 7602) ((-128 . -827) T) ((-128 . -101) T) ((-128 . -597) 7554) ((-128 . -1074) T) ((-127 . -125) 7538) ((-127 . -986) 7522) ((-127 . -34) T) ((-127 . -1185) T) ((-127 . -597) 7454) ((-127 . -304) 7392) ((-127 . -507) 7325) ((-127 . -1074) 7303) ((-127 . -101) 7281) ((-127 . -483) 7265) ((-127 . -119) 7249) ((-126 . -125) 7233) ((-126 . -986) 7217) ((-126 . -34) T) ((-126 . -1185) T) ((-126 . -597) 7149) ((-126 . -304) 7087) ((-126 . -507) 7020) ((-126 . -1074) 6998) ((-126 . -101) 6976) ((-126 . -483) 6960) ((-126 . -119) 6944) ((-121 . -125) 6928) ((-121 . -986) 6912) ((-121 . -34) T) ((-121 . -1185) T) ((-121 . -597) 6844) ((-121 . -304) 6782) ((-121 . -507) 6715) ((-121 . -1074) 6693) ((-121 . -101) 6671) ((-121 . -483) 6655) ((-121 . -119) 6639) ((-117 . -967) 6616) ((-117 . -1124) NIL) ((-117 . -1014) 6593) ((-117 . -598) NIL) ((-117 . -996) NIL) ((-117 . -886) NIL) ((-117 . -860) 6570) ((-117 . -825) NIL) ((-117 . -777) NIL) ((-117 . -774) NIL) ((-117 . -827) NIL) ((-117 . -772) NIL) ((-117 . -771) NIL) ((-117 . -800) NIL) ((-117 . -862) NIL) ((-117 . -1185) T) ((-117 . -395) 6547) ((-117 . -621) 6524) ((-117 . -372) 6501) ((-117 . -281) 6452) ((-117 . -304) 6409) ((-117 . -507) 6317) ((-117 . -333) 6294) ((-117 . -239) T) ((-117 . -111) 6223) ((-117 . -1031) 6168) ((-117 . -285) T) ((-117 . -698) 6113) ((-117 . -628) 6058) ((-117 . -38) 6003) ((-117 . -302) T) ((-117 . -446) T) ((-117 . -170) T) ((-117 . -545) T) ((-117 . -897) T) ((-117 . -1190) T) ((-117 . -358) T) ((-117 . -229) NIL) ((-117 . -876) NIL) ((-117 . -227) 5980) ((-117 . -145) T) ((-117 . -143) NIL) ((-117 . -130) T) ((-117 . -25) T) ((-117 . -101) T) ((-117 . -597) 5962) ((-117 . -1074) T) ((-117 . -23) T) ((-117 . -21) T) ((-117 . -1025) T) ((-117 . -1032) T) ((-117 . -1085) T) ((-117 . -707) T) ((-116 . -846) 5946) ((-116 . -897) T) ((-116 . -545) T) ((-116 . -285) T) ((-116 . -170) T) ((-116 . -698) 5933) ((-116 . -1031) 5920) ((-116 . -111) 5905) ((-116 . -38) 5892) ((-116 . -446) T) ((-116 . -302) T) ((-116 . -1025) T) ((-116 . -1032) T) ((-116 . -1085) T) ((-116 . -707) T) ((-116 . -21) T) ((-116 . -23) T) ((-116 . -1074) T) ((-116 . -597) 5874) ((-116 . -101) T) ((-116 . -25) T) ((-116 . -130) T) ((-116 . -628) 5861) ((-116 . -145) T) ((-113 . -827) T) ((-113 . -101) T) ((-113 . -597) 5843) ((-113 . -1074) T) ((-112 . -821) T) ((-112 . -827) T) ((-112 . -1074) T) ((-112 . -597) 5825) ((-112 . -101) T) ((-112 . -363) T) ((-112 . -642) T) ((-112 . -943) T) ((-112 . -598) 5807) ((-110 . -123) T) ((-110 . -367) 5789) ((-110 . -827) T) ((-110 . -149) 5771) ((-110 . -34) T) ((-110 . -1185) T) ((-110 . -597) 5753) ((-110 . -304) NIL) ((-110 . -507) NIL) ((-110 . -1074) T) ((-110 . -483) 5735) ((-110 . -598) 5717) ((-110 . -588) 5692) ((-110 . -281) 5667) ((-110 . -283) 5642) ((-110 . -631) 5624) ((-110 . -19) 5606) ((-110 . -101) T) ((-110 . -642) T) ((-109 . -360) 5580) ((-109 . -101) T) ((-109 . -597) 5562) ((-109 . -1074) T) ((-108 . -597) 5544) ((-107 . -967) 5526) ((-107 . -1124) T) ((-107 . -1014) 5486) ((-107 . -598) 5416) ((-107 . -996) T) ((-107 . -886) NIL) ((-107 . -860) 5398) ((-107 . -825) T) ((-107 . -777) T) ((-107 . -774) T) ((-107 . -827) T) ((-107 . -772) T) ((-107 . -771) T) ((-107 . -800) T) ((-107 . -862) 5380) ((-107 . -1185) T) ((-107 . -395) 5362) ((-107 . -621) 5344) ((-107 . -372) 5326) ((-107 . -281) NIL) ((-107 . -304) NIL) ((-107 . -507) NIL) ((-107 . -333) 5308) ((-107 . -239) T) ((-107 . -111) 5242) ((-107 . -1031) 5192) ((-107 . -285) T) ((-107 . -698) 5142) ((-107 . -628) 5092) ((-107 . -38) 5042) ((-107 . -302) T) ((-107 . -446) T) ((-107 . -170) T) ((-107 . -545) T) ((-107 . -897) T) ((-107 . -1190) T) ((-107 . -358) T) ((-107 . -229) T) ((-107 . -876) NIL) ((-107 . -227) 5024) ((-107 . -145) T) ((-107 . -143) NIL) ((-107 . -130) T) ((-107 . -25) T) ((-107 . -101) T) ((-107 . -597) 5006) ((-107 . -1074) T) ((-107 . -23) T) ((-107 . -21) T) ((-107 . -1025) T) ((-107 . -1032) T) ((-107 . -1085) T) ((-107 . -707) T) ((-104 . -1074) T) ((-104 . -597) 4988) ((-104 . -101) T) ((-102 . -125) 4972) ((-102 . -986) 4956) ((-102 . -34) T) ((-102 . -1185) T) ((-102 . -597) 4888) ((-102 . -304) 4826) ((-102 . -507) 4759) ((-102 . -1074) 4737) ((-102 . -101) 4715) ((-102 . -483) 4699) ((-102 . -119) 4683) ((-98 . -467) T) ((-98 . -1085) T) ((-98 . -101) T) ((-98 . -597) 4665) ((-98 . -1074) T) ((-98 . -707) T) ((-98 . -281) 4644) ((-96 . -1074) T) ((-96 . -597) 4626) ((-96 . -101) T) ((-95 . -1056) T) ((-95 . -597) 4592) ((-95 . -1074) T) ((-95 . -101) T) ((-95 . -92) T) ((-90 . -1094) 4576) ((-90 . -483) 4560) ((-90 . -101) 4538) ((-90 . -1074) 4516) ((-90 . -507) 4449) ((-90 . -304) 4387) ((-90 . -597) 4319) ((-90 . -1185) T) ((-90 . -34) T) ((-90 . -106) 4303) ((-88 . -392) T) ((-88 . -597) 4285) ((-88 . -1185) T) ((-88 . -391) T) ((-87 . -380) T) ((-87 . -597) 4267) ((-87 . -1185) T) ((-87 . -391) T) ((-86 . -434) T) ((-86 . -597) 4249) ((-86 . -1185) T) ((-86 . -391) T) ((-85 . -435) T) ((-85 . -597) 4231) ((-85 . -1185) T) ((-85 . -391) T) ((-84 . -380) T) ((-84 . -597) 4213) ((-84 . -1185) T) ((-84 . -391) T) ((-83 . -380) T) ((-83 . -597) 4195) ((-83 . -1185) T) ((-83 . -391) T) ((-82 . -435) T) ((-82 . -597) 4177) ((-82 . -1185) T) ((-82 . -391) T) ((-81 . -435) T) ((-81 . -597) 4159) ((-81 . -1185) T) ((-81 . -391) T) ((-80 . -435) T) ((-80 . -597) 4141) ((-80 . -1185) T) ((-80 . -391) T) ((-79 . -435) T) ((-79 . -597) 4123) ((-79 . -1185) T) ((-79 . -391) T) ((-78 . -435) T) ((-78 . -597) 4105) ((-78 . -1185) T) ((-78 . -391) T) ((-77 . -392) T) ((-77 . -597) 4087) ((-77 . -1185) T) ((-77 . -391) T) ((-76 . -435) T) ((-76 . -597) 4069) ((-76 . -1185) T) ((-76 . -391) T) ((-75 . -435) T) ((-75 . -597) 4051) ((-75 . -1185) T) ((-75 . -391) T) ((-74 . -392) T) ((-74 . -597) 4033) ((-74 . -1185) T) ((-74 . -391) T) ((-73 . -435) T) ((-73 . -597) 4015) ((-73 . -1185) T) ((-73 . -391) T) ((-72 . -378) T) ((-72 . -597) 3997) ((-72 . -1185) T) ((-72 . -391) T) ((-71 . -391) T) ((-71 . -1185) T) ((-71 . -597) 3979) ((-70 . -435) T) ((-70 . -597) 3961) ((-70 . -1185) T) ((-70 . -391) T) ((-69 . -378) T) ((-69 . -597) 3943) ((-69 . -1185) T) ((-69 . -391) T) ((-68 . -391) T) ((-68 . -1185) T) ((-68 . -597) 3925) ((-67 . -378) T) ((-67 . -597) 3907) ((-67 . -1185) T) ((-67 . -391) T) ((-66 . -378) T) ((-66 . -597) 3889) ((-66 . -1185) T) ((-66 . -391) T) ((-65 . -392) T) ((-65 . -597) 3871) ((-65 . -1185) T) ((-65 . -391) T) ((-64 . -380) T) ((-64 . -597) 3853) ((-64 . -1185) T) ((-64 . -391) T) ((-63 . -435) T) ((-63 . -597) 3835) ((-63 . -1185) T) ((-63 . -391) T) ((-62 . -391) T) ((-62 . -1185) T) ((-62 . -597) 3817) ((-61 . -435) T) ((-61 . -597) 3799) ((-61 . -1185) T) ((-61 . -391) T) ((-60 . -392) T) ((-60 . -597) 3781) ((-60 . -1185) T) ((-60 . -391) T) ((-59 . -56) 3743) ((-59 . -34) T) ((-59 . -1185) T) ((-59 . -597) 3675) ((-59 . -304) 3613) ((-59 . -507) 3546) ((-59 . -1074) 3524) ((-59 . -101) 3502) ((-59 . -483) 3486) ((-57 . -19) 3470) ((-57 . -631) 3454) ((-57 . -283) 3431) ((-57 . -281) 3408) ((-57 . -588) 3385) ((-57 . -598) 3346) ((-57 . -483) 3330) ((-57 . -101) 3280) ((-57 . -1074) 3230) ((-57 . -507) 3163) ((-57 . -304) 3101) ((-57 . -597) 3013) ((-57 . -1185) T) ((-57 . -34) T) ((-57 . -149) 2997) ((-57 . -827) 2976) ((-57 . -367) 2960) ((-51 . -1074) T) ((-51 . -597) 2942) ((-51 . -101) T) ((-50 . -603) 2926) ((-50 . -628) 2900) ((-50 . -707) T) ((-50 . -1085) T) ((-50 . -1032) T) ((-50 . -1025) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1074) T) ((-50 . -597) 2882) ((-50 . -101) T) ((-50 . -25) T) ((-50 . -130) T) ((-50 . -1014) 2866) ((-49 . -1074) T) ((-49 . -597) 2848) ((-49 . -101) T) ((-48 . -293) T) ((-48 . -1014) 2791) ((-48 . -1074) T) ((-48 . -597) 2773) ((-48 . -101) T) ((-48 . -827) T) ((-48 . -507) 2739) ((-48 . -304) 2726) ((-48 . -27) T) ((-48 . -978) T) ((-48 . -239) T) ((-48 . -111) 2682) ((-48 . -1031) 2647) ((-48 . -285) T) ((-48 . -698) 2612) ((-48 . -628) 2577) ((-48 . -130) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -1025) T) ((-48 . -1032) T) ((-48 . -1085) T) ((-48 . -707) T) ((-48 . -38) 2542) ((-48 . -302) T) ((-48 . -446) T) ((-48 . -170) T) ((-48 . -545) T) ((-48 . -897) T) ((-48 . -1190) T) ((-48 . -358) T) ((-48 . -621) 2502) ((-48 . -996) T) ((-48 . -598) 2447) ((-48 . -145) T) ((-48 . -229) T) ((-45 . -36) 2426) ((-45 . -588) 2351) ((-45 . -304) 2155) ((-45 . -507) 1947) ((-45 . -483) 1884) ((-45 . -281) 1809) ((-45 . -283) 1734) ((-45 . -594) 1713) ((-45 . -231) 1663) ((-45 . -106) 1613) ((-45 . -225) 1563) ((-45 . -1162) 1542) ((-45 . -277) 1492) ((-45 . -149) 1442) ((-45 . -34) T) ((-45 . -1185) T) ((-45 . -597) 1424) ((-45 . -1074) T) ((-45 . -101) T) ((-45 . -598) NIL) ((-45 . -631) 1374) ((-45 . -367) 1324) ((-45 . -827) NIL) ((-45 . -1122) 1274) ((-45 . -986) 1224) ((-45 . -1220) 1174) ((-45 . -646) 1124) ((-44 . -413) 1108) ((-44 . -725) 1092) ((-44 . -701) T) ((-44 . -742) T) ((-44 . -111) 1071) ((-44 . -1031) 1055) ((-44 . -21) T) ((-44 . -23) T) ((-44 . -1074) T) ((-44 . -597) 1037) ((-44 . -101) T) ((-44 . -25) T) ((-44 . -130) T) ((-44 . -628) 995) ((-44 . -698) 979) ((-44 . -362) 963) ((-40 . -337) 937) ((-40 . -170) T) ((-40 . -707) T) ((-40 . -1085) T) ((-40 . -1032) T) ((-40 . -1025) T) ((-40 . -628) 882) ((-40 . -130) T) ((-40 . -25) T) ((-40 . -101) T) ((-40 . -597) 864) ((-40 . -1074) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -1031) 809) ((-40 . -111) 738) ((-40 . -598) 722) ((-40 . -227) 699) ((-40 . -876) 651) ((-40 . -229) 623) ((-40 . -358) T) ((-40 . -1190) T) ((-40 . -897) T) ((-40 . -545) T) ((-40 . -698) 568) ((-40 . -38) 513) ((-40 . -446) T) ((-40 . -302) T) ((-40 . -285) T) ((-40 . -239) T) ((-40 . -363) NIL) ((-40 . -345) NIL) ((-40 . -1124) NIL) ((-40 . -143) 485) ((-40 . -397) NIL) ((-40 . -405) 457) ((-40 . -145) 429) ((-40 . -365) 401) ((-40 . -372) 378) ((-40 . -621) 317) ((-40 . -407) 294) ((-40 . -1014) 182) ((-40 . -705) 154) ((-31 . -1056) T) ((-31 . -597) 120) ((-31 . -1074) T) ((-31 . -101) T) ((-31 . -92) T) ((-30 . -931) T) ((-30 . -597) 102) ((0 . |EnumerationCategory|) T) ((0 . -597) 84) ((0 . -1074) T) ((0 . -101) T) ((-1 . -1074) T) ((-1 . -597) 66) ((-1 . -101) T) ((-2 . |RecordCategory|) T) ((-2 . -597) 48) ((-2 . -1074) T) ((-2 . -101) T) ((-3 . |UnionCategory|) T) ((-3 . -597) 30) ((-3 . -1074) T) ((-3 . -101) T)) \ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index e9ff6a49..175f5012 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
-(30 . 3432414583)
-(4351 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3432506629)
+(4356 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
|ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
|OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -45,11 +45,12 @@
|CommutativeRing| |Conduit| |ContinuedFraction| |Contour| |CoordinateSystems|
|CharacteristicPolynomialInMonogenicalAlgebra| |ComplexPatternMatch|
|CRApackage| |CoerceAst| |ComplexRootFindingPackage| |CyclicStreamTools|
- |ConstructorCall| |ComplexTrigonometricManipulations|
- |CoerceVectorMatrixPackage| |CycleIndicators| |CyclotomicPolynomialPackage|
- |d01AgentsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType|
- |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType|
- |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType|
+ |Constructor| |ConstructorCall| |ConstructorKind|
+ |ComplexTrigonometricManipulations| |CoerceVectorMatrixPackage|
+ |CycleIndicators| |CyclotomicPolynomialPackage| |d01AgentsPackage|
+ |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType|
+ |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType|
+ |d01fcfAnnaType| |d01gbfAnnaType| |d01TransformFunctionType|
|d01WeightsPackage| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType|
|d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType|
|d03fafAnnaType| |DataBuffer| |Database| |DoubleResultantPackage|
@@ -429,14 +430,14 @@
|bezoutMatrix| |bezoutResultant| |bezoutDiscriminant| |bfEntry| |bfKeys|
|inspect| |extract!| |bag| |binding| |position!| |test| |setProperties|
|setProperty| |deleteProperty!| |has?| |comparison| |equality| |nary?|
- |unary?| |nullary?| |arity| |properties| |derivative| |constantOperator|
+ |unary?| |nullary?| |properties| |derivative| |constantOperator|
|constantOpIfCan| |integerBound| |setright!| |setleft!|
|brillhartIrreducible?| |brillhartTrials| |noLinearFactor?| |insertRoot!|
|binarySearchTree| |nor| |nand| |node| |binaryTournament| |binaryTree|
|bitior| |bitand| |byte| |subtractIfCan| |setPosition|
|generalizedContinuumHypothesisAssumed|
|generalizedContinuumHypothesisAssumed?| |countable?| |Aleph| |unravel|
- |ravel| |leviCivitaSymbol| |kroneckerDelta| |reindex| |kind| |alphanumeric|
+ |ravel| |leviCivitaSymbol| |kroneckerDelta| |reindex| |alphanumeric|
|alphabetic| |hexDigit| |digit| |charClass| |alphanumeric?| |lowerCase?|
|upperCase?| |alphabetic?| |hexDigit?| |digit?| |escape| |char| |ord|
|mkIntegral| |radPoly| |rootPoly| |goodPoint| |chvar| |removeDuplicates|
@@ -452,9 +453,10 @@
|toroidal| |conical| |modTree| |multiEuclideanTree| |complexZeros|
|divisorCascade| |graeffe| |pleskenSplit| |reciprocalPolynomial| |rootRadius|
|schwerpunkt| |setErrorBound| |startPolynomial| |cycleElt|
- |computeCycleLength| |computeCycleEntry| |arguments| |constructorName|
- |coerceP| |powerSum| |elementary| |alternating| |cyclic| |dihedral| |cap|
- |cup| |wreath| |SFunction| |skewSFunction| |cyclotomicDecomposition|
+ |computeCycleLength| |computeCycleEntry| |arity| |kind| |arguments|
+ |constructorName| |package| |domain| |category| |coerceP| |powerSum|
+ |elementary| |alternating| |cyclic| |dihedral| |cap| |cup| |wreath|
+ |SFunction| |skewSFunction| |cyclotomicDecomposition|
|cyclotomicFactorization| |rangeIsFinite| |functionIsContinuousAtEndPoints|
|functionIsOscillatory| |changeName| |exprHasWeightCosWXorSinWX|
|exprHasAlgebraicWeight| |exprHasLogarithmicWeights|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index d63b31cf..118cb525 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5174 +1,5182 @@
-(3167315 . 3432414603)
-((-1843 (((-112) (-1 (-112) |#2| |#2|) $) 63) (((-112) $) NIL)) (-1841 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-4142 ((|#2| $ (-536) |#2|) NIL) ((|#2| $ (-1196 (-536)) |#2|) 34)) (-2372 (($ $) 59)) (-4197 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-3773 (((-536) (-1 (-112) |#2|) $) 22) (((-536) |#2| $) NIL) (((-536) |#2| $ (-536)) 73)) (-2063 (((-620 |#2|) $) 13)) (-3867 (($ (-1 (-112) |#2| |#2|) $ $) 48) (($ $ $) NIL)) (-2067 (($ (-1 |#2| |#2|) $) 29)) (-4313 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 44)) (-2377 (($ |#2| $ (-536)) NIL) (($ $ $ (-536)) 50)) (-1399 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 24)) (-2065 (((-112) (-1 (-112) |#2|) $) 21)) (-4154 ((|#2| $ (-536) |#2|) NIL) ((|#2| $ (-536)) NIL) (($ $ (-1196 (-536))) 49)) (-2378 (($ $ (-536)) 56) (($ $ (-1196 (-536))) 55)) (-2064 (((-749) (-1 (-112) |#2|) $) 26) (((-749) |#2| $) NIL)) (-1842 (($ $ $ (-536)) 52)) (-3754 (($ $) 51)) (-3879 (($ (-620 |#2|)) 53)) (-4156 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 64) (($ (-620 $)) 62)) (-4312 (((-838) $) 69)) (-2066 (((-112) (-1 (-112) |#2|) $) 20)) (-3382 (((-112) $ $) 72)) (-3013 (((-112) $ $) 75)))
-(((-18 |#1| |#2|) (-10 -8 (-15 -3382 ((-112) |#1| |#1|)) (-15 -4312 ((-838) |#1|)) (-15 -3013 ((-112) |#1| |#1|)) (-15 -1841 (|#1| |#1|)) (-15 -1841 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2372 (|#1| |#1|)) (-15 -1842 (|#1| |#1| |#1| (-536))) (-15 -1843 ((-112) |#1|)) (-15 -3867 (|#1| |#1| |#1|)) (-15 -3773 ((-536) |#2| |#1| (-536))) (-15 -3773 ((-536) |#2| |#1|)) (-15 -3773 ((-536) (-1 (-112) |#2|) |#1|)) (-15 -1843 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3867 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -4142 (|#2| |#1| (-1196 (-536)) |#2|)) (-15 -2377 (|#1| |#1| |#1| (-536))) (-15 -2377 (|#1| |#2| |#1| (-536))) (-15 -2378 (|#1| |#1| (-1196 (-536)))) (-15 -2378 (|#1| |#1| (-536))) (-15 -4154 (|#1| |#1| (-1196 (-536)))) (-15 -4313 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4156 (|#1| (-620 |#1|))) (-15 -4156 (|#1| |#1| |#1|)) (-15 -4156 (|#1| |#2| |#1|)) (-15 -4156 (|#1| |#1| |#2|)) (-15 -3879 (|#1| (-620 |#2|))) (-15 -1399 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -4197 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -4197 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -4197 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4154 (|#2| |#1| (-536))) (-15 -4154 (|#2| |#1| (-536) |#2|)) (-15 -4142 (|#2| |#1| (-536) |#2|)) (-15 -2064 ((-749) |#2| |#1|)) (-15 -2063 ((-620 |#2|) |#1|)) (-15 -2064 ((-749) (-1 (-112) |#2|) |#1|)) (-15 -2065 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2066 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2067 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4313 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3754 (|#1| |#1|))) (-19 |#2|) (-1183)) (T -18))
+(3168425 . 3432506650)
+((-1848 (((-112) (-1 (-112) |#2| |#2|) $) 63) (((-112) $) NIL)) (-1846 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-4147 ((|#2| $ (-538) |#2|) NIL) ((|#2| $ (-1198 (-538)) |#2|) 34)) (-2377 (($ $) 59)) (-4202 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-3778 (((-538) (-1 (-112) |#2|) $) 22) (((-538) |#2| $) NIL) (((-538) |#2| $ (-538)) 73)) (-2068 (((-622 |#2|) $) 13)) (-3872 (($ (-1 (-112) |#2| |#2|) $ $) 48) (($ $ $) NIL)) (-2072 (($ (-1 |#2| |#2|) $) 29)) (-4318 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 44)) (-2382 (($ |#2| $ (-538)) NIL) (($ $ $ (-538)) 50)) (-1399 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 24)) (-2070 (((-112) (-1 (-112) |#2|) $) 21)) (-4159 ((|#2| $ (-538) |#2|) NIL) ((|#2| $ (-538)) NIL) (($ $ (-1198 (-538))) 49)) (-2383 (($ $ (-538)) 56) (($ $ (-1198 (-538))) 55)) (-2069 (((-751) (-1 (-112) |#2|) $) 26) (((-751) |#2| $) NIL)) (-1847 (($ $ $ (-538)) 52)) (-3759 (($ $) 51)) (-3884 (($ (-622 |#2|)) 53)) (-4161 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 64) (($ (-622 $)) 62)) (-4317 (((-840) $) 69)) (-2071 (((-112) (-1 (-112) |#2|) $) 20)) (-3387 (((-112) $ $) 72)) (-3018 (((-112) $ $) 75)))
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NIL
-(-10 -8 (-15 -3382 ((-112) |#1| |#1|)) (-15 -4312 ((-838) |#1|)) (-15 -3013 ((-112) |#1| |#1|)) (-15 -1841 (|#1| |#1|)) (-15 -1841 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2372 (|#1| |#1|)) (-15 -1842 (|#1| |#1| |#1| (-536))) (-15 -1843 ((-112) |#1|)) (-15 -3867 (|#1| |#1| |#1|)) (-15 -3773 ((-536) |#2| |#1| (-536))) (-15 -3773 ((-536) |#2| |#1|)) (-15 -3773 ((-536) (-1 (-112) |#2|) |#1|)) (-15 -1843 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -3867 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -4142 (|#2| |#1| (-1196 (-536)) |#2|)) (-15 -2377 (|#1| |#1| |#1| (-536))) (-15 -2377 (|#1| |#2| |#1| (-536))) (-15 -2378 (|#1| |#1| (-1196 (-536)))) (-15 -2378 (|#1| |#1| (-536))) (-15 -4154 (|#1| |#1| (-1196 (-536)))) (-15 -4313 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4156 (|#1| (-620 |#1|))) (-15 -4156 (|#1| |#1| |#1|)) (-15 -4156 (|#1| |#2| |#1|)) (-15 -4156 (|#1| |#1| |#2|)) (-15 -3879 (|#1| (-620 |#2|))) (-15 -1399 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -4197 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -4197 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -4197 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -4154 (|#2| |#1| (-536))) (-15 -4154 (|#2| |#1| (-536) |#2|)) (-15 -4142 (|#2| |#1| (-536) |#2|)) (-15 -2064 ((-749) |#2| |#1|)) (-15 -2063 ((-620 |#2|) |#1|)) (-15 -2064 ((-749) (-1 (-112) |#2|) |#1|)) (-15 -2065 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2066 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2067 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -4313 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3754 (|#1| |#1|)))
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NIL
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NIL
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(((-21) (-138)) (T -21))
-((-4192 (*1 *1 *1) (-4 *1 (-21))) (-4192 (*1 *1 *1 *1) (-4 *1 (-21))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-21)) (-5 *2 (-536)))))
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-NIL
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+NIL
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(((-23) (-138)) (T -23))
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-((* (($ (-893) $) 10)))
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-NIL
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(((-25) (-138)) (T -25))
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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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(((-821) (-138)) (T -821))
NIL
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(((-825) (-138)) (T -825))
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-((-4328 (((-3 (-1229 (-400 (-536))) "failed") (-1229 |#1|) |#1|) 21)) (-4326 (((-112) (-1229 |#1|)) 12)) (-4327 (((-3 (-1229 (-536)) "failed") (-1229 |#1|)) 16)))
-(((-1257 |#1|) (-10 -7 (-15 -4326 ((-112) (-1229 |#1|))) (-15 -4327 ((-3 (-1229 (-536)) "failed") (-1229 |#1|))) (-15 -4328 ((-3 (-1229 (-400 (-536))) "failed") (-1229 |#1|) |#1|))) (-619 (-536))) (T -1257))
-((-4328 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1229 *4)) (-4 *4 (-619 (-536))) (-5 *2 (-1229 (-400 (-536)))) (-5 *1 (-1257 *4)))) (-4327 (*1 *2 *3) (|partial| -12 (-5 *3 (-1229 *4)) (-4 *4 (-619 (-536))) (-5 *2 (-1229 (-536))) (-5 *1 (-1257 *4)))) (-4326 (*1 *2 *3) (-12 (-5 *3 (-1229 *4)) (-4 *4 (-619 (-536))) (-5 *2 (-112)) (-5 *1 (-1257 *4)))))
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-(((-1258 |#1|) (-13 (-170) (-361) (-596 (-536)) (-1122)) (-893)) (T -1258))
-NIL
-(-13 (-170) (-361) (-596 (-536)) (-1122))
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
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3137147 3137202 "XFALG" 3139374 NIL XFALG (NIL T T) -9 NIL 3140163) (-1248 3131879 3134125 3134167 "XF" 3134788 NIL XF (NIL T) -9 NIL 3135188) (-1247 3131500 3131588 3131757 "XF-" 3131762 NIL XF- (NIL T T) -8 NIL NIL) (-1246 3130633 3130737 3130942 "XEXPPKG" 3131392 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1245 3128777 3130483 3130579 "XDPOLY" 3130584 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1244 3127693 3128259 3128302 "XALG" 3128365 NIL XALG (NIL T) -9 NIL 3128485) (-1243 3121189 3125670 3126164 "WUTSET" 3127285 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1242 3119040 3119801 3120154 "WP" 3120970 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1241 3118669 3118862 3118932 "WHILEAST" 3118992 T WHILEAST (NIL) -8 NIL NIL) (-1240 3118168 3118386 3118480 "WHEREAST" 3118597 T WHEREAST (NIL) -8 NIL NIL) (-1239 3117054 3117252 3117547 "WFFINTBS" 3117965 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1238 3114958 3115385 3115847 "WEIER" 3116626 NIL WEIER (NIL T) -7 NIL NIL) (-1237 3114105 3114529 3114571 "VSPACE" 3114707 NIL VSPACE (NIL T) -9 NIL 3114781) (-1236 3113943 3113970 3114061 "VSPACE-" 3114066 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1235 3113689 3113732 3113803 "VOID" 3113894 T VOID (NIL) -8 NIL NIL) (-1234 3110114 3110752 3111489 "VIEWDEF" 3112974 T VIEWDEF (NIL) -7 NIL NIL) (-1233 3099452 3101662 3103835 "VIEW3D" 3107963 T VIEW3D (NIL) -8 NIL NIL) (-1232 3091734 3093363 3094942 "VIEW2D" 3097895 T VIEW2D (NIL) -8 NIL NIL) (-1231 3089870 3090229 3090635 "VIEW" 3091350 T VIEW (NIL) -7 NIL NIL) (-1230 3088447 3088706 3089024 "VECTOR2" 3089600 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1229 3083851 3088217 3088309 "VECTOR" 3088390 NIL VECTOR (NIL T) -8 NIL NIL) (-1228 3077378 3081635 3081678 "VECTCAT" 3082671 NIL VECTCAT (NIL T) -9 NIL 3083257) (-1227 3076392 3076646 3077036 "VECTCAT-" 3077041 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1226 3075873 3076043 3076163 "VARIABLE" 3076307 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1225 3075806 3075811 3075841 "UTYPE" 3075846 T UTYPE (NIL) -9 NIL NIL) (-1224 3074636 3074790 3075052 "UTSODETL" 3075632 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1223 3072076 3072536 3073060 "UTSODE" 3074177 NIL UTSODE (NIL T T) -7 NIL NIL) (-1222 3063449 3068768 3068811 "UTSCAT" 3069923 NIL UTSCAT (NIL T) -9 NIL 3070680) (-1221 3060803 3061519 3062508 "UTSCAT-" 3062513 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1220 3060430 3060473 3060606 "UTS2" 3060754 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1219 3052306 3058056 3058545 "UTS" 3059999 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1218 3046582 3049146 3049189 "URAGG" 3051259 NIL URAGG (NIL T) -9 NIL 3051981) (-1217 3043524 3044386 3045508 "URAGG-" 3045513 NIL URAGG- (NIL T T) -8 NIL NIL) (-1216 3039255 3042138 3042610 "UPXSSING" 3043188 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1215 3032370 3039159 3039231 "UPXSCONS" 3039236 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1214 3022730 3029473 3029535 "UPXSCCA" 3030191 NIL UPXSCCA (NIL T T) -9 NIL 3030433) (-1213 3022368 3022453 3022627 "UPXSCCA-" 3022632 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1212 3012654 3019170 3019213 "UPXSCAT" 3019861 NIL UPXSCAT (NIL T) -9 NIL 3020469) (-1211 3012084 3012163 3012342 "UPXS2" 3012569 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1210 3004058 3011199 3011481 "UPXS" 3011860 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1209 3002715 3002967 3003317 "UPSQFREE" 3003802 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1208 2996633 2999642 2999697 "UPSCAT" 3000858 NIL UPSCAT (NIL T T) -9 NIL 3001632) (-1207 2995837 2996044 2996371 "UPSCAT-" 2996376 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1206 2995464 2995507 2995640 "UPOLYC2" 2995788 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1205 2981588 2989551 2989594 "UPOLYC" 2991695 NIL UPOLYC (NIL T) -9 NIL 2992916) (-1204 2972953 2975366 2978501 "UPOLYC-" 2978506 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1203 2972292 2972399 2972563 "UPMP" 2972842 NIL UPMP (NIL T T) -7 NIL NIL) (-1202 2971845 2971926 2972065 "UPDIVP" 2972205 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1201 2970413 2970662 2970978 "UPDECOMP" 2971594 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1200 2969648 2969760 2969945 "UPCDEN" 2970297 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1199 2969167 2969236 2969385 "UP2" 2969573 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1198 2960664 2968733 2968871 "UP" 2969077 NIL UP (NIL NIL T) -8 NIL NIL) (-1197 2959879 2960006 2960211 "UNISEG2" 2960507 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1196 2958396 2959083 2959360 "UNISEG" 2959637 NIL UNISEG (NIL T) -8 NIL NIL) (-1195 2957456 2957636 2957862 "UNIFACT" 2958212 NIL UNIFACT (NIL T) -7 NIL NIL) (-1194 2945514 2957360 2957432 "ULSCONS" 2957437 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1193 2928334 2940253 2940315 "ULSCCAT" 2941035 NIL ULSCCAT (NIL T T) -9 NIL 2941332) (-1192 2927420 2927653 2928029 "ULSCCAT-" 2928034 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1191 2917483 2923913 2923956 "ULSCAT" 2924819 NIL ULSCAT (NIL T) -9 NIL 2925549) (-1190 2916913 2916992 2917171 "ULS2" 2917398 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1189 2900898 2916090 2916341 "ULS" 2916720 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1188 2899336 2900259 2900289 "UFD" 2900501 T UFD (NIL) -9 NIL 2900615) (-1187 2899130 2899176 2899271 "UFD-" 2899276 NIL UFD- (NIL T) -8 NIL NIL) (-1186 2898212 2898395 2898611 "UDVO" 2898936 T UDVO (NIL) -7 NIL NIL) (-1185 2896028 2896437 2896908 "UDPO" 2897776 NIL UDPO (NIL T) -7 NIL NIL) (-1184 2895815 2895983 2896014 "TYPEAST" 2896019 T TYPEAST (NIL) -8 NIL NIL) (-1183 2895748 2895753 2895783 "TYPE" 2895788 T TYPE (NIL) -9 NIL NIL) (-1182 2894719 2894921 2895161 "TWOFACT" 2895542 NIL TWOFACT (NIL T) -7 NIL NIL) (-1181 2893657 2893994 2894257 "TUPLE" 2894491 NIL TUPLE (NIL T) -8 NIL NIL) (-1180 2891348 2891867 2892406 "TUBETOOL" 2893140 T TUBETOOL (NIL) -7 NIL NIL) (-1179 2890197 2890402 2890643 "TUBE" 2891141 NIL TUBE (NIL T) -8 NIL NIL) (-1178 2878864 2882956 2883053 "TSETCAT" 2888322 NIL TSETCAT (NIL T T T T) -9 NIL 2889853) (-1177 2873598 2875196 2877087 "TSETCAT-" 2877092 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1176 2868362 2872570 2872853 "TS" 2873350 NIL TS (NIL T) -8 NIL NIL) (-1175 2862625 2863471 2864413 "TRMANIP" 2867498 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1174 2862066 2862129 2862292 "TRIMAT" 2862557 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1173 2859862 2860099 2860463 "TRIGMNIP" 2861815 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1172 2859382 2859495 2859525 "TRIGCAT" 2859738 T TRIGCAT (NIL) -9 NIL NIL) (-1171 2859051 2859130 2859271 "TRIGCAT-" 2859276 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1170 2855951 2857911 2858191 "TREE" 2858806 NIL TREE (NIL T) -8 NIL NIL) (-1169 2855225 2855753 2855783 "TRANFUN" 2855818 T TRANFUN (NIL) -9 NIL 2855884) (-1168 2854504 2854695 2854975 "TRANFUN-" 2854980 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1167 2854308 2854340 2854401 "TOPSP" 2854465 T TOPSP (NIL) -7 NIL NIL) (-1166 2853656 2853771 2853925 "TOOLSIGN" 2854189 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1165 2852317 2852833 2853072 "TEXTFILE" 2853439 T TEXTFILE (NIL) -8 NIL NIL) (-1164 2852098 2852129 2852201 "TEX1" 2852280 NIL TEX1 (NIL T) -7 NIL NIL) (-1163 2849963 2850477 2850915 "TEX" 2851682 T TEX (NIL) -8 NIL NIL) (-1162 2849611 2849674 2849764 "TEMUTL" 2849895 T TEMUTL (NIL) -7 NIL NIL) (-1161 2847765 2848045 2848370 "TBCMPPK" 2849334 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1160 2839655 2845925 2845981 "TBAGG" 2846381 NIL TBAGG (NIL T T) -9 NIL 2846592) (-1159 2834725 2836213 2837967 "TBAGG-" 2837972 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1158 2834109 2834216 2834361 "TANEXP" 2834614 NIL TANEXP (NIL T) -7 NIL NIL) (-1157 2833521 2833620 2833758 "TABLEAU" 2834006 NIL TABLEAU (NIL T) -8 NIL NIL) (-1156 2827024 2833378 2833471 "TABLE" 2833476 NIL TABLE (NIL T T) -8 NIL NIL) (-1155 2821632 2822852 2824100 "TABLBUMP" 2825810 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1154 2821060 2821160 2821288 "SYSTEM" 2821526 T SYSTEM (NIL) -7 NIL NIL) (-1153 2817523 2818218 2819001 "SYSSOLP" 2820311 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1152 2813815 2814522 2815256 "SYNTAX" 2816811 T SYNTAX (NIL) -8 NIL NIL) (-1151 2810973 2811575 2812207 "SYMTAB" 2813205 T SYMTAB (NIL) -8 NIL NIL) (-1150 2806246 2807142 2808119 "SYMS" 2810018 T SYMS (NIL) -8 NIL NIL) (-1149 2803528 2805707 2805937 "SYMPOLY" 2806054 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1148 2803045 2803120 2803243 "SYMFUNC" 2803440 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1147 2799022 2800282 2801104 "SYMBOL" 2802245 T SYMBOL (NIL) -8 NIL NIL) (-1146 2792561 2794250 2795970 "SWITCH" 2797324 T SWITCH (NIL) -8 NIL NIL) (-1145 2785831 2791382 2791685 "SUTS" 2792316 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1144 2777804 2784946 2785228 "SUPXS" 2785607 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1143 2776963 2777090 2777307 "SUPFRACF" 2777672 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1142 2776584 2776643 2776756 "SUP2" 2776898 NIL SUP2 (NIL T T) -7 NIL NIL) (-1141 2768153 2776202 2776328 "SUP" 2776493 NIL SUP (NIL T) -8 NIL NIL) (-1140 2766566 2766840 2767203 "SUMRF" 2767852 NIL SUMRF (NIL T) -7 NIL NIL) (-1139 2765880 2765946 2766145 "SUMFS" 2766487 NIL SUMFS (NIL T T) -7 NIL NIL) (-1138 2749905 2765057 2765308 "SULS" 2765687 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1137 2749534 2749727 2749797 "SUCHTAST" 2749857 T SUCHTAST (NIL) -8 NIL NIL) (-1136 2748856 2749059 2749199 "SUCH" 2749442 NIL SUCH (NIL T T) -8 NIL NIL) (-1135 2742750 2743762 2744721 "SUBSPACE" 2747944 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1134 2742180 2742270 2742434 "SUBRESP" 2742638 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1133 2736353 2737473 2738620 "STTFNC" 2741080 NIL STTFNC (NIL T) -7 NIL NIL) (-1132 2729722 2731018 2732329 "STTF" 2735089 NIL STTF (NIL T) -7 NIL NIL) (-1131 2721037 2722904 2724698 "STTAYLOR" 2727963 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1130 2714283 2720901 2720984 "STRTBL" 2720989 NIL STRTBL (NIL T) -8 NIL NIL) (-1129 2709674 2714238 2714269 "STRING" 2714274 T STRING (NIL) -8 NIL NIL) (-1128 2704562 2709047 2709077 "STRICAT" 2709136 T STRICAT (NIL) -9 NIL 2709198) (-1127 2704072 2704149 2704293 "STREAM3" 2704479 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1126 2703054 2703237 2703472 "STREAM2" 2703885 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1125 2702742 2702794 2702887 "STREAM1" 2702996 NIL STREAM1 (NIL T) -7 NIL NIL) (-1124 2695457 2700265 2700885 "STREAM" 2702157 NIL STREAM (NIL T) -8 NIL NIL) (-1123 2694473 2694654 2694885 "STINPROD" 2695273 NIL STINPROD (NIL T) -7 NIL NIL) (-1122 2694051 2694235 2694265 "STEP" 2694345 T STEP (NIL) -9 NIL 2694423) (-1121 2687596 2693950 2694027 "STBL" 2694032 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1120 2682773 2686818 2686861 "STAGG" 2687014 NIL STAGG (NIL T) -9 NIL 2687103) (-1119 2680481 2681081 2681951 "STAGG-" 2681956 NIL STAGG- (NIL T T) -8 NIL NIL) (-1118 2678676 2680251 2680343 "STACK" 2680424 NIL STACK (NIL T) -8 NIL NIL) (-1117 2671428 2676817 2677273 "SREGSET" 2678306 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1116 2663854 2665222 2666735 "SRDCMPK" 2670034 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1115 2656821 2661294 2661324 "SRAGG" 2662627 T SRAGG (NIL) -9 NIL 2663235) (-1114 2655838 2656093 2656472 "SRAGG-" 2656477 NIL SRAGG- (NIL T) -8 NIL NIL) (-1113 2650337 2654785 2655206 "SQMATRIX" 2655464 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1112 2644090 2647057 2647783 "SPLTREE" 2649683 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1111 2640080 2640746 2641392 "SPLNODE" 2643516 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1110 2639127 2639360 2639390 "SPFCAT" 2639834 T SPFCAT (NIL) -9 NIL NIL) (-1109 2637864 2638074 2638338 "SPECOUT" 2638885 T SPECOUT (NIL) -7 NIL NIL) (-1108 2629553 2631297 2631327 "SPADXPT" 2635719 T SPADXPT (NIL) -9 NIL 2637753) (-1107 2629314 2629354 2629423 "SPADPRSR" 2629506 T SPADPRSR (NIL) -7 NIL NIL) (-1106 2627497 2629269 2629300 "SPADAST" 2629305 T SPADAST (NIL) -8 NIL NIL) (-1105 2619468 2621215 2621258 "SPACEC" 2625631 NIL SPACEC (NIL T) -9 NIL 2627447) (-1104 2617639 2619400 2619449 "SPACE3" 2619454 NIL SPACE3 (NIL T) -8 NIL NIL) (-1103 2616391 2616562 2616853 "SORTPAK" 2617444 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1102 2614441 2614744 2615163 "SOLVETRA" 2616055 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1101 2613452 2613674 2613948 "SOLVESER" 2614214 NIL SOLVESER (NIL T) -7 NIL NIL) (-1100 2608672 2609553 2610555 "SOLVERAD" 2612504 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1099 2604487 2605096 2605825 "SOLVEFOR" 2608039 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1098 2598811 2603836 2603933 "SNTSCAT" 2603938 NIL SNTSCAT (NIL T T T T) -9 NIL 2604008) (-1097 2592954 2597134 2597525 "SMTS" 2598501 NIL SMTS (NIL T T T) -8 NIL NIL) (-1096 2587430 2592842 2592919 "SMP" 2592924 NIL SMP (NIL T T) -8 NIL NIL) (-1095 2585589 2585890 2586288 "SMITH" 2587127 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1094 2578570 2582721 2582824 "SMATCAT" 2584178 NIL SMATCAT (NIL NIL T T T) -9 NIL 2584728) (-1093 2575531 2576347 2577518 "SMATCAT-" 2577523 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1092 2573244 2574767 2574810 "SKAGG" 2575071 NIL SKAGG (NIL T) -9 NIL 2575206) (-1091 2569362 2572348 2572626 "SINT" 2572988 T SINT (NIL) -8 NIL NIL) (-1090 2569134 2569172 2569238 "SIMPAN" 2569318 T SIMPAN (NIL) -7 NIL NIL) (-1089 2567993 2568207 2568475 "SIGNRF" 2568900 NIL SIGNRF (NIL T) -7 NIL NIL) (-1088 2566819 2566963 2567247 "SIGNEF" 2567829 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1087 2566152 2566402 2566526 "SIGAST" 2566717 T SIGAST (NIL) -8 NIL NIL) (-1086 2565459 2565687 2565827 "SIG" 2566034 T SIG (NIL) -8 NIL NIL) (-1085 2563149 2563603 2564109 "SHP" 2565000 NIL SHP (NIL T NIL) -7 NIL NIL) (-1084 2557062 2563050 2563126 "SHDP" 2563131 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1083 2556661 2556827 2556857 "SGROUP" 2556950 T SGROUP (NIL) -9 NIL 2557012) (-1082 2556519 2556545 2556618 "SGROUP-" 2556623 NIL SGROUP- (NIL T) -8 NIL NIL) (-1081 2553355 2554052 2554775 "SGCF" 2555818 T SGCF (NIL) -7 NIL NIL) (-1080 2547777 2552802 2552899 "SFRTCAT" 2552904 NIL SFRTCAT (NIL T T T T) -9 NIL 2552943) (-1079 2541201 2542216 2543352 "SFRGCD" 2546760 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1078 2534329 2535400 2536586 "SFQCMPK" 2540134 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1077 2533951 2534040 2534150 "SFORT" 2534270 NIL SFORT (NIL T T) -8 NIL NIL) (-1076 2533096 2533791 2533912 "SEXOF" 2533917 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1075 2527872 2528561 2528656 "SEXCAT" 2532427 NIL SEXCAT (NIL T T T T T) -9 NIL 2533046) (-1074 2527006 2527753 2527821 "SEX" 2527826 T SEX (NIL) -8 NIL NIL) (-1073 2525263 2525723 2526026 "SETMN" 2526749 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1072 2524869 2524995 2525025 "SETCAT" 2525142 T SETCAT (NIL) -9 NIL 2525227) (-1071 2524649 2524701 2524800 "SETCAT-" 2524805 NIL SETCAT- (NIL T) -8 NIL NIL) (-1070 2521036 2523110 2523153 "SETAGG" 2524023 NIL SETAGG (NIL T) -9 NIL 2524363) (-1069 2520494 2520610 2520847 "SETAGG-" 2520852 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1068 2517674 2520428 2520476 "SET" 2520481 NIL SET (NIL T) -8 NIL NIL) (-1067 2517144 2517370 2517471 "SEQAST" 2517595 T SEQAST (NIL) -8 NIL NIL) (-1066 2516348 2516641 2516702 "SEGXCAT" 2516988 NIL SEGXCAT (NIL T T) -9 NIL 2517108) (-1065 2515255 2515468 2515511 "SEGCAT" 2516093 NIL SEGCAT (NIL T) -9 NIL 2516331) (-1064 2514876 2514935 2515048 "SEGBIND2" 2515190 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1063 2513925 2514255 2514455 "SEGBIND" 2514711 NIL SEGBIND (NIL T) -8 NIL NIL) (-1062 2513526 2513726 2513803 "SEGAST" 2513870 T SEGAST (NIL) -8 NIL NIL) (-1061 2512745 2512871 2513075 "SEG2" 2513370 NIL SEG2 (NIL T T) -7 NIL NIL) (-1060 2511801 2512411 2512593 "SEG" 2512598 NIL SEG (NIL T) -8 NIL NIL) (-1059 2511238 2511736 2511783 "SDVAR" 2511788 NIL SDVAR (NIL T) -8 NIL NIL) (-1058 2503569 2511008 2511138 "SDPOL" 2511143 NIL SDPOL (NIL T) -8 NIL NIL) (-1057 2502162 2502428 2502747 "SCPKG" 2503284 NIL SCPKG (NIL T) -7 NIL NIL) (-1056 2501298 2501478 2501678 "SCOPE" 2501984 T SCOPE (NIL) -8 NIL NIL) (-1055 2500519 2500652 2500831 "SCACHE" 2501153 NIL SCACHE (NIL T) -7 NIL NIL) (-1054 2500228 2500388 2500418 "SASTCAT" 2500423 T SASTCAT (NIL) -9 NIL 2500436) (-1053 2499667 2499988 2500073 "SAOS" 2500165 T SAOS (NIL) -8 NIL NIL) (-1052 2499232 2499267 2499440 "SAERFFC" 2499626 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1051 2498825 2498860 2499019 "SAEFACT" 2499191 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1050 2492808 2498722 2498802 "SAE" 2498807 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1049 2491129 2491443 2491844 "RURPK" 2492474 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1048 2489765 2490044 2490356 "RULESET" 2490963 NIL RULESET (NIL T T T) -8 NIL NIL) (-1047 2489404 2489559 2489642 "RULECOLD" 2489717 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1046 2486591 2487094 2487559 "RULE" 2489085 NIL RULE (NIL T T T) -8 NIL NIL) (-1045 2486089 2486308 2486402 "RSTRCAST" 2486519 T RSTRCAST (NIL) -8 NIL NIL) (-1044 2480938 2481732 2482652 "RSETGCD" 2485288 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1043 2470222 2475247 2475344 "RSETCAT" 2479463 NIL RSETCAT (NIL T T T T) -9 NIL 2480560) (-1042 2468149 2468688 2469512 "RSETCAT-" 2469517 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1041 2460536 2461911 2463431 "RSDCMPK" 2466748 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1040 2458541 2458982 2459056 "RRCC" 2460142 NIL RRCC (NIL T T) -9 NIL 2460486) (-1039 2457892 2458066 2458345 "RRCC-" 2458350 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1038 2457362 2457588 2457689 "RPTAST" 2457813 T RPTAST (NIL) -8 NIL NIL) (-1037 2431621 2441175 2441242 "RPOLCAT" 2451906 NIL RPOLCAT (NIL T T T) -9 NIL 2455065) (-1036 2423157 2425483 2428593 "RPOLCAT-" 2428598 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1035 2414206 2421368 2421850 "ROUTINE" 2422697 T ROUTINE (NIL) -8 NIL NIL) (-1034 2410966 2413757 2413906 "ROMAN" 2414079 T ROMAN (NIL) -8 NIL NIL) (-1033 2409243 2409826 2410086 "ROIRC" 2410771 NIL ROIRC (NIL T T) -8 NIL NIL) (-1032 2405698 2407933 2407963 "RNS" 2408267 T RNS (NIL) -9 NIL 2408539) (-1031 2404207 2404590 2405124 "RNS-" 2405199 NIL RNS- (NIL T) -8 NIL NIL) (-1030 2403656 2404038 2404068 "RNG" 2404073 T RNG (NIL) -9 NIL 2404094) (-1029 2403048 2403410 2403453 "RMODULE" 2403515 NIL RMODULE (NIL T) -9 NIL 2403557) (-1028 2401884 2401978 2402314 "RMCAT2" 2402949 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1027 2398589 2401058 2401383 "RMATRIX" 2401618 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1026 2391531 2393765 2393880 "RMATCAT" 2397239 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2398221) (-1025 2390906 2391053 2391360 "RMATCAT-" 2391365 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1024 2390473 2390548 2390676 "RINTERP" 2390825 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1023 2389561 2390081 2390111 "RING" 2390223 T RING (NIL) -9 NIL 2390318) (-1022 2389353 2389397 2389494 "RING-" 2389499 NIL RING- (NIL T) -8 NIL NIL) (-1021 2388194 2388431 2388689 "RIDIST" 2389117 T RIDIST (NIL) -7 NIL NIL) (-1020 2379537 2387662 2387868 "RGCHAIN" 2388042 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1019 2378913 2379293 2379334 "RGBCSPC" 2379392 NIL RGBCSPC (NIL T) -9 NIL 2379444) (-1018 2378097 2378452 2378493 "RGBCMDL" 2378725 NIL RGBCMDL (NIL T) -9 NIL 2378839) (-1017 2377743 2377806 2377909 "RFFACTOR" 2378028 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1016 2377468 2377503 2377600 "RFFACT" 2377702 NIL RFFACT (NIL T) -7 NIL NIL) (-1015 2375585 2375949 2376331 "RFDIST" 2377108 T RFDIST (NIL) -7 NIL NIL) (-1014 2372579 2373193 2373863 "RF" 2374949 NIL RF (NIL T) -7 NIL NIL) (-1013 2372032 2372124 2372287 "RETSOL" 2372481 NIL RETSOL (NIL T T) -7 NIL NIL) (-1012 2371620 2371700 2371743 "RETRACT" 2371936 NIL RETRACT (NIL T) -9 NIL NIL) (-1011 2371469 2371494 2371581 "RETRACT-" 2371586 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1010 2371098 2371291 2371361 "RETAST" 2371421 T RETAST (NIL) -8 NIL NIL) (-1009 2363954 2370751 2370878 "RESULT" 2370993 T RESULT (NIL) -8 NIL NIL) (-1008 2362580 2363223 2363422 "RESRING" 2363857 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1007 2362216 2362265 2362363 "RESLATC" 2362517 NIL RESLATC (NIL T) -7 NIL NIL) (-1006 2361922 2361956 2362063 "REPSQ" 2362175 NIL REPSQ (NIL T) -7 NIL NIL) (-1005 2361620 2361654 2361765 "REPDB" 2361881 NIL REPDB (NIL T) -7 NIL NIL) (-1004 2355530 2356909 2358132 "REP2" 2360432 NIL REP2 (NIL T) -7 NIL NIL) (-1003 2351907 2352588 2353396 "REP1" 2354757 NIL REP1 (NIL T) -7 NIL NIL) (-1002 2349329 2349909 2350511 "REP" 2351327 T REP (NIL) -7 NIL NIL) (-1001 2342082 2347470 2347926 "REGSET" 2348959 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1000 2340895 2341230 2341480 "REF" 2341867 NIL REF (NIL T) -8 NIL NIL) (-999 2340276 2340379 2340544 "REDORDER" 2340779 NIL REDORDER (NIL T T) -7 NIL NIL) (-998 2336327 2339504 2339727 "RECLOS" 2340105 NIL RECLOS (NIL T) -8 NIL NIL) (-997 2335384 2335565 2335778 "REALSOLV" 2336134 T REALSOLV (NIL) -7 NIL NIL) (-996 2331875 2332677 2333559 "REAL0Q" 2334549 NIL REAL0Q (NIL T) -7 NIL NIL) (-995 2327486 2328474 2329533 "REAL0" 2330856 NIL REAL0 (NIL T) -7 NIL NIL) (-994 2327334 2327375 2327403 "REAL" 2327408 T REAL (NIL) -9 NIL 2327443) (-993 2326836 2327055 2327147 "RDUCEAST" 2327262 T RDUCEAST (NIL) -8 NIL NIL) (-992 2326244 2326316 2326521 "RDIV" 2326758 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-991 2325317 2325491 2325702 "RDIST" 2326066 NIL RDIST (NIL T) -7 NIL NIL) (-990 2323918 2324205 2324575 "RDETRS" 2325025 NIL RDETRS (NIL T T) -7 NIL NIL) (-989 2321735 2322189 2322725 "RDETR" 2323460 NIL RDETR (NIL T T) -7 NIL NIL) (-988 2320349 2320627 2321029 "RDEEFS" 2321451 NIL RDEEFS (NIL T T) -7 NIL NIL) (-987 2318847 2319153 2319583 "RDEEF" 2320037 NIL RDEEF (NIL T T) -7 NIL NIL) (-986 2313193 2316055 2316083 "RCFIELD" 2317360 T RCFIELD (NIL) -9 NIL 2318090) (-985 2311262 2311766 2312459 "RCFIELD-" 2312532 NIL RCFIELD- (NIL T) -8 NIL NIL) (-984 2307593 2309378 2309419 "RCAGG" 2310490 NIL RCAGG (NIL T) -9 NIL 2310955) (-983 2307224 2307318 2307478 "RCAGG-" 2307483 NIL RCAGG- (NIL T T) -8 NIL NIL) (-982 2306564 2306676 2306839 "RATRET" 2307108 NIL RATRET (NIL T) -7 NIL NIL) (-981 2306121 2306188 2306307 "RATFACT" 2306492 NIL RATFACT (NIL T) -7 NIL NIL) (-980 2305436 2305556 2305706 "RANDSRC" 2305991 T RANDSRC (NIL) -7 NIL NIL) (-979 2305173 2305217 2305288 "RADUTIL" 2305385 T RADUTIL (NIL) -7 NIL NIL) (-978 2298259 2303916 2304233 "RADIX" 2304888 NIL RADIX (NIL NIL) -8 NIL NIL) (-977 2289926 2298103 2298231 "RADFF" 2298236 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-976 2289578 2289653 2289681 "RADCAT" 2289838 T RADCAT (NIL) -9 NIL NIL) (-975 2289363 2289411 2289508 "RADCAT-" 2289513 NIL RADCAT- (NIL T) -8 NIL NIL) (-974 2287514 2289138 2289227 "QUEUE" 2289307 NIL QUEUE (NIL T) -8 NIL NIL) (-973 2287152 2287195 2287322 "QUATCT2" 2287465 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-972 2281019 2284313 2284353 "QUATCAT" 2285133 NIL QUATCAT (NIL T) -9 NIL 2285899) (-971 2277184 2278214 2279594 "QUATCAT-" 2279688 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-970 2273767 2277121 2277166 "QUAT" 2277171 NIL QUAT (NIL T) -8 NIL NIL) (-969 2271287 2272851 2272892 "QUAGG" 2273267 NIL QUAGG (NIL T) -9 NIL 2273442) (-968 2270919 2271112 2271180 "QQUTAST" 2271239 T QQUTAST (NIL) -8 NIL NIL) (-967 2269844 2270317 2270489 "QFORM" 2270791 NIL QFORM (NIL NIL T) -8 NIL NIL) (-966 2269482 2269525 2269652 "QFCAT2" 2269795 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-965 2260831 2266018 2266058 "QFCAT" 2266716 NIL QFCAT (NIL T) -9 NIL 2267715) (-964 2256439 2257628 2259207 "QFCAT-" 2259301 NIL QFCAT- (NIL T T) -8 NIL NIL) (-963 2255899 2256009 2256139 "QEQUAT" 2256329 T QEQUAT (NIL) -8 NIL NIL) (-962 2249047 2250118 2251302 "QCMPACK" 2254832 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-961 2248292 2248466 2248698 "QALGSET2" 2248867 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-960 2245874 2246293 2246719 "QALGSET" 2247949 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-959 2244565 2244788 2245105 "PWFFINTB" 2245647 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-958 2242764 2242932 2243286 "PUSHVAR" 2244379 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-957 2238682 2239736 2239777 "PTRANFN" 2241661 NIL PTRANFN (NIL T) -9 NIL NIL) (-956 2237084 2237375 2237697 "PTPACK" 2238393 NIL PTPACK (NIL T) -7 NIL NIL) (-955 2236716 2236773 2236882 "PTFUNC2" 2237021 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-954 2231182 2235527 2235568 "PTCAT" 2235941 NIL PTCAT (NIL T) -9 NIL 2236103) (-953 2230840 2230875 2230999 "PSQFR" 2231141 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-952 2229435 2229733 2230067 "PSEUDLIN" 2230538 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-951 2216204 2218569 2220893 "PSETPK" 2227195 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-950 2209248 2211962 2212058 "PSETCAT" 2215079 NIL PSETCAT (NIL T T T T) -9 NIL 2215893) (-949 2207084 2207718 2208539 "PSETCAT-" 2208544 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-948 2206433 2206598 2206626 "PSCURVE" 2206894 T PSCURVE (NIL) -9 NIL 2207061) (-947 2202914 2204396 2204461 "PSCAT" 2205305 NIL PSCAT (NIL T T T) -9 NIL 2205545) (-946 2201977 2202193 2202593 "PSCAT-" 2202598 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-945 2200629 2201262 2201476 "PRTITION" 2201783 T PRTITION (NIL) -8 NIL NIL) (-944 2200131 2200350 2200442 "PRTDAST" 2200557 T PRTDAST (NIL) -8 NIL NIL) (-943 2189229 2191435 2193623 "PRS" 2197993 NIL PRS (NIL T T) -7 NIL NIL) (-942 2187087 2188579 2188619 "PRQAGG" 2188802 NIL PRQAGG (NIL T) -9 NIL 2188904) (-941 2186473 2186702 2186730 "PROPLOG" 2186915 T PROPLOG (NIL) -9 NIL 2187037) (-940 2183643 2184287 2184751 "PROPFRML" 2186041 NIL PROPFRML (NIL T) -8 NIL NIL) (-939 2183103 2183213 2183343 "PROPERTY" 2183533 T PROPERTY (NIL) -8 NIL NIL) (-938 2177188 2181269 2182089 "PRODUCT" 2182329 NIL PRODUCT (NIL T T) -8 NIL NIL) (-937 2176984 2177016 2177075 "PRINT" 2177149 T PRINT (NIL) -7 NIL NIL) (-936 2176324 2176441 2176593 "PRIMES" 2176864 NIL PRIMES (NIL T) -7 NIL NIL) (-935 2174389 2174790 2175256 "PRIMELT" 2175903 NIL PRIMELT (NIL T) -7 NIL NIL) (-934 2174118 2174167 2174195 "PRIMCAT" 2174319 T PRIMCAT (NIL) -9 NIL NIL) (-933 2173125 2173303 2173531 "PRIMARR2" 2173936 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-932 2169286 2173063 2173108 "PRIMARR" 2173113 NIL PRIMARR (NIL T) -8 NIL NIL) (-931 2168929 2168985 2169096 "PREASSOC" 2169224 NIL PREASSOC (NIL T T) -7 NIL NIL) (-930 2166249 2168387 2168621 "PR" 2168740 NIL PR (NIL T T) -8 NIL NIL) (-929 2165724 2165857 2165885 "PPCURVE" 2166090 T PPCURVE (NIL) -9 NIL 2166226) (-928 2165346 2165519 2165602 "PORTNUM" 2165661 T PORTNUM (NIL) -8 NIL NIL) (-927 2162705 2163104 2163696 "POLYROOT" 2164927 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-926 2162088 2162146 2162380 "POLYLIFT" 2162641 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-925 2158363 2158812 2159441 "POLYCATQ" 2161633 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-924 2145416 2150758 2150823 "POLYCAT" 2154337 NIL POLYCAT (NIL T T T) -9 NIL 2156265) (-923 2138923 2140765 2143130 "POLYCAT-" 2143135 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-922 2138510 2138578 2138698 "POLY2UP" 2138849 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-921 2138142 2138199 2138308 "POLY2" 2138447 NIL POLY2 (NIL T T) -7 NIL NIL) (-920 2132118 2137746 2137906 "POLY" 2138015 NIL POLY (NIL T) -8 NIL NIL) (-919 2130803 2131042 2131318 "POLUTIL" 2131892 NIL POLUTIL (NIL T T) -7 NIL NIL) (-918 2129158 2129435 2129766 "POLTOPOL" 2130525 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-917 2124676 2129094 2129140 "POINT" 2129145 NIL POINT (NIL T) -8 NIL NIL) (-916 2122863 2123220 2123595 "PNTHEORY" 2124321 T PNTHEORY (NIL) 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2113496 2113655 2113837 "PMASS" 2114171 T PMASS (NIL) -7 NIL NIL) (-902 2113151 2113219 2113313 "PLOTTOOL" 2113422 T PLOTTOOL (NIL) -7 NIL NIL) (-901 2108965 2109999 2110920 "PLOT3D" 2112250 T PLOT3D (NIL) -8 NIL NIL) (-900 2107877 2108054 2108289 "PLOT1" 2108769 NIL PLOT1 (NIL T) -7 NIL NIL) (-899 2102499 2103688 2104836 "PLOT" 2106749 T PLOT (NIL) -8 NIL NIL) (-898 2077893 2082565 2087416 "PLEQN" 2097765 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-897 2077586 2077633 2077736 "PINTERPA" 2077840 NIL PINTERPA (NIL T T) -7 NIL NIL) (-896 2076904 2077026 2077206 "PINTERP" 2077451 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-895 2075336 2076277 2076305 "PID" 2076487 T PID (NIL) -9 NIL 2076621) (-894 2075061 2075098 2075186 "PICOERCE" 2075293 NIL PICOERCE (NIL T) -7 NIL NIL) (-893 2074346 2074867 2074954 "PI" 2074994 T PI (NIL) -8 NIL NIL) (-892 2073666 2073805 2073981 "PGROEB" 2074202 NIL PGROEB (NIL T) -7 NIL NIL) (-891 2069253 2070067 2070972 "PGE" 2072781 T PGE (NIL) -7 NIL NIL) (-890 2067377 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2043888) (-877 2041818 2041859 2041983 "PERMAN" 2042118 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-876 2037734 2039194 2039870 "PERM" 2041175 NIL PERM (NIL T) -8 NIL NIL) (-875 2035176 2037303 2037434 "PENDTREE" 2037636 NIL PENDTREE (NIL T) -8 NIL NIL) (-874 2033289 2034023 2034064 "PDRING" 2034721 NIL PDRING (NIL T) -9 NIL 2035007) (-873 2032392 2032610 2032972 "PDRING-" 2032977 NIL PDRING- (NIL T T) -8 NIL NIL) (-872 2029533 2030284 2030975 "PDEPROB" 2031721 T PDEPROB (NIL) -8 NIL NIL) (-871 2027080 2027582 2028137 "PDEPACK" 2028998 T PDEPACK (NIL) -7 NIL NIL) (-870 2025992 2026182 2026433 "PDECOMP" 2026879 NIL PDECOMP (NIL T T) -7 NIL NIL) (-869 2023597 2024414 2024442 "PDECAT" 2025229 T PDECAT (NIL) -9 NIL 2025942) (-868 2023348 2023381 2023471 "PCOMP" 2023558 NIL PCOMP (NIL T T) -7 NIL NIL) (-867 2021553 2022149 2022446 "PBWLB" 2023077 NIL PBWLB (NIL T) -8 NIL NIL) (-866 2021185 2021242 2021351 "PATTERN2" 2021490 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-865 2018942 2019330 2019787 "PATTERN1" 2020774 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-864 2011448 2013015 2014353 "PATTERN" 2017625 NIL PATTERN (NIL T) -8 NIL NIL) (-863 2011012 2011079 2011211 "PATRES2" 2011375 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-862 2008407 2008961 2009442 "PATRES" 2010577 NIL PATRES (NIL T T) -8 NIL NIL) (-861 2006290 2006695 2007102 "PATMATCH" 2008074 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-860 2005826 2006009 2006050 "PATMAB" 2006157 NIL PATMAB (NIL T) -9 NIL 2006240) (-859 2004371 2004680 2004938 "PATLRES" 2005631 NIL PATLRES (NIL T T T) -8 NIL NIL) (-858 2003917 2004040 2004081 "PATAB" 2004086 NIL PATAB (NIL T) -9 NIL 2004258) (-857 2001398 2001930 2002503 "PARTPERM" 2003364 T PARTPERM (NIL) -7 NIL NIL) (-856 2001019 2001082 2001184 "PARSURF" 2001329 NIL PARSURF (NIL T) -8 NIL NIL) (-855 2000651 2000708 2000817 "PARSU2" 2000956 NIL PARSU2 (NIL T T) -7 NIL NIL) (-854 2000415 2000455 2000522 "PARSER" 2000604 T PARSER (NIL) -7 NIL NIL) (-853 2000036 2000099 2000201 "PARSCURV" 2000346 NIL PARSCURV (NIL T) -8 NIL NIL) (-852 1999668 1999725 1999834 "PARSC2" 1999973 NIL PARSC2 (NIL T T) -7 NIL NIL) (-851 1999307 1999365 1999462 "PARPCURV" 1999604 NIL PARPCURV (NIL T) -8 NIL NIL) (-850 1998939 1998996 1999105 "PARPC2" 1999244 NIL PARPC2 (NIL T T) -7 NIL NIL) (-849 1998459 1998545 1998664 "PAN2EXPR" 1998840 T PAN2EXPR (NIL) -7 NIL NIL) (-848 1997265 1997580 1997808 "PALETTE" 1998251 T PALETTE (NIL) -8 NIL NIL) (-847 1995733 1996270 1996630 "PAIR" 1996951 NIL PAIR (NIL T T) -8 NIL NIL) (-846 1989662 1994992 1995186 "PADICRC" 1995588 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-845 1982949 1989008 1989192 "PADICRAT" 1989510 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-844 1980196 1981724 1981764 "PADICCT" 1982345 NIL PADICCT (NIL NIL) -9 NIL 1982627) (-843 1978548 1980133 1980178 "PADIC" 1980183 NIL PADIC (NIL NIL) -8 NIL NIL) (-842 1977505 1977705 1977973 "PADEPAC" 1978335 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-841 1976717 1976850 1977056 "PADE" 1977367 NIL PADE (NIL T T T) -7 NIL NIL) (-840 1974767 1975553 1975870 "OWP" 1976484 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-839 1973876 1974372 1974544 "OVAR" 1974635 NIL OVAR (NIL NIL) -8 NIL NIL) (-838 1962783 1964985 1967185 "OUTFORM" 1971696 T OUTFORM (NIL) -8 NIL NIL) (-837 1962204 1962380 1962507 "OUTBFILE" 1962676 T OUTBFILE (NIL) -8 NIL NIL) (-836 1961841 1961924 1961952 "OUTBCON" 1962103 T OUTBCON (NIL) -9 NIL 1962188) (-835 1961681 1961716 1961792 "OUTBCON-" 1961797 NIL OUTBCON- (NIL T) -8 NIL NIL) (-834 1960945 1961066 1961227 "OUT" 1961540 T OUT (NIL) -7 NIL NIL) (-833 1960353 1960674 1960763 "OSI" 1960876 T OSI (NIL) -8 NIL NIL) (-832 1959909 1960221 1960249 "OSGROUP" 1960254 T OSGROUP (NIL) -9 NIL 1960276) (-831 1958654 1958881 1959166 "ORTHPOL" 1959656 NIL ORTHPOL (NIL T) -7 NIL NIL) (-830 1956078 1958313 1958452 "OREUP" 1958597 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-829 1953530 1955769 1955896 "ORESUP" 1956020 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-828 1951058 1951558 1952119 "OREPCTO" 1953019 NIL OREPCTO (NIL T T) -7 NIL NIL) (-827 1944976 1947136 1947177 "OREPCAT" 1949525 NIL OREPCAT (NIL T) -9 NIL 1950629) (-826 1942144 1942919 1943970 "OREPCAT-" 1943975 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-825 1941321 1941593 1941621 "ORDSET" 1941930 T ORDSET (NIL) -9 NIL 1942094) (-824 1940840 1940962 1941155 "ORDSET-" 1941160 NIL ORDSET- (NIL T) -8 NIL NIL) (-823 1939494 1940251 1940279 "ORDRING" 1940481 T ORDRING (NIL) -9 NIL 1940606) (-822 1939139 1939233 1939377 "ORDRING-" 1939382 NIL ORDRING- (NIL T) -8 NIL NIL) (-821 1938545 1938982 1939010 "ORDMON" 1939015 T ORDMON (NIL) -9 NIL 1939036) (-820 1937707 1937854 1938049 "ORDFUNS" 1938394 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-819 1937218 1937577 1937605 "ORDFIN" 1937610 T ORDFIN (NIL) -9 NIL 1937631) (-818 1936484 1936611 1936797 "ORDCOMP2" 1937078 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-817 1933083 1935070 1935479 "ORDCOMP" 1936108 NIL ORDCOMP (NIL T) -8 NIL NIL) (-816 1929590 1930473 1931310 "OPTPROB" 1932266 T OPTPROB (NIL) -8 NIL NIL) (-815 1926392 1927031 1927735 "OPTPACK" 1928906 T OPTPACK (NIL) -7 NIL NIL) (-814 1924105 1924845 1924873 "OPTCAT" 1925692 T OPTCAT (NIL) -9 NIL 1926342) (-813 1923873 1923912 1923978 "OPQUERY" 1924059 T OPQUERY (NIL) -7 NIL NIL) (-812 1921041 1922184 1922688 "OP" 1923402 NIL OP (NIL T) -8 NIL NIL) (-811 1920346 1920461 1920635 "ONECOMP2" 1920913 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-810 1917198 1919143 1919512 "ONECOMP" 1920010 NIL ONECOMP (NIL T) -8 NIL NIL) (-809 1916617 1916723 1916853 "OMSERVER" 1917088 T OMSERVER (NIL) -7 NIL NIL) (-808 1913505 1916057 1916097 "OMSAGG" 1916158 NIL OMSAGG (NIL T) -9 NIL 1916222) (-807 1912128 1912391 1912673 "OMPKG" 1913243 T OMPKG (NIL) -7 NIL NIL) (-806 1910710 1911677 1911846 "OMLO" 1912009 NIL OMLO (NIL T T) -8 NIL NIL) (-805 1909635 1909782 1910009 "OMEXPR" 1910536 NIL OMEXPR (NIL T) -7 NIL NIL) (-804 1908813 1909056 1909216 "OMERRK" 1909495 T OMERRK (NIL) -8 NIL NIL) (-803 1908131 1908359 1908495 "OMERR" 1908697 T OMERR (NIL) -8 NIL NIL) (-802 1907609 1907808 1907916 "OMENC" 1908043 T OMENC (NIL) -8 NIL NIL) (-801 1901504 1902689 1903860 "OMDEV" 1906458 T OMDEV (NIL) -8 NIL NIL) (-800 1900573 1900744 1900938 "OMCONN" 1901330 T OMCONN (NIL) -8 NIL NIL) (-799 1900003 1900106 1900134 "OM" 1900433 T OM (NIL) -9 NIL NIL) (-798 1898659 1899601 1899629 "OINTDOM" 1899634 T OINTDOM (NIL) -9 NIL 1899655) (-797 1894465 1895649 1896365 "OFMONOID" 1897975 NIL OFMONOID (NIL T) -8 NIL NIL) (-796 1893903 1894402 1894447 "ODVAR" 1894452 NIL ODVAR (NIL T) -8 NIL NIL) (-795 1891115 1893400 1893585 "ODR" 1893778 NIL ODR (NIL T T NIL) -8 NIL NIL) (-794 1883500 1890891 1891017 "ODPOL" 1891022 NIL ODPOL (NIL T) -8 NIL NIL) (-793 1877383 1883372 1883477 "ODP" 1883482 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-792 1876149 1876364 1876639 "ODETOOLS" 1877157 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-791 1873118 1873774 1874490 "ODESYS" 1875482 NIL ODESYS (NIL T T) -7 NIL NIL) (-790 1868000 1868908 1869933 "ODERTRIC" 1872193 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-789 1867426 1867508 1867702 "ODERED" 1867912 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-788 1864322 1864868 1865543 "ODERAT" 1866851 NIL ODERAT (NIL T T) -7 NIL NIL) (-787 1861282 1861746 1862343 "ODEPRRIC" 1863851 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-786 1859151 1859720 1860229 "ODEPROB" 1860793 T ODEPROB (NIL) -8 NIL NIL) (-785 1855673 1856156 1856803 "ODEPRIM" 1858630 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-784 1854922 1855024 1855284 "ODEPAL" 1855565 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-783 1851084 1851875 1852739 "ODEPACK" 1854078 T ODEPACK (NIL) -7 NIL NIL) (-782 1850117 1850224 1850453 "ODEINT" 1850973 NIL ODEINT (NIL T T) -7 NIL NIL) (-781 1844218 1845643 1847090 "ODEIFTBL" 1848690 T ODEIFTBL (NIL) -8 NIL NIL) (-780 1839567 1840349 1841304 "ODEEF" 1843381 NIL ODEEF (NIL T T) -7 NIL NIL) (-779 1838902 1838991 1839221 "ODECONST" 1839472 NIL ODECONST (NIL T T T) -7 NIL NIL) (-778 1837053 1837688 1837716 "ODECAT" 1838321 T ODECAT (NIL) -9 NIL 1838852) (-777 1836691 1836734 1836861 "OCTCT2" 1837004 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-776 1833610 1836403 1836522 "OCT" 1836604 NIL OCT (NIL T) -8 NIL NIL) (-775 1832988 1833430 1833458 "OCAMON" 1833463 T OCAMON (NIL) -9 NIL 1833484) (-774 1827856 1830249 1830289 "OC" 1831386 NIL OC (NIL T) -9 NIL 1832244) (-773 1825104 1825845 1826828 "OC-" 1826922 NIL OC- (NIL T T) -8 NIL NIL) (-772 1824661 1824976 1825004 "OASGP" 1825009 T OASGP (NIL) -9 NIL 1825029) (-771 1823948 1824411 1824439 "OAMONS" 1824479 T OAMONS (NIL) -9 NIL 1824522) (-770 1823388 1823795 1823823 "OAMON" 1823828 T OAMON (NIL) -9 NIL 1823848) (-769 1822692 1823184 1823212 "OAGROUP" 1823217 T OAGROUP (NIL) -9 NIL 1823237) (-768 1822382 1822432 1822520 "NUMTUBE" 1822636 NIL NUMTUBE (NIL T) -7 NIL NIL) (-767 1815955 1817473 1819009 "NUMQUAD" 1820866 T NUMQUAD (NIL) -7 NIL NIL) (-766 1811711 1812699 1813724 "NUMODE" 1814950 T NUMODE (NIL) -7 NIL NIL) (-765 1809092 1809946 1809974 "NUMINT" 1810897 T NUMINT (NIL) -9 NIL 1811661) (-764 1808040 1808237 1808455 "NUMFMT" 1808894 T NUMFMT (NIL) -7 NIL NIL) (-763 1794399 1797344 1799876 "NUMERIC" 1805547 NIL NUMERIC (NIL T) -7 NIL NIL) (-762 1788823 1793848 1793943 "NTSCAT" 1793948 NIL NTSCAT (NIL T T T T) -9 NIL 1793987) (-761 1788017 1788182 1788375 "NTPOLFN" 1788662 NIL NTPOLFN (NIL T) -7 NIL NIL) (-760 1787649 1787706 1787815 "NSUP2" 1787954 NIL NSUP2 (NIL T T) -7 NIL NIL) (-759 1775534 1784474 1785286 "NSUP" 1786870 NIL NSUP (NIL T) -8 NIL NIL) (-758 1765579 1775308 1775441 "NSMP" 1775446 NIL NSMP (NIL T T) -8 NIL NIL) (-757 1764011 1764312 1764669 "NREP" 1765267 NIL NREP (NIL T) -7 NIL NIL) (-756 1762602 1762854 1763212 "NPCOEF" 1763754 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-755 1761668 1761783 1761999 "NORMRETR" 1762483 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-754 1759709 1759999 1760408 "NORMPK" 1761376 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-753 1759394 1759422 1759546 "NORMMA" 1759675 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-752 1759183 1759212 1759281 "NONE1" 1759358 NIL NONE1 (NIL T) -7 NIL NIL) (-751 1759010 1759140 1759169 "NONE" 1759174 T NONE (NIL) -8 NIL NIL) (-750 1758493 1758555 1758741 "NODE1" 1758942 NIL NODE1 (NIL T T) -7 NIL NIL) (-749 1756833 1757656 1757911 "NNI" 1758258 T NNI (NIL) -8 NIL NIL) (-748 1755253 1755566 1755930 "NLINSOL" 1756501 NIL NLINSOL (NIL T) -7 NIL NIL) (-747 1751420 1752388 1753310 "NIPROB" 1754351 T NIPROB (NIL) -8 NIL NIL) (-746 1750177 1750411 1750713 "NFINTBAS" 1751182 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-745 1748885 1749116 1749397 "NCODIV" 1749945 NIL NCODIV (NIL T T) -7 NIL NIL) (-744 1748647 1748684 1748759 "NCNTFRAC" 1748842 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-743 1746827 1747191 1747611 "NCEP" 1748272 NIL NCEP (NIL T) -7 NIL NIL) (-742 1745745 1746477 1746505 "NASRING" 1746615 T NASRING (NIL) -9 NIL 1746689) (-741 1745540 1745584 1745678 "NASRING-" 1745683 NIL NASRING- (NIL T) -8 NIL NIL) (-740 1744693 1745192 1745220 "NARNG" 1745337 T NARNG (NIL) -9 NIL 1745428) (-739 1744385 1744452 1744586 "NARNG-" 1744591 NIL NARNG- (NIL T) -8 NIL NIL) (-738 1743264 1743471 1743706 "NAGSP" 1744170 T NAGSP (NIL) -7 NIL NIL) (-737 1734536 1736220 1737893 "NAGS" 1741611 T NAGS (NIL) -7 NIL NIL) (-736 1733084 1733392 1733723 "NAGF07" 1734225 T NAGF07 (NIL) -7 NIL NIL) (-735 1727622 1728913 1730220 "NAGF04" 1731797 T NAGF04 (NIL) -7 NIL NIL) (-734 1720590 1722204 1723837 "NAGF02" 1726009 T NAGF02 (NIL) -7 NIL NIL) (-733 1715814 1716914 1718031 "NAGF01" 1719493 T NAGF01 (NIL) -7 NIL NIL) (-732 1709442 1711008 1712593 "NAGE04" 1714249 T NAGE04 (NIL) -7 NIL NIL) (-731 1700611 1702732 1704862 "NAGE02" 1707332 T NAGE02 (NIL) -7 NIL NIL) (-730 1696564 1697511 1698475 "NAGE01" 1699667 T NAGE01 (NIL) -7 NIL NIL) (-729 1694359 1694893 1695451 "NAGD03" 1696026 T NAGD03 (NIL) -7 NIL NIL) (-728 1686109 1688037 1689991 "NAGD02" 1692425 T NAGD02 (NIL) -7 NIL NIL) (-727 1679920 1681345 1682785 "NAGD01" 1684689 T NAGD01 (NIL) -7 NIL NIL) (-726 1676129 1676951 1677788 "NAGC06" 1679103 T NAGC06 (NIL) -7 NIL NIL) (-725 1674594 1674926 1675282 "NAGC05" 1675793 T NAGC05 (NIL) -7 NIL NIL) (-724 1673970 1674089 1674233 "NAGC02" 1674470 T NAGC02 (NIL) -7 NIL NIL) (-723 1673030 1673587 1673627 "NAALG" 1673706 NIL NAALG (NIL T) -9 NIL 1673767) (-722 1672865 1672894 1672984 "NAALG-" 1672989 NIL NAALG- (NIL T T) -8 NIL NIL) (-721 1666815 1667923 1669110 "MULTSQFR" 1671761 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-720 1666134 1666209 1666393 "MULTFACT" 1666727 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-719 1659357 1663222 1663275 "MTSCAT" 1664345 NIL MTSCAT (NIL T T) -9 NIL 1664859) (-718 1659069 1659123 1659215 "MTHING" 1659297 NIL MTHING (NIL T) -7 NIL NIL) (-717 1658861 1658894 1658954 "MSYSCMD" 1659029 T MSYSCMD (NIL) -7 NIL NIL) (-716 1655956 1658422 1658463 "MSETAGG" 1658468 NIL MSETAGG (NIL T) -9 NIL 1658502) (-715 1652068 1654711 1655031 "MSET" 1655669 NIL MSET (NIL T) -8 NIL NIL) (-714 1647953 1649447 1650192 "MRING" 1651368 NIL MRING (NIL T T) -8 NIL NIL) (-713 1647519 1647586 1647717 "MRF2" 1647880 NIL MRF2 (NIL T T T) -7 NIL NIL) (-712 1647137 1647172 1647316 "MRATFAC" 1647478 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-711 1644749 1645044 1645475 "MPRFF" 1646842 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-710 1638835 1644603 1644700 "MPOLY" 1644705 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-709 1638325 1638360 1638568 "MPCPF" 1638794 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-708 1637839 1637882 1638066 "MPC3" 1638276 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-707 1637034 1637115 1637336 "MPC2" 1637754 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-706 1635335 1635672 1636062 "MONOTOOL" 1636694 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-705 1634586 1634877 1634905 "MONOID" 1635124 T MONOID (NIL) -9 NIL 1635271) (-704 1634132 1634251 1634432 "MONOID-" 1634437 NIL MONOID- (NIL T) -8 NIL NIL) (-703 1625191 1631088 1631147 "MONOGEN" 1631821 NIL MONOGEN (NIL T T) -9 NIL 1632277) (-702 1622430 1623158 1624151 "MONOGEN-" 1624270 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-701 1621289 1621709 1621737 "MONADWU" 1622129 T MONADWU (NIL) -9 NIL 1622367) (-700 1620661 1620820 1621068 "MONADWU-" 1621073 NIL MONADWU- (NIL T) -8 NIL NIL) (-699 1620046 1620264 1620292 "MONAD" 1620499 T MONAD (NIL) -9 NIL 1620611) (-698 1619731 1619809 1619941 "MONAD-" 1619946 NIL MONAD- (NIL T) -8 NIL NIL) (-697 1618047 1618644 1618923 "MOEBIUS" 1619484 NIL MOEBIUS (NIL T) -8 NIL NIL) (-696 1617439 1617817 1617857 "MODULE" 1617862 NIL MODULE (NIL T) -9 NIL 1617888) (-695 1617007 1617103 1617293 "MODULE-" 1617298 NIL MODULE- (NIL T T) -8 NIL NIL) (-694 1614766 1615415 1615742 "MODRING" 1616831 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-693 1611754 1612871 1613392 "MODOP" 1614295 NIL MODOP (NIL T T) -8 NIL NIL) (-692 1609941 1610393 1610734 "MODMONOM" 1611553 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-691 1599689 1608133 1608556 "MODMON" 1609569 NIL MODMON (NIL T T) -8 NIL NIL) (-690 1596906 1598557 1598833 "MODFIELD" 1599564 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-689 1595910 1596187 1596377 "MMLFORM" 1596736 T MMLFORM (NIL) -8 NIL NIL) (-688 1595436 1595479 1595658 "MMAP" 1595861 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-687 1593705 1594438 1594479 "MLO" 1594902 NIL MLO (NIL T) -9 NIL 1595144) (-686 1591072 1591587 1592189 "MLIFT" 1593186 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-685 1590463 1590547 1590701 "MKUCFUNC" 1590983 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-684 1590062 1590132 1590255 "MKRECORD" 1590386 NIL MKRECORD (NIL T T) -7 NIL NIL) (-683 1589110 1589271 1589499 "MKFUNC" 1589873 NIL MKFUNC (NIL T) -7 NIL NIL) (-682 1588498 1588602 1588758 "MKFLCFN" 1588993 NIL MKFLCFN (NIL T) -7 NIL NIL) (-681 1587924 1588291 1588380 "MKCHSET" 1588442 NIL MKCHSET (NIL T) -8 NIL NIL) (-680 1587201 1587303 1587488 "MKBCFUNC" 1587817 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-679 1583945 1586755 1586891 "MINT" 1587085 T MINT (NIL) -8 NIL NIL) (-678 1582757 1583000 1583277 "MHROWRED" 1583700 NIL MHROWRED (NIL T) -7 NIL NIL) (-677 1578192 1581292 1581697 "MFLOAT" 1582372 T MFLOAT (NIL) -8 NIL NIL) (-676 1577549 1577625 1577796 "MFINFACT" 1578104 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-675 1573884 1574727 1575606 "MESH" 1576690 T MESH (NIL) -7 NIL NIL) (-674 1572274 1572586 1572939 "MDDFACT" 1573571 NIL MDDFACT (NIL T) -7 NIL NIL) (-673 1569116 1571433 1571474 "MDAGG" 1571729 NIL MDAGG (NIL T) -9 NIL 1571872) (-672 1558914 1568409 1568616 "MCMPLX" 1568929 T MCMPLX (NIL) -8 NIL NIL) (-671 1558055 1558201 1558401 "MCDEN" 1558763 NIL MCDEN (NIL T T) -7 NIL NIL) (-670 1555945 1556215 1556595 "MCALCFN" 1557785 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-669 1554856 1555029 1555270 "MAYBE" 1555743 NIL MAYBE (NIL T) -8 NIL NIL) (-668 1552468 1552991 1553553 "MATSTOR" 1554327 NIL MATSTOR (NIL T) -7 NIL NIL) (-667 1548473 1551840 1552088 "MATRIX" 1552253 NIL MATRIX (NIL T) -8 NIL NIL) (-666 1544242 1544946 1545682 "MATLIN" 1547830 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-665 1542836 1542989 1543322 "MATCAT2" 1544077 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-664 1532984 1536125 1536202 "MATCAT" 1541085 NIL MATCAT (NIL T T T) -9 NIL 1542502) (-663 1529348 1530361 1531717 "MATCAT-" 1531722 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-662 1527460 1527784 1528168 "MAPPKG3" 1529023 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-661 1526441 1526614 1526836 "MAPPKG2" 1527284 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-660 1524940 1525224 1525551 "MAPPKG1" 1526147 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-659 1524046 1524346 1524523 "MAPPAST" 1524783 T MAPPAST (NIL) -8 NIL NIL) (-658 1523657 1523715 1523838 "MAPHACK3" 1523982 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-657 1523249 1523310 1523424 "MAPHACK2" 1523589 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-656 1522687 1522790 1522932 "MAPHACK1" 1523140 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-655 1520793 1521387 1521691 "MAGMA" 1522415 NIL MAGMA (NIL T) -8 NIL NIL) (-654 1520299 1520517 1520608 "MACROAST" 1520722 T MACROAST (NIL) -8 NIL NIL) (-653 1516766 1518538 1518999 "M3D" 1519871 NIL M3D (NIL T) -8 NIL NIL) (-652 1510923 1515136 1515177 "LZSTAGG" 1515959 NIL LZSTAGG (NIL T) -9 NIL 1516254) (-651 1506896 1508054 1509511 "LZSTAGG-" 1509516 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-650 1504010 1504787 1505274 "LWORD" 1506441 NIL LWORD (NIL T) -8 NIL NIL) (-649 1503613 1503814 1503889 "LSTAST" 1503955 T LSTAST (NIL) -8 NIL NIL) (-648 1496845 1503384 1503518 "LSQM" 1503523 NIL LSQM (NIL NIL T) -8 NIL NIL) (-647 1496069 1496208 1496436 "LSPP" 1496700 NIL LSPP (NIL T T T T) -7 NIL NIL) (-646 1492911 1493568 1494281 "LSMP1" 1495388 NIL LSMP1 (NIL T) -7 NIL NIL) (-645 1490746 1491040 1491489 "LSMP" 1492607 NIL LSMP (NIL T T T T) -7 NIL NIL) (-644 1484674 1489914 1489955 "LSAGG" 1490017 NIL LSAGG (NIL T) -9 NIL 1490095) (-643 1481369 1482293 1483506 "LSAGG-" 1483511 NIL LSAGG- (NIL T T) -8 NIL NIL) (-642 1478995 1480513 1480762 "LPOLY" 1481164 NIL LPOLY (NIL T T) -8 NIL NIL) (-641 1478577 1478662 1478785 "LPEFRAC" 1478904 NIL LPEFRAC (NIL T) -7 NIL NIL) (-640 1478229 1478341 1478369 "LOGIC" 1478480 T LOGIC (NIL) -9 NIL 1478561) (-639 1478091 1478114 1478185 "LOGIC-" 1478190 NIL LOGIC- (NIL T) -8 NIL NIL) (-638 1477284 1477424 1477617 "LODOOPS" 1477947 NIL LODOOPS (NIL T T) -7 NIL NIL) (-637 1475822 1476057 1476410 "LODOF" 1477031 NIL LODOF (NIL T T) -7 NIL NIL) (-636 1472279 1474662 1474703 "LODOCAT" 1475141 NIL LODOCAT (NIL T) -9 NIL 1475352) (-635 1472012 1472070 1472197 "LODOCAT-" 1472202 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-634 1469381 1471853 1471971 "LODO2" 1471976 NIL LODO2 (NIL T T) -8 NIL NIL) (-633 1466865 1469318 1469363 "LODO1" 1469368 NIL LODO1 (NIL T) -8 NIL NIL) (-632 1464337 1466781 1466847 "LODO" 1466852 NIL LODO (NIL T NIL) -8 NIL NIL) (-631 1463197 1463362 1463674 "LODEEF" 1464160 NIL LODEEF (NIL T T T) -7 NIL NIL) (-630 1461544 1462291 1462544 "LO" 1463029 NIL LO (NIL T T T) -8 NIL NIL) (-629 1456830 1459674 1459715 "LNAGG" 1460662 NIL LNAGG (NIL T) -9 NIL 1461106) (-628 1455977 1456191 1456533 "LNAGG-" 1456538 NIL LNAGG- (NIL T T) -8 NIL NIL) (-627 1452140 1452902 1453541 "LMOPS" 1455392 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-626 1451535 1451897 1451938 "LMODULE" 1451999 NIL LMODULE (NIL T) -9 NIL 1452041) (-625 1448781 1451180 1451303 "LMDICT" 1451445 NIL LMDICT (NIL T) -8 NIL NIL) (-624 1448507 1448689 1448749 "LITERAL" 1448754 NIL LITERAL (NIL T) -8 NIL NIL) (-623 1448032 1448106 1448245 "LIST3" 1448427 NIL LIST3 (NIL T T T) -7 NIL NIL) (-622 1446166 1446478 1446877 "LIST2MAP" 1447679 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-621 1445173 1445351 1445579 "LIST2" 1445984 NIL LIST2 (NIL T T) -7 NIL NIL) (-620 1438402 1444119 1444417 "LIST" 1444908 NIL LIST (NIL T) -8 NIL NIL) (-619 1437152 1437788 1437829 "LINEXP" 1438084 NIL LINEXP (NIL T) -9 NIL 1438233) (-618 1435799 1436059 1436356 "LINDEP" 1436904 NIL LINDEP (NIL T T) -7 NIL NIL) (-617 1432637 1433337 1434095 "LIMITRF" 1435073 NIL LIMITRF (NIL T) -7 NIL NIL) (-616 1430936 1431224 1431633 "LIMITPS" 1432339 NIL LIMITPS (NIL T T) -7 NIL NIL) (-615 1429985 1430428 1430468 "LIECAT" 1430608 NIL LIECAT (NIL T) -9 NIL 1430759) (-614 1429826 1429853 1429941 "LIECAT-" 1429946 NIL LIECAT- (NIL T T) -8 NIL NIL) (-613 1424313 1429337 1429565 "LIE" 1429647 NIL LIE (NIL T T) -8 NIL NIL) (-612 1416927 1423762 1423927 "LIB" 1424168 T LIB (NIL) -8 NIL NIL) (-611 1412564 1413445 1414380 "LGROBP" 1416044 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-610 1411404 1412096 1412124 "LFCAT" 1412331 T LFCAT (NIL) -9 NIL 1412470) (-609 1409270 1409544 1409906 "LF" 1411125 NIL LF (NIL T T) -7 NIL NIL) (-608 1406174 1406802 1407490 "LEXTRIPK" 1408634 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-607 1402945 1403744 1404247 "LEXP" 1405754 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-606 1402448 1402666 1402758 "LETAST" 1402873 T LETAST (NIL) -8 NIL NIL) (-605 1400846 1401159 1401560 "LEADCDET" 1402130 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-604 1400036 1400110 1400339 "LAZM3PK" 1400767 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-603 1395006 1398113 1398651 "LAUPOL" 1399548 NIL LAUPOL (NIL T T) -8 NIL NIL) (-602 1394571 1394615 1394783 "LAPLACE" 1394956 NIL LAPLACE (NIL T T) -7 NIL NIL) (-601 1393672 1394222 1394263 "LALG" 1394325 NIL LALG (NIL T) -9 NIL 1394384) (-600 1393386 1393445 1393581 "LALG-" 1393586 NIL LALG- (NIL T T) -8 NIL NIL) (-599 1391360 1392487 1392738 "LA" 1393219 NIL LA (NIL T T T) -8 NIL NIL) (-598 1390160 1390577 1390806 "KTVLOGIC" 1391151 T KTVLOGIC (NIL) -8 NIL NIL) (-597 1389064 1389251 1389550 "KOVACIC" 1389960 NIL KOVACIC (NIL T T) -7 NIL NIL) (-596 1388899 1388923 1388964 "KONVERT" 1389026 NIL KONVERT (NIL T) -9 NIL NIL) (-595 1388734 1388758 1388799 "KOERCE" 1388861 NIL KOERCE (NIL T) -9 NIL NIL) (-594 1388236 1388317 1388447 "KERNEL2" 1388648 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-593 1385970 1386730 1387123 "KERNEL" 1387875 NIL KERNEL (NIL T) -8 NIL NIL) (-592 1379821 1384509 1384563 "KDAGG" 1384940 NIL KDAGG (NIL T T) -9 NIL 1385146) (-591 1379350 1379474 1379679 "KDAGG-" 1379684 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-590 1372527 1379011 1379166 "KAFILE" 1379228 NIL KAFILE (NIL T) -8 NIL NIL) (-589 1367014 1372038 1372266 "JORDAN" 1372348 NIL JORDAN (NIL T T) -8 NIL NIL) (-588 1366420 1366663 1366784 "JOINAST" 1366913 T JOINAST (NIL) -8 NIL NIL) (-587 1366149 1366208 1366295 "JAVACODE" 1366353 T JAVACODE (NIL) -8 NIL NIL) (-586 1362448 1364354 1364408 "IXAGG" 1365337 NIL IXAGG (NIL T T) -9 NIL 1365796) (-585 1361367 1361673 1362092 "IXAGG-" 1362097 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-584 1356947 1361289 1361348 "IVECTOR" 1361353 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-583 1355713 1355950 1356216 "ITUPLE" 1356714 NIL ITUPLE (NIL T) -8 NIL NIL) (-582 1354149 1354326 1354632 "ITRIGMNP" 1355535 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-581 1352894 1353098 1353381 "ITFUN3" 1353925 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-580 1352526 1352583 1352692 "ITFUN2" 1352831 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-579 1350363 1351388 1351687 "ITAYLOR" 1352260 NIL ITAYLOR (NIL T) -8 NIL NIL) (-578 1339345 1344500 1345663 "ISUPS" 1349233 NIL ISUPS (NIL T) -8 NIL NIL) (-577 1338449 1338589 1338825 "ISUMP" 1339192 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-576 1333713 1338250 1338329 "ISTRING" 1338402 NIL ISTRING (NIL NIL) -8 NIL NIL) (-575 1333216 1333434 1333526 "ISAST" 1333641 T ISAST (NIL) -8 NIL NIL) (-574 1332426 1332507 1332723 "IRURPK" 1333130 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-573 1331362 1331563 1331803 "IRSN" 1332206 T IRSN (NIL) -7 NIL NIL) (-572 1329391 1329746 1330182 "IRRF2F" 1331000 NIL IRRF2F (NIL T) -7 NIL NIL) (-571 1329138 1329176 1329252 "IRREDFFX" 1329347 NIL IRREDFFX (NIL T) -7 NIL NIL) (-570 1327753 1328012 1328311 "IROOT" 1328871 NIL IROOT (NIL T) -7 NIL NIL) (-569 1326825 1326938 1327159 "IR2F" 1327636 NIL IR2F (NIL T T) -7 NIL NIL) (-568 1324438 1324933 1325499 "IR2" 1326303 NIL IR2 (NIL T T) -7 NIL NIL) (-567 1321070 1322122 1322814 "IR" 1323778 NIL IR (NIL T) -8 NIL NIL) (-566 1320861 1320895 1320955 "IPRNTPK" 1321030 T IPRNTPK (NIL) -7 NIL NIL) (-565 1317482 1320750 1320819 "IPF" 1320824 NIL IPF (NIL NIL) -8 NIL NIL) (-564 1315847 1317407 1317464 "IPADIC" 1317469 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-563 1315347 1315551 1315661 "IOMODE" 1315757 T IOMODE (NIL) -8 NIL NIL) (-562 1315111 1315251 1315279 "IOBCON" 1315284 T IOBCON (NIL) -9 NIL 1315305) (-561 1314608 1314666 1314856 "INVLAPLA" 1315047 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-560 1304305 1306646 1309020 "INTTR" 1312284 NIL INTTR (NIL T T) -7 NIL NIL) (-559 1300649 1301391 1302255 "INTTOOLS" 1303490 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-558 1300235 1300326 1300443 "INTSLPE" 1300552 T INTSLPE (NIL) -7 NIL NIL) (-557 1298230 1300158 1300217 "INTRVL" 1300222 NIL INTRVL (NIL T) -8 NIL NIL) (-556 1295832 1296344 1296919 "INTRF" 1297715 NIL INTRF (NIL T) -7 NIL NIL) (-555 1295243 1295340 1295482 "INTRET" 1295730 NIL INTRET (NIL T) -7 NIL NIL) (-554 1293240 1293629 1294099 "INTRAT" 1294851 NIL INTRAT (NIL T T) -7 NIL NIL) (-553 1290468 1291051 1291677 "INTPM" 1292725 NIL INTPM (NIL T T) -7 NIL NIL) (-552 1287194 1287786 1288524 "INTPAF" 1289861 NIL INTPAF (NIL T T T) -7 NIL NIL) (-551 1282373 1283335 1284386 "INTPACK" 1286163 T INTPACK (NIL) -7 NIL NIL) (-550 1281625 1281777 1281985 "INTHERTR" 1282215 NIL INTHERTR (NIL T T) -7 NIL NIL) (-549 1281064 1281144 1281332 "INTHERAL" 1281539 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-548 1278910 1279353 1279810 "INTHEORY" 1280627 T INTHEORY (NIL) -7 NIL NIL) (-547 1270276 1271879 1273640 "INTG0" 1277280 NIL INTG0 (NIL T T T) -7 NIL NIL) (-546 1256549 1259914 1263299 "INTFTBL" 1266911 T INTFTBL (NIL) -8 NIL NIL) (-545 1255798 1255936 1256109 "INTFACT" 1256408 NIL INTFACT (NIL T) -7 NIL NIL) (-544 1253189 1253633 1254195 "INTEF" 1255354 NIL INTEF (NIL T T) -7 NIL NIL) (-543 1251691 1252396 1252424 "INTDOM" 1252725 T INTDOM (NIL) -9 NIL 1252932) (-542 1251060 1251234 1251476 "INTDOM-" 1251481 NIL INTDOM- (NIL T) -8 NIL NIL) (-541 1247593 1249479 1249533 "INTCAT" 1250332 NIL INTCAT (NIL T) -9 NIL 1250652) (-540 1247066 1247168 1247296 "INTBIT" 1247485 T INTBIT (NIL) -7 NIL NIL) (-539 1245737 1245891 1246205 "INTALG" 1246911 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-538 1245194 1245284 1245454 "INTAF" 1245641 NIL INTAF (NIL T T) -7 NIL NIL) (-537 1238650 1245004 1245144 "INTABL" 1245149 NIL INTABL (NIL T T T) -8 NIL NIL) (-536 1235564 1238379 1238506 "INT" 1238543 T INT (NIL) -8 NIL NIL) (-535 1230621 1233290 1233318 "INS" 1234252 T INS (NIL) -9 NIL 1234916) (-534 1227861 1228632 1229606 "INS-" 1229679 NIL INS- (NIL T) -8 NIL NIL) (-533 1226709 1226914 1227190 "INPSIGN" 1227636 NIL INPSIGN (NIL T T) -7 NIL NIL) (-532 1225827 1225944 1226141 "INPRODPF" 1226589 NIL INPRODPF (NIL T T) -7 NIL NIL) (-531 1224721 1224838 1225075 "INPRODFF" 1225707 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-530 1223721 1223873 1224133 "INNMFACT" 1224557 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-529 1222918 1223015 1223203 "INMODGCD" 1223620 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-528 1221427 1221671 1221995 "INFSP" 1222663 NIL INFSP (NIL T T T) -7 NIL NIL) (-527 1220611 1220728 1220911 "INFPROD0" 1221307 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-526 1220221 1220281 1220379 "INFORM1" 1220546 NIL INFORM1 (NIL T) -7 NIL NIL) (-525 1217103 1218286 1218801 "INFORM" 1219714 T INFORM (NIL) -8 NIL NIL) (-524 1216626 1216715 1216829 "INFINITY" 1217009 T INFINITY (NIL) -7 NIL NIL) (-523 1215243 1215492 1215813 "INEP" 1216374 NIL INEP (NIL T T T) -7 NIL NIL) (-522 1214519 1215140 1215205 "INDE" 1215210 NIL INDE (NIL T) -8 NIL NIL) (-521 1214083 1214151 1214268 "INCRMAPS" 1214446 NIL INCRMAPS (NIL T) -7 NIL NIL) (-520 1213386 1213579 1213729 "INBFILE" 1213953 T INBFILE (NIL) -8 NIL NIL) (-519 1208697 1209622 1210566 "INBFF" 1212474 NIL INBFF (NIL T) -7 NIL NIL) (-518 1208366 1208442 1208470 "INBCON" 1208603 T INBCON (NIL) -9 NIL 1208681) (-517 1208206 1208241 1208317 "INBCON-" 1208322 NIL INBCON- (NIL T) -8 NIL NIL) (-516 1207708 1207927 1208019 "INAST" 1208134 T INAST (NIL) -8 NIL NIL) (-515 1207162 1207387 1207493 "IMPTAST" 1207622 T IMPTAST (NIL) -8 NIL NIL) (-514 1203655 1207006 1207110 "IMATRIX" 1207115 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-513 1202367 1202490 1202805 "IMATQF" 1203511 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-512 1200587 1200814 1201151 "IMATLIN" 1202123 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-511 1195215 1200511 1200569 "ILIST" 1200574 NIL ILIST (NIL T NIL) -8 NIL NIL) (-510 1193168 1195075 1195188 "IIARRAY2" 1195193 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-509 1188603 1193079 1193143 "IFF" 1193148 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-508 1187977 1188220 1188336 "IFAST" 1188507 T IFAST (NIL) -8 NIL NIL) (-507 1183020 1187269 1187457 "IFARRAY" 1187834 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-506 1182227 1182924 1182997 "IFAMON" 1183002 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-505 1181811 1181876 1181930 "IEVALAB" 1182137 NIL IEVALAB (NIL T T) -9 NIL NIL) (-504 1181486 1181554 1181714 "IEVALAB-" 1181719 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-503 1180763 1181375 1181450 "IDPOAMS" 1181455 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-502 1180097 1180652 1180727 "IDPOAM" 1180732 NIL IDPOAM (NIL T T) -8 NIL NIL) (-501 1179755 1180011 1180074 "IDPO" 1180079 NIL IDPO (NIL T T) -8 NIL NIL) (-500 1178840 1179090 1179143 "IDPC" 1179556 NIL IDPC (NIL T T) -9 NIL 1179705) (-499 1178336 1178732 1178805 "IDPAM" 1178810 NIL IDPAM (NIL T T) -8 NIL NIL) (-498 1177739 1178228 1178301 "IDPAG" 1178306 NIL IDPAG (NIL T T) -8 NIL NIL) (-497 1177469 1177654 1177704 "IDENT" 1177709 T IDENT (NIL) -8 NIL NIL) (-496 1173724 1174572 1175467 "IDECOMP" 1176626 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-495 1166597 1167647 1168694 "IDEAL" 1172760 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-494 1165761 1165873 1166072 "ICDEN" 1166481 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-493 1164860 1165241 1165388 "ICARD" 1165634 T ICARD (NIL) -8 NIL NIL) (-492 1162920 1163233 1163638 "IBPTOOLS" 1164537 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-491 1158554 1162540 1162653 "IBITS" 1162839 NIL IBITS (NIL NIL) -8 NIL NIL) (-490 1155277 1155853 1156548 "IBATOOL" 1157971 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-489 1153057 1153518 1154051 "IBACHIN" 1154812 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-488 1150934 1152903 1153006 "IARRAY2" 1153011 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-487 1147087 1150860 1150917 "IARRAY1" 1150922 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-486 1141091 1145501 1145981 "IAN" 1146627 T IAN (NIL) -8 NIL NIL) (-485 1140602 1140659 1140832 "IALGFACT" 1141028 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-484 1140130 1140243 1140271 "HYPCAT" 1140478 T HYPCAT (NIL) -9 NIL NIL) (-483 1139668 1139785 1139971 "HYPCAT-" 1139976 NIL HYPCAT- (NIL T) -8 NIL NIL) (-482 1139290 1139463 1139546 "HOSTNAME" 1139605 T HOSTNAME (NIL) -8 NIL NIL) (-481 1135969 1137300 1137341 "HOAGG" 1138322 NIL HOAGG (NIL T) -9 NIL 1139001) (-480 1134563 1134962 1135488 "HOAGG-" 1135493 NIL HOAGG- (NIL T T) -8 NIL NIL) (-479 1128472 1134004 1134170 "HEXADEC" 1134417 T HEXADEC (NIL) -8 NIL NIL) (-478 1127220 1127442 1127705 "HEUGCD" 1128249 NIL HEUGCD (NIL T) -7 NIL NIL) (-477 1126323 1127057 1127187 "HELLFDIV" 1127192 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-476 1124551 1126100 1126188 "HEAP" 1126267 NIL HEAP (NIL T) -8 NIL NIL) (-475 1123842 1124103 1124237 "HEADAST" 1124437 T HEADAST (NIL) -8 NIL NIL) (-474 1117769 1123757 1123819 "HDP" 1123824 NIL HDP (NIL NIL T) -8 NIL NIL) (-473 1111551 1117404 1117556 "HDMP" 1117670 NIL HDMP (NIL NIL T) -8 NIL NIL) (-472 1110876 1111015 1111179 "HB" 1111407 T HB (NIL) -7 NIL NIL) (-471 1104375 1110722 1110826 "HASHTBL" 1110831 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-470 1103878 1104096 1104188 "HASAST" 1104303 T HASAST (NIL) -8 NIL NIL) (-469 1101696 1103502 1103683 "HACKPI" 1103717 T HACKPI (NIL) -8 NIL NIL) (-468 1097418 1101549 1101662 "GTSET" 1101667 NIL GTSET (NIL T T T T) -8 NIL NIL) (-467 1090946 1097296 1097394 "GSTBL" 1097399 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-466 1083261 1089977 1090242 "GSERIES" 1090737 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-465 1082428 1082819 1082847 "GROUP" 1083050 T GROUP (NIL) -9 NIL 1083184) (-464 1081794 1081953 1082204 "GROUP-" 1082209 NIL GROUP- (NIL T) -8 NIL NIL) (-463 1080163 1080482 1080869 "GROEBSOL" 1081471 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-462 1079103 1079365 1079416 "GRMOD" 1079945 NIL GRMOD (NIL T T) -9 NIL 1080113) (-461 1078871 1078907 1079035 "GRMOD-" 1079040 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-460 1074196 1075225 1076225 "GRIMAGE" 1077891 T GRIMAGE (NIL) -8 NIL NIL) (-459 1072663 1072923 1073247 "GRDEF" 1073892 T GRDEF (NIL) -7 NIL NIL) (-458 1072107 1072223 1072364 "GRAY" 1072542 T GRAY (NIL) -7 NIL NIL) (-457 1071338 1071718 1071769 "GRALG" 1071922 NIL GRALG (NIL T T) -9 NIL 1072015) (-456 1070999 1071072 1071235 "GRALG-" 1071240 NIL GRALG- (NIL T T T) -8 NIL NIL) (-455 1067803 1070584 1070762 "GPOLSET" 1070906 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-454 1067157 1067214 1067472 "GOSPER" 1067740 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-453 1062916 1063595 1064121 "GMODPOL" 1066856 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-452 1061921 1062105 1062343 "GHENSEL" 1062728 NIL GHENSEL (NIL T T) -7 NIL NIL) (-451 1055972 1056815 1057842 "GENUPS" 1061005 NIL GENUPS (NIL T T) -7 NIL NIL) (-450 1055669 1055720 1055809 "GENUFACT" 1055915 NIL GENUFACT (NIL T) -7 NIL NIL) (-449 1055081 1055158 1055323 "GENPGCD" 1055587 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-448 1054555 1054590 1054803 "GENMFACT" 1055040 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-447 1053123 1053378 1053685 "GENEEZ" 1054298 NIL GENEEZ (NIL T T) -7 NIL NIL) (-446 1047067 1052734 1052896 "GDMP" 1053046 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-445 1036466 1040838 1041944 "GCNAALG" 1046050 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-444 1034928 1035756 1035784 "GCDDOM" 1036039 T GCDDOM (NIL) -9 NIL 1036196) (-443 1034398 1034525 1034740 "GCDDOM-" 1034745 NIL GCDDOM- (NIL T) -8 NIL NIL) (-442 1023018 1025344 1027736 "GBINTERN" 1032089 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-441 1020855 1021147 1021568 "GBF" 1022693 NIL GBF (NIL T T T T) -7 NIL NIL) (-440 1019636 1019801 1020068 "GBEUCLID" 1020671 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-439 1018308 1018493 1018797 "GB" 1019415 NIL GB (NIL T T T T) -7 NIL NIL) (-438 1017657 1017782 1017931 "GAUSSFAC" 1018179 T GAUSSFAC (NIL) -7 NIL NIL) (-437 1016024 1016326 1016640 "GALUTIL" 1017376 NIL GALUTIL (NIL T) -7 NIL NIL) (-436 1014332 1014606 1014930 "GALPOLYU" 1015751 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-435 1011697 1011987 1012394 "GALFACTU" 1014029 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-434 1003503 1005002 1006610 "GALFACT" 1010129 NIL GALFACT (NIL T) -7 NIL NIL) (-433 1000891 1001549 1001577 "FVFUN" 1002733 T FVFUN (NIL) -9 NIL 1003453) (-432 1000157 1000339 1000367 "FVC" 1000658 T FVC (NIL) -9 NIL 1000841) (-431 999799 999954 1000035 "FUNCTION" 1000109 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-430 998617 999100 999303 "FTEM" 999616 T FTEM (NIL) -8 NIL NIL) (-429 996299 996847 997333 "FT" 998151 T FT (NIL) -8 NIL NIL) (-428 994555 994844 995248 "FSUPFACT" 995990 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-427 992952 993241 993573 "FST" 994243 T FST (NIL) -8 NIL NIL) (-426 992123 992229 992424 "FSRED" 992834 NIL FSRED (NIL T T) -7 NIL NIL) (-425 990802 991057 991411 "FSPRMELT" 991838 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-424 987887 988325 988824 "FSPECF" 990365 NIL FSPECF (NIL T T) -7 NIL NIL) (-423 987401 987455 987632 "FSINT" 987828 NIL FSINT (NIL T T) -7 NIL NIL) (-422 985728 986394 986697 "FSERIES" 987180 NIL FSERIES (NIL T T) -8 NIL NIL) (-421 984742 984858 985089 "FSCINT" 985608 NIL FSCINT (NIL T T) -7 NIL NIL) (-420 983784 983927 984154 "FSAGG2" 984595 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-419 980018 982728 982769 "FSAGG" 983139 NIL FSAGG (NIL T) -9 NIL 983398) (-418 977780 978381 979177 "FSAGG-" 979272 NIL FSAGG- (NIL T T) -8 NIL NIL) (-417 975435 975714 976268 "FS2UPS" 977498 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-416 974292 974463 974772 "FS2EXPXP" 975260 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-415 973874 973917 974072 "FS2" 974243 NIL FS2 (NIL T T T T) -7 NIL NIL) (-414 956345 964758 964798 "FS" 968646 NIL FS (NIL T) -9 NIL 970935) (-413 945076 948039 952068 "FS-" 952365 NIL FS- (NIL T T) -8 NIL NIL) (-412 944502 944617 944769 "FRUTIL" 944956 NIL FRUTIL (NIL T) -7 NIL NIL) (-411 939609 942220 942260 "FRNAALG" 943656 NIL FRNAALG (NIL T) -9 NIL 944263) (-410 935338 936392 937650 "FRNAALG-" 938400 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-409 934976 935019 935146 "FRNAAF2" 935289 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-408 933383 933830 934125 "FRMOD" 934788 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-407 932578 932665 932954 "FRIDEAL2" 933290 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-406 930357 930961 931278 "FRIDEAL" 932369 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-405 929606 930013 930054 "FRETRCT" 930059 NIL FRETRCT (NIL T) -9 NIL 930235) (-404 928739 928963 929307 "FRETRCT-" 929312 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-403 925989 927165 927224 "FRAMALG" 928106 NIL FRAMALG (NIL T T) -9 NIL 928398) (-402 924123 924578 925208 "FRAMALG-" 925431 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-401 923759 923816 923923 "FRAC2" 924060 NIL FRAC2 (NIL T T) -7 NIL NIL) (-400 917740 923234 923510 "FRAC" 923515 NIL FRAC (NIL T) -8 NIL NIL) (-399 917376 917433 917540 "FR2" 917677 NIL FR2 (NIL T T) -7 NIL NIL) (-398 908952 912956 914285 "FR" 916079 NIL FR (NIL T) -8 NIL NIL) (-397 903686 906530 906558 "FPS" 907677 T FPS (NIL) -9 NIL 908234) (-396 903135 903244 903408 "FPS-" 903554 NIL FPS- (NIL T) -8 NIL NIL) (-395 900643 902276 902304 "FPC" 902529 T FPC (NIL) -9 NIL 902671) (-394 900436 900476 900573 "FPC-" 900578 NIL FPC- (NIL T) -8 NIL NIL) (-393 899314 899924 899965 "FPATMAB" 899970 NIL FPATMAB (NIL T) -9 NIL 900122) (-392 897014 897490 897916 "FPARFRAC" 898951 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-391 892446 892945 893627 "FORTRAN" 896446 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-390 890122 890684 890712 "FORTFN" 891772 T FORTFN (NIL) -9 NIL 892396) (-389 889886 889936 889964 "FORTCAT" 890023 T FORTCAT (NIL) -9 NIL 890085) (-388 887602 888102 888641 "FORT" 889367 T FORT (NIL) -7 NIL NIL) (-387 887390 887420 887489 "FORMULA1" 887566 NIL FORMULA1 (NIL T) -7 NIL NIL) (-386 885450 885933 886332 "FORMULA" 887011 T FORMULA (NIL) -8 NIL NIL) (-385 884973 885025 885198 "FORDER" 885392 NIL FORDER (NIL T T T T) -7 NIL NIL) (-384 884069 884233 884426 "FOP" 884800 T FOP (NIL) -7 NIL NIL) (-383 882677 883349 883523 "FNLA" 883951 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-382 881345 881734 881762 "FNCAT" 882334 T FNCAT (NIL) -9 NIL 882627) (-381 880911 881304 881332 "FNAME" 881337 T FNAME (NIL) -8 NIL NIL) (-380 879609 880538 880566 "FMTC" 880571 T FMTC (NIL) -9 NIL 880607) (-379 875971 877132 877761 "FMONOID" 879013 NIL FMONOID (NIL T) -8 NIL NIL) (-378 873395 874041 874069 "FMFUN" 875213 T FMFUN (NIL) -9 NIL 875921) (-377 870607 871441 871495 "FMCAT" 872690 NIL FMCAT (NIL T T) -9 NIL 873185) (-376 869876 870057 870085 "FMC" 870375 T FMC (NIL) -9 NIL 870557) (-375 868769 869642 869742 "FM1" 869821 NIL FM1 (NIL T T) -8 NIL NIL) (-374 867988 868511 868660 "FM" 868665 NIL FM (NIL T T) -8 NIL NIL) (-373 865762 866178 866672 "FLOATRP" 867539 NIL FLOATRP (NIL T) -7 NIL NIL) (-372 863200 863700 864278 "FLOATCP" 865229 NIL FLOATCP (NIL T) -7 NIL NIL) (-371 856755 860856 861486 "FLOAT" 862590 T FLOAT (NIL) -8 NIL NIL) (-370 855584 856388 856429 "FLINEXP" 856434 NIL FLINEXP (NIL T) -9 NIL 856527) (-369 854738 854973 855301 "FLINEXP-" 855306 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-368 853814 853958 854182 "FLASORT" 854590 NIL FLASORT (NIL T T) -7 NIL NIL) (-367 851031 851873 851925 "FLALG" 853152 NIL FLALG (NIL T T) -9 NIL 853619) (-366 850073 850216 850443 "FLAGG2" 850884 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-365 843857 847559 847600 "FLAGG" 848862 NIL FLAGG (NIL T) -9 NIL 849514) (-364 842583 842922 843412 "FLAGG-" 843417 NIL FLAGG- (NIL T T) -8 NIL NIL) (-363 839596 840570 840629 "FINRALG" 841757 NIL FINRALG (NIL T T) -9 NIL 842265) (-362 838756 838985 839324 "FINRALG-" 839329 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-361 838162 838375 838403 "FINITE" 838599 T FINITE (NIL) -9 NIL 838706) (-360 830620 832781 832821 "FINAALG" 836488 NIL FINAALG (NIL T) -9 NIL 837941) (-359 825961 827002 828146 "FINAALG-" 829525 NIL FINAALG- (NIL T T) -8 NIL NIL) (-358 824645 824957 825011 "FILECAT" 825695 NIL FILECAT (NIL T T) -9 NIL 825911) (-357 824040 824400 824503 "FILE" 824575 NIL FILE (NIL T) -8 NIL NIL) (-356 821962 823454 823482 "FIELD" 823522 T FIELD (NIL) -9 NIL 823602) (-355 820582 820967 821478 "FIELD-" 821483 NIL FIELD- (NIL T) -8 NIL NIL) (-354 818460 819217 819564 "FGROUP" 820268 NIL FGROUP (NIL T) -8 NIL NIL) (-353 817550 817714 817934 "FGLMICPK" 818292 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-352 813419 817475 817532 "FFX" 817537 NIL FFX (NIL T NIL) -8 NIL NIL) (-351 813020 813081 813216 "FFSLPE" 813352 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-350 812524 812560 812769 "FFPOLY2" 812978 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-349 808517 809296 810092 "FFPOLY" 811760 NIL FFPOLY (NIL T) -7 NIL NIL) (-348 804405 808436 808499 "FFP" 808504 NIL FFP (NIL T NIL) -8 NIL NIL) (-347 799568 803748 803938 "FFNBX" 804259 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-346 794544 798703 798961 "FFNBP" 799422 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-345 789214 793828 794039 "FFNB" 794377 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-344 788046 788244 788559 "FFINTBAS" 789011 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-343 784332 786505 786533 "FFIELDC" 787153 T FFIELDC (NIL) -9 NIL 787529) (-342 782995 783365 783862 "FFIELDC-" 783867 NIL FFIELDC- (NIL T) -8 NIL NIL) (-341 782565 782610 782734 "FFHOM" 782937 NIL FFHOM (NIL T T T) -7 NIL NIL) (-340 780263 780747 781264 "FFF" 782080 NIL FFF (NIL T) -7 NIL NIL) (-339 775918 780005 780106 "FFCGX" 780206 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-338 771587 775650 775757 "FFCGP" 775861 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-337 766807 771314 771422 "FFCG" 771523 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-336 766218 766261 766496 "FFCAT2" 766758 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-335 748285 757312 757398 "FFCAT" 762563 NIL FFCAT (NIL T T T) -9 NIL 764014) (-334 743483 744530 745844 "FFCAT-" 747074 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-333 738918 743394 743458 "FF" 743463 NIL FF (NIL NIL NIL) -8 NIL NIL) (-332 728132 731890 733110 "FEXPR" 737770 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-331 727132 727567 727608 "FEVALAB" 727692 NIL FEVALAB (NIL T) -9 NIL 727953) (-330 726291 726501 726839 "FEVALAB-" 726844 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-329 723357 724072 724187 "FDIVCAT" 725755 NIL FDIVCAT (NIL T T T T) -9 NIL 726192) (-328 723119 723146 723316 "FDIVCAT-" 723321 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-327 722339 722426 722703 "FDIV2" 723026 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-326 720932 721722 721925 "FDIV" 722238 NIL FDIV (NIL T T T T) -8 NIL NIL) (-325 719618 719877 720166 "FCPAK1" 720663 T FCPAK1 (NIL) -7 NIL NIL) (-324 718746 719118 719259 "FCOMP" 719509 NIL FCOMP (NIL T) -8 NIL NIL) (-323 702381 705795 709356 "FC" 715205 T FC (NIL) -8 NIL NIL) (-322 695036 699015 699055 "FAXF" 700857 NIL FAXF (NIL T) -9 NIL 701549) (-321 692315 692970 693795 "FAXF-" 694260 NIL FAXF- (NIL T T) -8 NIL NIL) (-320 687415 691691 691867 "FARRAY" 692172 NIL FARRAY (NIL T) -8 NIL NIL) (-319 682829 684854 684907 "FAMR" 685930 NIL FAMR (NIL T T) -9 NIL 686390) (-318 681719 682021 682456 "FAMR-" 682461 NIL FAMR- (NIL T T T) -8 NIL NIL) (-317 680915 681641 681694 "FAMONOID" 681699 NIL FAMONOID (NIL T) -8 NIL NIL) (-316 678745 679429 679482 "FAMONC" 680423 NIL FAMONC (NIL T T) -9 NIL 680809) (-315 677437 678499 678636 "FAGROUP" 678641 NIL FAGROUP (NIL T) -8 NIL NIL) (-314 675232 675551 675954 "FACUTIL" 677118 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-313 674331 674516 674738 "FACTFUNC" 675042 NIL FACTFUNC (NIL T) -7 NIL NIL) (-312 666738 673582 673794 "EXPUPXS" 674187 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-311 664221 664761 665347 "EXPRTUBE" 666172 T EXPRTUBE (NIL) -7 NIL NIL) (-310 660415 661007 661744 "EXPRODE" 663560 NIL EXPRODE (NIL T T) -7 NIL NIL) (-309 654822 655409 656222 "EXPR2UPS" 659713 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-308 654458 654515 654622 "EXPR2" 654759 NIL EXPR2 (NIL T T) -7 NIL NIL) (-307 639893 653113 653541 "EXPR" 654062 NIL EXPR (NIL T) -8 NIL NIL) (-306 631326 639025 639322 "EXPEXPAN" 639730 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-305 630833 631050 631141 "EXITAST" 631255 T EXITAST (NIL) -8 NIL NIL) (-304 630660 630790 630819 "EXIT" 630824 T EXIT (NIL) -8 NIL NIL) (-303 630287 630349 630462 "EVALCYC" 630592 NIL EVALCYC (NIL T) -7 NIL NIL) (-302 629828 629946 629987 "EVALAB" 630157 NIL EVALAB (NIL T) -9 NIL 630261) (-301 629309 629431 629652 "EVALAB-" 629657 NIL EVALAB- (NIL T T) -8 NIL NIL) (-300 626812 628080 628108 "EUCDOM" 628663 T EUCDOM (NIL) -9 NIL 629013) (-299 625217 625659 626249 "EUCDOM-" 626254 NIL EUCDOM- (NIL T) -8 NIL NIL) (-298 624849 624906 625015 "ESTOOLS2" 625154 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-297 624600 624642 624722 "ESTOOLS1" 624801 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-296 612140 614898 617648 "ESTOOLS" 621870 T ESTOOLS (NIL) -7 NIL NIL) (-295 611885 611917 611999 "ESCONT1" 612102 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-294 608260 609020 609800 "ESCONT" 611125 T ESCONT (NIL) -7 NIL NIL) (-293 607935 607985 608085 "ES2" 608204 NIL ES2 (NIL T T) -7 NIL NIL) (-292 607565 607623 607732 "ES1" 607871 NIL ES1 (NIL T T) -7 NIL NIL) (-291 601490 603218 603246 "ES" 606014 T ES (NIL) -9 NIL 607423) (-290 596437 597724 599541 "ES-" 599705 NIL ES- (NIL T) -8 NIL NIL) (-289 595653 595782 595958 "ERROR" 596281 T ERROR (NIL) -7 NIL NIL) (-288 589158 595512 595603 "EQTBL" 595608 NIL EQTBL (NIL T T) -8 NIL NIL) (-287 588790 588847 588956 "EQ2" 589095 NIL EQ2 (NIL T T) -7 NIL NIL) (-286 581347 584104 585553 "EQ" 587374 NIL -3885 (NIL T) -8 NIL NIL) (-285 576639 577685 578778 "EP" 580286 NIL EP (NIL T) -7 NIL NIL) (-284 575221 575522 575839 "ENV" 576342 T ENV (NIL) -8 NIL NIL) (-283 574420 574940 574968 "ENTIRER" 574973 T ENTIRER (NIL) -9 NIL 575019) (-282 570978 572429 572799 "EMR" 574219 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-281 570122 570307 570361 "ELTAGG" 570741 NIL ELTAGG (NIL T T) -9 NIL 570952) (-280 569841 569903 570044 "ELTAGG-" 570049 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-279 569630 569659 569713 "ELTAB" 569797 NIL ELTAB (NIL T T) -9 NIL NIL) (-278 568756 568902 569101 "ELFUTS" 569481 NIL ELFUTS (NIL T T) -7 NIL NIL) (-277 568498 568554 568582 "ELEMFUN" 568687 T ELEMFUN (NIL) -9 NIL NIL) (-276 568368 568389 568457 "ELEMFUN-" 568462 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-275 563259 566468 566509 "ELAGG" 567449 NIL ELAGG (NIL T) -9 NIL 567912) (-274 561544 561978 562641 "ELAGG-" 562646 NIL ELAGG- (NIL T T) -8 NIL NIL) (-273 560201 560481 560776 "ELABEXPR" 561269 T ELABEXPR (NIL) -8 NIL NIL) (-272 553194 554868 555695 "EFUPXS" 559477 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-271 546771 548445 549255 "EFULS" 552470 NIL EFULS (NIL T T T) -8 NIL NIL) (-270 544193 544551 545030 "EFSTRUC" 546403 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-269 533265 534830 536390 "EF" 542708 NIL EF (NIL T T) -7 NIL NIL) (-268 532366 532750 532899 "EAB" 533136 T EAB (NIL) -8 NIL NIL) (-267 531575 532325 532353 "E04UCFA" 532358 T E04UCFA (NIL) -8 NIL NIL) (-266 530784 531534 531562 "E04NAFA" 531567 T E04NAFA (NIL) -8 NIL NIL) (-265 529993 530743 530771 "E04MBFA" 530776 T E04MBFA (NIL) -8 NIL NIL) (-264 529202 529952 529980 "E04JAFA" 529985 T E04JAFA (NIL) -8 NIL NIL) (-263 528413 529161 529189 "E04GCFA" 529194 T E04GCFA (NIL) -8 NIL NIL) (-262 527624 528372 528400 "E04FDFA" 528405 T E04FDFA (NIL) -8 NIL NIL) (-261 526833 527583 527611 "E04DGFA" 527616 T E04DGFA (NIL) -8 NIL NIL) (-260 521011 522358 523722 "E04AGNT" 525489 T E04AGNT (NIL) -7 NIL NIL) (-259 519735 520215 520255 "DVARCAT" 520730 NIL DVARCAT (NIL T) -9 NIL 520929) (-258 518939 519151 519465 "DVARCAT-" 519470 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-257 511880 518738 518867 "DSMP" 518872 NIL DSMP (NIL T T T) -8 NIL NIL) (-256 511545 511604 511702 "DROPT1" 511815 NIL DROPT1 (NIL T) -7 NIL NIL) (-255 506660 507786 508923 "DROPT0" 510428 T DROPT0 (NIL) -7 NIL NIL) (-254 501470 502605 503673 "DROPT" 505612 T DROPT (NIL) -8 NIL NIL) (-253 499815 500140 500526 "DRAWPT" 501104 T DRAWPT (NIL) -7 NIL NIL) (-252 499448 499501 499619 "DRAWHACK" 499756 NIL DRAWHACK (NIL T) -7 NIL NIL) (-251 498179 498448 498739 "DRAWCX" 499177 T DRAWCX (NIL) -7 NIL NIL) (-250 497695 497763 497914 "DRAWCURV" 498105 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-249 488166 490125 492240 "DRAWCFUN" 495600 T DRAWCFUN (NIL) -7 NIL NIL) (-248 482753 483676 484755 "DRAW" 487140 NIL DRAW (NIL T) -7 NIL NIL) (-247 479566 481448 481489 "DQAGG" 482118 NIL DQAGG (NIL T) -9 NIL 482391) (-246 468121 474782 474865 "DPOLCAT" 476717 NIL DPOLCAT (NIL T T T T) -9 NIL 477262) (-245 463011 464340 466281 "DPOLCAT-" 466286 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-244 456173 462872 462970 "DPMO" 462975 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-243 449238 455953 456120 "DPMM" 456125 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-242 448658 448861 448975 "DOMAIN" 449144 T DOMAIN (NIL) -8 NIL NIL) (-241 442440 448293 448445 "DMP" 448559 NIL DMP (NIL NIL T) -8 NIL NIL) (-240 442040 442096 442240 "DLP" 442378 NIL DLP (NIL T) -7 NIL NIL) (-239 435686 441141 441368 "DLIST" 441845 NIL DLIST (NIL T) -8 NIL NIL) (-238 432533 434541 434582 "DLAGG" 435132 NIL DLAGG (NIL T) -9 NIL 435361) (-237 431383 432013 432041 "DIVRING" 432133 T DIVRING (NIL) -9 NIL 432216) (-236 430620 430810 431110 "DIVRING-" 431115 NIL DIVRING- (NIL T) -8 NIL NIL) (-235 428722 429079 429485 "DISPLAY" 430234 T DISPLAY (NIL) -7 NIL NIL) (-234 427570 427773 428038 "DIRPROD2" 428515 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-233 421519 427484 427547 "DIRPROD" 427552 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-232 411064 417009 417062 "DIRPCAT" 417472 NIL DIRPCAT (NIL NIL T) -9 NIL 418312) (-231 408390 409032 409913 "DIRPCAT-" 410250 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-230 407677 407837 408023 "DIOSP" 408224 T DIOSP (NIL) -7 NIL NIL) (-229 404379 406589 406630 "DIOPS" 407064 NIL DIOPS (NIL T) -9 NIL 407293) (-228 403928 404042 404233 "DIOPS-" 404238 NIL DIOPS- (NIL T T) -8 NIL NIL) (-227 402840 403434 403462 "DIFRING" 403649 T DIFRING (NIL) -9 NIL 403759) (-226 402486 402563 402715 "DIFRING-" 402720 NIL DIFRING- (NIL T) -8 NIL NIL) (-225 400311 401549 401590 "DIFEXT" 401953 NIL DIFEXT (NIL T) -9 NIL 402247) (-224 398596 399024 399690 "DIFEXT-" 399695 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-223 395918 398128 398169 "DIAGG" 398174 NIL DIAGG (NIL T) -9 NIL 398194) (-222 395302 395459 395711 "DIAGG-" 395716 NIL DIAGG- (NIL T T) -8 NIL NIL) (-221 390766 394261 394538 "DHMATRIX" 395071 NIL DHMATRIX (NIL T) -8 NIL NIL) (-220 386378 387287 388297 "DFSFUN" 389776 T DFSFUN (NIL) -7 NIL NIL) (-219 381498 385309 385621 "DFLOAT" 386086 T DFLOAT (NIL) -8 NIL NIL) (-218 379726 380007 380403 "DFINTTLS" 381206 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-217 376791 377747 378147 "DERHAM" 379392 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-216 374640 376566 376655 "DEQUEUE" 376735 NIL DEQUEUE (NIL T) -8 NIL NIL) (-215 373855 373988 374184 "DEGRED" 374502 NIL DEGRED (NIL T T) -7 NIL NIL) (-214 370430 371130 371938 "DEFINTRF" 373128 NIL DEFINTRF (NIL T) -7 NIL NIL) (-213 368069 368510 369081 "DEFINTEF" 369977 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-212 367446 367689 367804 "DEFAST" 367974 T DEFAST (NIL) -8 NIL NIL) (-211 361355 366887 367053 "DECIMAL" 367300 T DECIMAL (NIL) -8 NIL NIL) (-210 358867 359325 359831 "DDFACT" 360899 NIL DDFACT (NIL T T) -7 NIL NIL) (-209 358463 358506 358657 "DBLRESP" 358818 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-208 356173 356507 356876 "DBASE" 358221 NIL DBASE (NIL T) -8 NIL NIL) (-207 355442 355653 355799 "DATABUF" 356072 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-206 354575 355401 355429 "D03FAFA" 355434 T D03FAFA (NIL) -8 NIL NIL) (-205 353709 354534 354562 "D03EEFA" 354567 T D03EEFA (NIL) -8 NIL NIL) (-204 351659 352125 352614 "D03AGNT" 353240 T D03AGNT (NIL) -7 NIL NIL) (-203 350975 351618 351646 "D02EJFA" 351651 T D02EJFA (NIL) -8 NIL NIL) (-202 350291 350934 350962 "D02CJFA" 350967 T D02CJFA (NIL) -8 NIL NIL) (-201 349607 350250 350278 "D02BHFA" 350283 T D02BHFA (NIL) -8 NIL NIL) (-200 348923 349566 349594 "D02BBFA" 349599 T D02BBFA (NIL) -8 NIL NIL) (-199 342121 343709 345315 "D02AGNT" 347337 T D02AGNT (NIL) -7 NIL NIL) (-198 339890 340412 340958 "D01WGTS" 341595 T D01WGTS (NIL) -7 NIL NIL) (-197 338985 339849 339877 "D01TRNS" 339882 T D01TRNS (NIL) -8 NIL NIL) (-196 338080 338944 338972 "D01GBFA" 338977 T D01GBFA (NIL) -8 NIL NIL) (-195 337175 338039 338067 "D01FCFA" 338072 T D01FCFA (NIL) -8 NIL NIL) (-194 336270 337134 337162 "D01ASFA" 337167 T D01ASFA (NIL) -8 NIL NIL) (-193 335365 336229 336257 "D01AQFA" 336262 T D01AQFA (NIL) -8 NIL NIL) (-192 334460 335324 335352 "D01APFA" 335357 T D01APFA (NIL) -8 NIL NIL) (-191 333555 334419 334447 "D01ANFA" 334452 T D01ANFA (NIL) -8 NIL NIL) (-190 332650 333514 333542 "D01AMFA" 333547 T D01AMFA (NIL) -8 NIL NIL) (-189 331745 332609 332637 "D01ALFA" 332642 T D01ALFA (NIL) -8 NIL NIL) (-188 330840 331704 331732 "D01AKFA" 331737 T D01AKFA (NIL) -8 NIL NIL) (-187 329935 330799 330827 "D01AJFA" 330832 T D01AJFA (NIL) -8 NIL NIL) (-186 323232 324783 326344 "D01AGNT" 328394 T D01AGNT (NIL) -7 NIL NIL) (-185 322569 322697 322849 "CYCLOTOM" 323100 T CYCLOTOM (NIL) -7 NIL NIL) (-184 319304 320017 320744 "CYCLES" 321862 T CYCLES (NIL) -7 NIL NIL) (-183 318616 318750 318921 "CVMP" 319165 NIL CVMP (NIL T) -7 NIL NIL) (-182 316387 316645 317021 "CTRIGMNP" 318344 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-181 315898 316087 316186 "CTORCALL" 316308 T CTORCALL (NIL) -8 NIL NIL) (-180 315272 315371 315524 "CSTTOOLS" 315795 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-179 311071 311728 312486 "CRFP" 314584 NIL CRFP (NIL T T) -7 NIL NIL) (-178 310573 310792 310884 "CRCEAST" 310999 T CRCEAST (NIL) -8 NIL NIL) (-177 309620 309805 310033 "CRAPACK" 310377 NIL CRAPACK (NIL T) -7 NIL NIL) (-176 309004 309105 309309 "CPMATCH" 309496 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-175 308729 308757 308863 "CPIMA" 308970 NIL CPIMA (NIL T T T) -7 NIL NIL) (-174 305093 305765 306483 "COORDSYS" 308064 NIL COORDSYS (NIL T) -7 NIL NIL) (-173 304477 304606 304756 "CONTOUR" 304963 T CONTOUR (NIL) -8 NIL NIL) (-172 300405 302480 302972 "CONTFRAC" 304017 NIL CONTFRAC (NIL T) -8 NIL NIL) (-171 300285 300306 300334 "CONDUIT" 300371 T CONDUIT (NIL) -9 NIL NIL) (-170 299478 299998 300026 "COMRING" 300031 T COMRING (NIL) -9 NIL 300083) (-169 298559 298836 299020 "COMPPROP" 299314 T COMPPROP (NIL) -8 NIL NIL) (-168 298220 298255 298383 "COMPLPAT" 298518 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-167 297856 297913 298020 "COMPLEX2" 298157 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-166 287933 297665 297774 "COMPLEX" 297779 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 287651 287686 287784 "COMPFACT" 287892 NIL COMPFACT (NIL T T) -7 NIL NIL) (-164 272058 282265 282305 "COMPCAT" 283309 NIL COMPCAT (NIL T) -9 NIL 284704) (-163 261594 264511 268131 "COMPCAT-" 268487 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-162 261323 261351 261454 "COMMUPC" 261560 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-161 261118 261151 261210 "COMMONOP" 261284 T COMMONOP (NIL) -7 NIL NIL) (-160 260722 260922 260997 "COMMAAST" 261063 T COMMAAST (NIL) -8 NIL NIL) (-159 260305 260473 260560 "COMM" 260655 T COMM (NIL) -8 NIL NIL) (-158 259554 259748 259776 "COMBOPC" 260114 T COMBOPC (NIL) -9 NIL 260289) (-157 258450 258660 258902 "COMBINAT" 259344 NIL COMBINAT (NIL T) -7 NIL NIL) (-156 254648 255221 255861 "COMBF" 257872 NIL COMBF (NIL T T) -7 NIL NIL) (-155 253434 253764 253999 "COLOR" 254433 T COLOR (NIL) -8 NIL NIL) (-154 252937 253155 253247 "COLONAST" 253362 T COLONAST (NIL) -8 NIL NIL) (-153 252577 252624 252749 "CMPLXRT" 252884 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-152 252052 252277 252376 "CLLCTAST" 252498 T CLLCTAST (NIL) -8 NIL NIL) (-151 247554 248582 249662 "CLIP" 250992 T CLIP (NIL) -7 NIL NIL) (-150 245936 246660 246899 "CLIF" 247381 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-149 242158 244082 244123 "CLAGG" 245052 NIL CLAGG (NIL T) -9 NIL 245588) (-148 240580 241037 241620 "CLAGG-" 241625 NIL 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3138209 3138264 "XFALG" 3140436 NIL XFALG (NIL T T) -9 NIL 3141225) (-1250 3132941 3135187 3135229 "XF" 3135850 NIL XF (NIL T) -9 NIL 3136250) (-1249 3132562 3132650 3132819 "XF-" 3132824 NIL XF- (NIL T T) -8 NIL NIL) (-1248 3131695 3131799 3132004 "XEXPPKG" 3132454 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1247 3129839 3131545 3131641 "XDPOLY" 3131646 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1246 3128755 3129321 3129364 "XALG" 3129427 NIL XALG (NIL T) -9 NIL 3129547) (-1245 3122251 3126732 3127226 "WUTSET" 3128347 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1244 3120102 3120863 3121216 "WP" 3122032 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1243 3119731 3119924 3119994 "WHILEAST" 3120054 T WHILEAST (NIL) -8 NIL NIL) (-1242 3119230 3119448 3119542 "WHEREAST" 3119659 T WHEREAST (NIL) -8 NIL NIL) (-1241 3118116 3118314 3118609 "WFFINTBS" 3119027 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1240 3116020 3116447 3116909 "WEIER" 3117688 NIL WEIER (NIL T) -7 NIL NIL) (-1239 3115167 3115591 3115633 "VSPACE" 3115769 NIL VSPACE (NIL T) -9 NIL 3115843) (-1238 3115005 3115032 3115123 "VSPACE-" 3115128 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1237 3114751 3114794 3114865 "VOID" 3114956 T VOID (NIL) -8 NIL NIL) (-1236 3111176 3111814 3112551 "VIEWDEF" 3114036 T VIEWDEF (NIL) -7 NIL NIL) (-1235 3100514 3102724 3104897 "VIEW3D" 3109025 T VIEW3D (NIL) -8 NIL NIL) (-1234 3092796 3094425 3096004 "VIEW2D" 3098957 T VIEW2D (NIL) -8 NIL NIL) (-1233 3090932 3091291 3091697 "VIEW" 3092412 T VIEW (NIL) -7 NIL NIL) (-1232 3089509 3089768 3090086 "VECTOR2" 3090662 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1231 3084913 3089279 3089371 "VECTOR" 3089452 NIL VECTOR (NIL T) -8 NIL NIL) (-1230 3078440 3082697 3082740 "VECTCAT" 3083733 NIL VECTCAT (NIL T) -9 NIL 3084319) (-1229 3077454 3077708 3078098 "VECTCAT-" 3078103 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1228 3076935 3077105 3077225 "VARIABLE" 3077369 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1227 3076868 3076873 3076903 "UTYPE" 3076908 T UTYPE (NIL) -9 NIL NIL) (-1226 3075698 3075852 3076114 "UTSODETL" 3076694 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1225 3073138 3073598 3074122 "UTSODE" 3075239 NIL UTSODE (NIL T T) -7 NIL NIL) (-1224 3064511 3069830 3069873 "UTSCAT" 3070985 NIL UTSCAT (NIL T) -9 NIL 3071742) (-1223 3061865 3062581 3063570 "UTSCAT-" 3063575 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1222 3061492 3061535 3061668 "UTS2" 3061816 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1221 3053368 3059118 3059607 "UTS" 3061061 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1220 3047644 3050208 3050251 "URAGG" 3052321 NIL URAGG (NIL T) -9 NIL 3053043) (-1219 3044586 3045448 3046570 "URAGG-" 3046575 NIL URAGG- (NIL T T) -8 NIL NIL) (-1218 3040317 3043200 3043672 "UPXSSING" 3044250 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1217 3033432 3040221 3040293 "UPXSCONS" 3040298 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1216 3023792 3030535 3030597 "UPXSCCA" 3031253 NIL UPXSCCA (NIL T T) -9 NIL 3031495) (-1215 3023430 3023515 3023689 "UPXSCCA-" 3023694 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1214 3013716 3020232 3020275 "UPXSCAT" 3020923 NIL UPXSCAT (NIL T) -9 NIL 3021531) (-1213 3013146 3013225 3013404 "UPXS2" 3013631 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1212 3005120 3012261 3012543 "UPXS" 3012922 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1211 3003777 3004029 3004379 "UPSQFREE" 3004864 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1210 2997695 3000704 3000759 "UPSCAT" 3001920 NIL UPSCAT (NIL T T) -9 NIL 3002694) (-1209 2996899 2997106 2997433 "UPSCAT-" 2997438 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1208 2996526 2996569 2996702 "UPOLYC2" 2996850 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1207 2982650 2990613 2990656 "UPOLYC" 2992757 NIL UPOLYC (NIL T) -9 NIL 2993978) (-1206 2974015 2976428 2979563 "UPOLYC-" 2979568 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1205 2973354 2973461 2973625 "UPMP" 2973904 NIL UPMP (NIL T T) -7 NIL NIL) (-1204 2972907 2972988 2973127 "UPDIVP" 2973267 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1203 2971475 2971724 2972040 "UPDECOMP" 2972656 NIL UPDECOMP (NIL T 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-8 NIL NIL) (-1190 2900398 2901321 2901351 "UFD" 2901563 T UFD (NIL) -9 NIL 2901677) (-1189 2900192 2900238 2900333 "UFD-" 2900338 NIL UFD- (NIL T) -8 NIL NIL) (-1188 2899274 2899457 2899673 "UDVO" 2899998 T UDVO (NIL) -7 NIL NIL) (-1187 2897090 2897499 2897970 "UDPO" 2898838 NIL UDPO (NIL T) -7 NIL NIL) (-1186 2896877 2897045 2897076 "TYPEAST" 2897081 T TYPEAST (NIL) -8 NIL NIL) (-1185 2896810 2896815 2896845 "TYPE" 2896850 T TYPE (NIL) -9 NIL NIL) (-1184 2895781 2895983 2896223 "TWOFACT" 2896604 NIL TWOFACT (NIL T) -7 NIL NIL) (-1183 2894719 2895056 2895319 "TUPLE" 2895553 NIL TUPLE (NIL T) -8 NIL NIL) (-1182 2892410 2892929 2893468 "TUBETOOL" 2894202 T TUBETOOL (NIL) -7 NIL NIL) (-1181 2891259 2891464 2891705 "TUBE" 2892203 NIL TUBE (NIL T) -8 NIL NIL) (-1180 2879926 2884018 2884115 "TSETCAT" 2889384 NIL TSETCAT (NIL T T T T) -9 NIL 2890915) (-1179 2874660 2876258 2878149 "TSETCAT-" 2878154 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1178 2869424 2873632 2873915 "TS" 2874412 NIL TS (NIL T) -8 NIL NIL) (-1177 2863687 2864533 2865475 "TRMANIP" 2868560 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1176 2863128 2863191 2863354 "TRIMAT" 2863619 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1175 2860924 2861161 2861525 "TRIGMNIP" 2862877 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1174 2860444 2860557 2860587 "TRIGCAT" 2860800 T TRIGCAT (NIL) -9 NIL NIL) (-1173 2860113 2860192 2860333 "TRIGCAT-" 2860338 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1172 2857013 2858973 2859253 "TREE" 2859868 NIL TREE (NIL T) -8 NIL NIL) (-1171 2856287 2856815 2856845 "TRANFUN" 2856880 T TRANFUN (NIL) -9 NIL 2856946) (-1170 2855566 2855757 2856037 "TRANFUN-" 2856042 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1169 2855370 2855402 2855463 "TOPSP" 2855527 T TOPSP (NIL) -7 NIL NIL) (-1168 2854718 2854833 2854987 "TOOLSIGN" 2855251 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1167 2853379 2853895 2854134 "TEXTFILE" 2854501 T TEXTFILE (NIL) -8 NIL NIL) (-1166 2853160 2853191 2853263 "TEX1" 2853342 NIL TEX1 (NIL T) -7 NIL NIL) (-1165 2851025 2851539 2851977 "TEX" 2852744 T TEX (NIL) -8 NIL NIL) (-1164 2850673 2850736 2850826 "TEMUTL" 2850957 T TEMUTL (NIL) -7 NIL NIL) (-1163 2848827 2849107 2849432 "TBCMPPK" 2850396 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1162 2840717 2846987 2847043 "TBAGG" 2847443 NIL TBAGG (NIL T T) -9 NIL 2847654) (-1161 2835787 2837275 2839029 "TBAGG-" 2839034 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1160 2835171 2835278 2835423 "TANEXP" 2835676 NIL TANEXP (NIL T) -7 NIL NIL) (-1159 2834583 2834682 2834820 "TABLEAU" 2835068 NIL TABLEAU (NIL T) -8 NIL NIL) (-1158 2828086 2834440 2834533 "TABLE" 2834538 NIL TABLE (NIL T T) -8 NIL NIL) (-1157 2822694 2823914 2825162 "TABLBUMP" 2826872 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1156 2822122 2822222 2822350 "SYSTEM" 2822588 T SYSTEM (NIL) -7 NIL NIL) (-1155 2818585 2819280 2820063 "SYSSOLP" 2821373 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1154 2814877 2815584 2816318 "SYNTAX" 2817873 T SYNTAX (NIL) -8 NIL NIL) (-1153 2812035 2812637 2813269 "SYMTAB" 2814267 T SYMTAB (NIL) -8 NIL NIL) (-1152 2807308 2808204 2809181 "SYMS" 2811080 T SYMS (NIL) -8 NIL NIL) (-1151 2804590 2806769 2806999 "SYMPOLY" 2807116 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1150 2804107 2804182 2804305 "SYMFUNC" 2804502 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1149 2800084 2801344 2802166 "SYMBOL" 2803307 T SYMBOL (NIL) -8 NIL NIL) (-1148 2793623 2795312 2797032 "SWITCH" 2798386 T SWITCH (NIL) -8 NIL NIL) (-1147 2786893 2792444 2792747 "SUTS" 2793378 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1146 2778866 2786008 2786290 "SUPXS" 2786669 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1145 2778025 2778152 2778369 "SUPFRACF" 2778734 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1144 2777646 2777705 2777818 "SUP2" 2777960 NIL SUP2 (NIL T T) -7 NIL NIL) (-1143 2769215 2777264 2777390 "SUP" 2777555 NIL SUP (NIL T) -8 NIL NIL) (-1142 2767628 2767902 2768265 "SUMRF" 2768914 NIL SUMRF (NIL T) -7 NIL NIL) (-1141 2766942 2767008 2767207 "SUMFS" 2767549 NIL SUMFS (NIL T T) -7 NIL NIL) (-1140 2750967 2766119 2766370 "SULS" 2766749 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1139 2750596 2750789 2750859 "SUCHTAST" 2750919 T SUCHTAST (NIL) -8 NIL NIL) (-1138 2749918 2750121 2750261 "SUCH" 2750504 NIL SUCH (NIL T T) -8 NIL NIL) (-1137 2743812 2744824 2745783 "SUBSPACE" 2749006 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1136 2743242 2743332 2743496 "SUBRESP" 2743700 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1135 2737415 2738535 2739682 "STTFNC" 2742142 NIL STTFNC (NIL T) -7 NIL NIL) (-1134 2730784 2732080 2733391 "STTF" 2736151 NIL STTF (NIL T) -7 NIL NIL) (-1133 2722099 2723966 2725760 "STTAYLOR" 2729025 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1132 2715345 2721963 2722046 "STRTBL" 2722051 NIL STRTBL (NIL T) -8 NIL NIL) (-1131 2710736 2715300 2715331 "STRING" 2715336 T STRING (NIL) -8 NIL NIL) (-1130 2705624 2710109 2710139 "STRICAT" 2710198 T STRICAT (NIL) -9 NIL 2710260) (-1129 2705134 2705211 2705355 "STREAM3" 2705541 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1128 2704116 2704299 2704534 "STREAM2" 2704947 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1127 2703804 2703856 2703949 "STREAM1" 2704058 NIL STREAM1 (NIL T) -7 NIL NIL) (-1126 2696519 2701327 2701947 "STREAM" 2703219 NIL STREAM (NIL T) -8 NIL NIL) (-1125 2695535 2695716 2695947 "STINPROD" 2696335 NIL STINPROD (NIL T) -7 NIL NIL) (-1124 2695113 2695297 2695327 "STEP" 2695407 T STEP (NIL) -9 NIL 2695485) (-1123 2688658 2695012 2695089 "STBL" 2695094 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1122 2683835 2687880 2687923 "STAGG" 2688076 NIL STAGG (NIL T) -9 NIL 2688165) (-1121 2681543 2682143 2683013 "STAGG-" 2683018 NIL STAGG- (NIL T T) -8 NIL NIL) (-1120 2679738 2681313 2681405 "STACK" 2681486 NIL STACK (NIL T) -8 NIL NIL) (-1119 2672490 2677879 2678335 "SREGSET" 2679368 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1118 2664916 2666284 2667797 "SRDCMPK" 2671096 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1117 2657883 2662356 2662386 "SRAGG" 2663689 T SRAGG (NIL) -9 NIL 2664297) (-1116 2656900 2657155 2657534 "SRAGG-" 2657539 NIL SRAGG- (NIL T) -8 NIL NIL) (-1115 2651399 2655847 2656268 "SQMATRIX" 2656526 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1114 2645152 2648119 2648845 "SPLTREE" 2650745 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1113 2641142 2641808 2642454 "SPLNODE" 2644578 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1112 2640189 2640422 2640452 "SPFCAT" 2640896 T SPFCAT (NIL) -9 NIL NIL) (-1111 2638926 2639136 2639400 "SPECOUT" 2639947 T SPECOUT (NIL) -7 NIL NIL) (-1110 2630615 2632359 2632389 "SPADXPT" 2636781 T SPADXPT (NIL) -9 NIL 2638815) (-1109 2630376 2630416 2630485 "SPADPRSR" 2630568 T SPADPRSR (NIL) -7 NIL NIL) (-1108 2628559 2630331 2630362 "SPADAST" 2630367 T SPADAST (NIL) -8 NIL NIL) (-1107 2620530 2622277 2622320 "SPACEC" 2626693 NIL SPACEC (NIL T) -9 NIL 2628509) (-1106 2618701 2620462 2620511 "SPACE3" 2620516 NIL SPACE3 (NIL T) -8 NIL NIL) (-1105 2617453 2617624 2617915 "SORTPAK" 2618506 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1104 2615503 2615806 2616225 "SOLVETRA" 2617117 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1103 2614514 2614736 2615010 "SOLVESER" 2615276 NIL SOLVESER (NIL T) -7 NIL NIL) (-1102 2609734 2610615 2611617 "SOLVERAD" 2613566 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1101 2605549 2606158 2606887 "SOLVEFOR" 2609101 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1100 2599873 2604898 2604995 "SNTSCAT" 2605000 NIL SNTSCAT (NIL T T T T) -9 NIL 2605070) (-1099 2594016 2598196 2598587 "SMTS" 2599563 NIL SMTS (NIL T T T) -8 NIL NIL) (-1098 2588492 2593904 2593981 "SMP" 2593986 NIL SMP (NIL T T) -8 NIL NIL) (-1097 2586651 2586952 2587350 "SMITH" 2588189 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1096 2579632 2583783 2583886 "SMATCAT" 2585240 NIL SMATCAT (NIL NIL T T T) -9 NIL 2585790) (-1095 2576593 2577409 2578580 "SMATCAT-" 2578585 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1094 2574306 2575829 2575872 "SKAGG" 2576133 NIL SKAGG (NIL T) -9 NIL 2576268) (-1093 2570424 2573410 2573688 "SINT" 2574050 T SINT (NIL) -8 NIL NIL) (-1092 2570196 2570234 2570300 "SIMPAN" 2570380 T SIMPAN (NIL) -7 NIL NIL) (-1091 2569055 2569269 2569537 "SIGNRF" 2569962 NIL SIGNRF (NIL T) -7 NIL NIL) (-1090 2567881 2568025 2568309 "SIGNEF" 2568891 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1089 2567214 2567464 2567588 "SIGAST" 2567779 T SIGAST (NIL) -8 NIL NIL) (-1088 2566521 2566749 2566889 "SIG" 2567096 T SIG (NIL) -8 NIL NIL) (-1087 2564211 2564665 2565171 "SHP" 2566062 NIL SHP (NIL T NIL) -7 NIL NIL) (-1086 2558124 2564112 2564188 "SHDP" 2564193 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1085 2557723 2557889 2557919 "SGROUP" 2558012 T SGROUP (NIL) -9 NIL 2558074) (-1084 2557581 2557607 2557680 "SGROUP-" 2557685 NIL SGROUP- (NIL T) -8 NIL NIL) (-1083 2554417 2555114 2555837 "SGCF" 2556880 T SGCF (NIL) -7 NIL NIL) (-1082 2548839 2553864 2553961 "SFRTCAT" 2553966 NIL SFRTCAT (NIL T T T T) -9 NIL 2554005) (-1081 2542263 2543278 2544414 "SFRGCD" 2547822 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1080 2535391 2536462 2537648 "SFQCMPK" 2541196 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1079 2535013 2535102 2535212 "SFORT" 2535332 NIL SFORT (NIL T T) -8 NIL NIL) (-1078 2534158 2534853 2534974 "SEXOF" 2534979 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1077 2528934 2529623 2529718 "SEXCAT" 2533489 NIL SEXCAT (NIL T T T T T) -9 NIL 2534108) (-1076 2528068 2528815 2528883 "SEX" 2528888 T SEX (NIL) -8 NIL NIL) (-1075 2526325 2526785 2527088 "SETMN" 2527811 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1074 2525931 2526057 2526087 "SETCAT" 2526204 T SETCAT (NIL) -9 NIL 2526289) (-1073 2525711 2525763 2525862 "SETCAT-" 2525867 NIL SETCAT- (NIL T) -8 NIL NIL) (-1072 2522098 2524172 2524215 "SETAGG" 2525085 NIL SETAGG (NIL T) -9 NIL 2525425) (-1071 2521556 2521672 2521909 "SETAGG-" 2521914 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1070 2518736 2521490 2521538 "SET" 2521543 NIL SET (NIL T) -8 NIL NIL) (-1069 2518206 2518432 2518533 "SEQAST" 2518657 T SEQAST (NIL) -8 NIL NIL) (-1068 2517410 2517703 2517764 "SEGXCAT" 2518050 NIL SEGXCAT (NIL T T) -9 NIL 2518170) (-1067 2516317 2516530 2516573 "SEGCAT" 2517155 NIL SEGCAT (NIL T) -9 NIL 2517393) (-1066 2515938 2515997 2516110 "SEGBIND2" 2516252 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1065 2514987 2515317 2515517 "SEGBIND" 2515773 NIL SEGBIND (NIL T) -8 NIL NIL) (-1064 2514588 2514788 2514865 "SEGAST" 2514932 T SEGAST (NIL) -8 NIL NIL) (-1063 2513807 2513933 2514137 "SEG2" 2514432 NIL SEG2 (NIL T T) -7 NIL NIL) (-1062 2512863 2513473 2513655 "SEG" 2513660 NIL SEG (NIL T) -8 NIL NIL) (-1061 2512300 2512798 2512845 "SDVAR" 2512850 NIL SDVAR (NIL T) -8 NIL NIL) (-1060 2504631 2512070 2512200 "SDPOL" 2512205 NIL SDPOL (NIL T) -8 NIL NIL) (-1059 2503224 2503490 2503809 "SCPKG" 2504346 NIL SCPKG (NIL T) -7 NIL NIL) (-1058 2502360 2502540 2502740 "SCOPE" 2503046 T SCOPE (NIL) -8 NIL NIL) (-1057 2501581 2501714 2501893 "SCACHE" 2502215 NIL SCACHE (NIL T) -7 NIL NIL) (-1056 2501290 2501450 2501480 "SASTCAT" 2501485 T SASTCAT (NIL) -9 NIL 2501498) (-1055 2500729 2501050 2501135 "SAOS" 2501227 T SAOS (NIL) -8 NIL NIL) (-1054 2500294 2500329 2500502 "SAERFFC" 2500688 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1053 2499887 2499922 2500081 "SAEFACT" 2500253 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1052 2493870 2499784 2499864 "SAE" 2499869 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1051 2492191 2492505 2492906 "RURPK" 2493536 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1050 2490827 2491106 2491418 "RULESET" 2492025 NIL RULESET (NIL T T T) -8 NIL NIL) (-1049 2490466 2490621 2490704 "RULECOLD" 2490779 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1048 2487653 2488156 2488621 "RULE" 2490147 NIL RULE (NIL T T T) -8 NIL NIL) (-1047 2487151 2487370 2487464 "RSTRCAST" 2487581 T RSTRCAST (NIL) -8 NIL NIL) (-1046 2482000 2482794 2483714 "RSETGCD" 2486350 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1045 2471284 2476309 2476406 "RSETCAT" 2480525 NIL RSETCAT (NIL T T T T) -9 NIL 2481622) (-1044 2469211 2469750 2470574 "RSETCAT-" 2470579 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1043 2461598 2462973 2464493 "RSDCMPK" 2467810 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1042 2459603 2460044 2460118 "RRCC" 2461204 NIL RRCC (NIL T T) -9 NIL 2461548) (-1041 2458954 2459128 2459407 "RRCC-" 2459412 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1040 2458424 2458650 2458751 "RPTAST" 2458875 T RPTAST (NIL) -8 NIL NIL) (-1039 2432683 2442237 2442304 "RPOLCAT" 2452968 NIL RPOLCAT (NIL T T T) -9 NIL 2456127) (-1038 2424219 2426545 2429655 "RPOLCAT-" 2429660 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1037 2415268 2422430 2422912 "ROUTINE" 2423759 T ROUTINE (NIL) -8 NIL NIL) (-1036 2412028 2414819 2414968 "ROMAN" 2415141 T ROMAN (NIL) -8 NIL NIL) (-1035 2410305 2410888 2411148 "ROIRC" 2411833 NIL ROIRC (NIL T T) -8 NIL NIL) (-1034 2406760 2408995 2409025 "RNS" 2409329 T RNS (NIL) -9 NIL 2409601) (-1033 2405269 2405652 2406186 "RNS-" 2406261 NIL RNS- (NIL T) -8 NIL NIL) (-1032 2404718 2405100 2405130 "RNG" 2405135 T RNG (NIL) -9 NIL 2405156) (-1031 2404110 2404472 2404515 "RMODULE" 2404577 NIL RMODULE (NIL T) -9 NIL 2404619) (-1030 2402946 2403040 2403376 "RMCAT2" 2404011 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1029 2399651 2402120 2402445 "RMATRIX" 2402680 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1028 2392593 2394827 2394942 "RMATCAT" 2398301 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2399283) (-1027 2391968 2392115 2392422 "RMATCAT-" 2392427 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1026 2391535 2391610 2391738 "RINTERP" 2391887 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1025 2390623 2391143 2391173 "RING" 2391285 T RING (NIL) -9 NIL 2391380) (-1024 2390415 2390459 2390556 "RING-" 2390561 NIL RING- (NIL T) -8 NIL NIL) (-1023 2389256 2389493 2389751 "RIDIST" 2390179 T RIDIST (NIL) -7 NIL NIL) (-1022 2380599 2388724 2388930 "RGCHAIN" 2389104 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1021 2379975 2380355 2380396 "RGBCSPC" 2380454 NIL RGBCSPC (NIL T) -9 NIL 2380506) (-1020 2379159 2379514 2379555 "RGBCMDL" 2379787 NIL RGBCMDL (NIL T) -9 NIL 2379901) (-1019 2378805 2378868 2378971 "RFFACTOR" 2379090 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1018 2378530 2378565 2378662 "RFFACT" 2378764 NIL RFFACT (NIL T) -7 NIL NIL) (-1017 2376647 2377011 2377393 "RFDIST" 2378170 T RFDIST (NIL) -7 NIL NIL) (-1016 2373641 2374255 2374925 "RF" 2376011 NIL RF (NIL T) -7 NIL NIL) (-1015 2373094 2373186 2373349 "RETSOL" 2373543 NIL RETSOL (NIL T T) -7 NIL NIL) (-1014 2372682 2372762 2372805 "RETRACT" 2372998 NIL RETRACT (NIL T) -9 NIL NIL) (-1013 2372531 2372556 2372643 "RETRACT-" 2372648 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1012 2372160 2372353 2372423 "RETAST" 2372483 T RETAST (NIL) -8 NIL NIL) (-1011 2365016 2371813 2371940 "RESULT" 2372055 T RESULT (NIL) -8 NIL NIL) (-1010 2363642 2364285 2364484 "RESRING" 2364919 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1009 2363278 2363327 2363425 "RESLATC" 2363579 NIL RESLATC (NIL T) -7 NIL NIL) (-1008 2362984 2363018 2363125 "REPSQ" 2363237 NIL REPSQ (NIL T) -7 NIL NIL) (-1007 2362682 2362716 2362827 "REPDB" 2362943 NIL REPDB (NIL T) -7 NIL NIL) (-1006 2356592 2357971 2359194 "REP2" 2361494 NIL REP2 (NIL T) -7 NIL NIL) (-1005 2352969 2353650 2354458 "REP1" 2355819 NIL REP1 (NIL T) -7 NIL NIL) (-1004 2350391 2350971 2351573 "REP" 2352389 T REP (NIL) -7 NIL NIL) (-1003 2343144 2348532 2348988 "REGSET" 2350021 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1002 2341957 2342292 2342542 "REF" 2342929 NIL REF (NIL T) -8 NIL NIL) (-1001 2341334 2341437 2341604 "REDORDER" 2341841 NIL REDORDER (NIL T T) -7 NIL NIL) (-1000 2337376 2340553 2340778 "RECLOS" 2341163 NIL RECLOS (NIL T) -8 NIL NIL) (-999 2336433 2336614 2336827 "REALSOLV" 2337183 T REALSOLV (NIL) -7 NIL NIL) (-998 2332924 2333726 2334608 "REAL0Q" 2335598 NIL REAL0Q (NIL T) -7 NIL NIL) (-997 2328535 2329523 2330582 "REAL0" 2331905 NIL REAL0 (NIL T) -7 NIL NIL) (-996 2328383 2328424 2328452 "REAL" 2328457 T REAL (NIL) -9 NIL 2328492) (-995 2327885 2328104 2328196 "RDUCEAST" 2328311 T RDUCEAST (NIL) -8 NIL NIL) (-994 2327293 2327365 2327570 "RDIV" 2327807 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-993 2326366 2326540 2326751 "RDIST" 2327115 NIL RDIST (NIL T) -7 NIL NIL) (-992 2324967 2325254 2325624 "RDETRS" 2326074 NIL RDETRS (NIL T T) -7 NIL NIL) (-991 2322784 2323238 2323774 "RDETR" 2324509 NIL RDETR (NIL T T) -7 NIL NIL) (-990 2321398 2321676 2322078 "RDEEFS" 2322500 NIL RDEEFS (NIL T T) -7 NIL NIL) (-989 2319896 2320202 2320632 "RDEEF" 2321086 NIL RDEEF (NIL T T) -7 NIL NIL) (-988 2314242 2317104 2317132 "RCFIELD" 2318409 T RCFIELD (NIL) -9 NIL 2319139) (-987 2312311 2312815 2313508 "RCFIELD-" 2313581 NIL RCFIELD- (NIL T) -8 NIL NIL) (-986 2308642 2310427 2310468 "RCAGG" 2311539 NIL RCAGG (NIL T) -9 NIL 2312004) (-985 2308273 2308367 2308527 "RCAGG-" 2308532 NIL RCAGG- (NIL T T) -8 NIL NIL) (-984 2307613 2307725 2307888 "RATRET" 2308157 NIL RATRET (NIL T) -7 NIL NIL) (-983 2307170 2307237 2307356 "RATFACT" 2307541 NIL RATFACT (NIL T) -7 NIL NIL) (-982 2306485 2306605 2306755 "RANDSRC" 2307040 T RANDSRC (NIL) -7 NIL NIL) (-981 2306222 2306266 2306337 "RADUTIL" 2306434 T RADUTIL (NIL) -7 NIL NIL) (-980 2299308 2304965 2305282 "RADIX" 2305937 NIL RADIX (NIL NIL) -8 NIL NIL) (-979 2290975 2299152 2299280 "RADFF" 2299285 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-978 2290627 2290702 2290730 "RADCAT" 2290887 T RADCAT (NIL) -9 NIL NIL) (-977 2290412 2290460 2290557 "RADCAT-" 2290562 NIL RADCAT- (NIL T) -8 NIL NIL) (-976 2288563 2290187 2290276 "QUEUE" 2290356 NIL QUEUE (NIL T) -8 NIL NIL) (-975 2288201 2288244 2288371 "QUATCT2" 2288514 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-974 2282068 2285362 2285402 "QUATCAT" 2286182 NIL QUATCAT (NIL T) -9 NIL 2286948) (-973 2278233 2279263 2280643 "QUATCAT-" 2280737 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-972 2274816 2278170 2278215 "QUAT" 2278220 NIL QUAT (NIL T) -8 NIL NIL) (-971 2272336 2273900 2273941 "QUAGG" 2274316 NIL QUAGG (NIL T) -9 NIL 2274491) (-970 2271968 2272161 2272229 "QQUTAST" 2272288 T QQUTAST (NIL) -8 NIL NIL) (-969 2270893 2271366 2271538 "QFORM" 2271840 NIL QFORM (NIL NIL T) -8 NIL NIL) (-968 2270531 2270574 2270701 "QFCAT2" 2270844 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-967 2261880 2267067 2267107 "QFCAT" 2267765 NIL QFCAT (NIL T) -9 NIL 2268764) (-966 2257488 2258677 2260256 "QFCAT-" 2260350 NIL QFCAT- (NIL T T) -8 NIL NIL) (-965 2256948 2257058 2257188 "QEQUAT" 2257378 T QEQUAT (NIL) -8 NIL NIL) (-964 2250096 2251167 2252351 "QCMPACK" 2255881 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-963 2249341 2249515 2249747 "QALGSET2" 2249916 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-962 2246923 2247342 2247768 "QALGSET" 2248998 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-961 2245614 2245837 2246154 "PWFFINTB" 2246696 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-960 2243813 2243981 2244335 "PUSHVAR" 2245428 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-959 2239731 2240785 2240826 "PTRANFN" 2242710 NIL PTRANFN (NIL T) -9 NIL NIL) (-958 2238133 2238424 2238746 "PTPACK" 2239442 NIL PTPACK (NIL T) -7 NIL NIL) (-957 2237765 2237822 2237931 "PTFUNC2" 2238070 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-956 2232231 2236576 2236617 "PTCAT" 2236990 NIL PTCAT (NIL T) -9 NIL 2237152) (-955 2231889 2231924 2232048 "PSQFR" 2232190 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-954 2230484 2230782 2231116 "PSEUDLIN" 2231587 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-953 2217253 2219618 2221942 "PSETPK" 2228244 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-952 2210297 2213011 2213107 "PSETCAT" 2216128 NIL PSETCAT (NIL T T T T) -9 NIL 2216942) (-951 2208133 2208767 2209588 "PSETCAT-" 2209593 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-950 2207482 2207647 2207675 "PSCURVE" 2207943 T PSCURVE (NIL) -9 NIL 2208110) (-949 2203963 2205445 2205510 "PSCAT" 2206354 NIL PSCAT (NIL T T T) -9 NIL 2206594) (-948 2203026 2203242 2203642 "PSCAT-" 2203647 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-947 2201678 2202311 2202525 "PRTITION" 2202832 T PRTITION (NIL) -8 NIL NIL) (-946 2201180 2201399 2201491 "PRTDAST" 2201606 T PRTDAST (NIL) -8 NIL NIL) (-945 2190278 2192484 2194672 "PRS" 2199042 NIL PRS (NIL T T) -7 NIL NIL) (-944 2188136 2189628 2189668 "PRQAGG" 2189851 NIL PRQAGG (NIL T) -9 NIL 2189953) (-943 2187522 2187751 2187779 "PROPLOG" 2187964 T PROPLOG (NIL) -9 NIL 2188086) (-942 2184692 2185336 2185800 "PROPFRML" 2187090 NIL PROPFRML (NIL T) -8 NIL NIL) (-941 2184152 2184262 2184392 "PROPERTY" 2184582 T PROPERTY (NIL) -8 NIL NIL) (-940 2178237 2182318 2183138 "PRODUCT" 2183378 NIL PRODUCT (NIL T T) -8 NIL NIL) (-939 2178033 2178065 2178124 "PRINT" 2178198 T PRINT (NIL) -7 NIL NIL) (-938 2177373 2177490 2177642 "PRIMES" 2177913 NIL PRIMES (NIL T) -7 NIL NIL) (-937 2175438 2175839 2176305 "PRIMELT" 2176952 NIL PRIMELT (NIL T) -7 NIL NIL) (-936 2175167 2175216 2175244 "PRIMCAT" 2175368 T PRIMCAT (NIL) -9 NIL NIL) (-935 2174174 2174352 2174580 "PRIMARR2" 2174985 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-934 2170335 2174112 2174157 "PRIMARR" 2174162 NIL PRIMARR (NIL T) -8 NIL NIL) (-933 2169978 2170034 2170145 "PREASSOC" 2170273 NIL PREASSOC (NIL T T) -7 NIL NIL) (-932 2167298 2169436 2169670 "PR" 2169789 NIL PR (NIL T T) -8 NIL NIL) (-931 2166773 2166906 2166934 "PPCURVE" 2167139 T PPCURVE (NIL) -9 NIL 2167275) (-930 2166395 2166568 2166651 "PORTNUM" 2166710 T PORTNUM (NIL) -8 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1760407 NIL NONE1 (NIL T) -7 NIL NIL) (-753 1760059 1760189 1760218 "NONE" 1760223 T NONE (NIL) -8 NIL NIL) (-752 1759542 1759604 1759790 "NODE1" 1759991 NIL NODE1 (NIL T T) -7 NIL NIL) (-751 1757882 1758705 1758960 "NNI" 1759307 T NNI (NIL) -8 NIL NIL) (-750 1756302 1756615 1756979 "NLINSOL" 1757550 NIL NLINSOL (NIL T) -7 NIL NIL) (-749 1752469 1753437 1754359 "NIPROB" 1755400 T NIPROB (NIL) -8 NIL NIL) (-748 1751226 1751460 1751762 "NFINTBAS" 1752231 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-747 1749934 1750165 1750446 "NCODIV" 1750994 NIL NCODIV (NIL T T) -7 NIL NIL) (-746 1749696 1749733 1749808 "NCNTFRAC" 1749891 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-745 1747876 1748240 1748660 "NCEP" 1749321 NIL NCEP (NIL T) -7 NIL NIL) (-744 1746794 1747526 1747554 "NASRING" 1747664 T NASRING (NIL) -9 NIL 1747738) (-743 1746589 1746633 1746727 "NASRING-" 1746732 NIL NASRING- (NIL T) -8 NIL NIL) (-742 1745742 1746241 1746269 "NARNG" 1746386 T NARNG (NIL) -9 NIL 1746477) (-741 1745434 1745501 1745635 "NARNG-" 1745640 NIL NARNG- (NIL T) -8 NIL NIL) (-740 1744313 1744520 1744755 "NAGSP" 1745219 T NAGSP (NIL) -7 NIL NIL) (-739 1735585 1737269 1738942 "NAGS" 1742660 T NAGS (NIL) -7 NIL NIL) (-738 1734133 1734441 1734772 "NAGF07" 1735274 T NAGF07 (NIL) -7 NIL NIL) (-737 1728671 1729962 1731269 "NAGF04" 1732846 T NAGF04 (NIL) -7 NIL NIL) (-736 1721639 1723253 1724886 "NAGF02" 1727058 T NAGF02 (NIL) -7 NIL NIL) (-735 1716863 1717963 1719080 "NAGF01" 1720542 T NAGF01 (NIL) -7 NIL NIL) (-734 1710491 1712057 1713642 "NAGE04" 1715298 T NAGE04 (NIL) -7 NIL NIL) (-733 1701660 1703781 1705911 "NAGE02" 1708381 T NAGE02 (NIL) -7 NIL NIL) (-732 1697613 1698560 1699524 "NAGE01" 1700716 T NAGE01 (NIL) -7 NIL NIL) (-731 1695408 1695942 1696500 "NAGD03" 1697075 T NAGD03 (NIL) -7 NIL NIL) (-730 1687158 1689086 1691040 "NAGD02" 1693474 T NAGD02 (NIL) -7 NIL NIL) (-729 1680969 1682394 1683834 "NAGD01" 1685738 T NAGD01 (NIL) -7 NIL NIL) (-728 1677178 1678000 1678837 "NAGC06" 1680152 T NAGC06 (NIL) -7 NIL NIL) (-727 1675643 1675975 1676331 "NAGC05" 1676842 T NAGC05 (NIL) -7 NIL NIL) (-726 1675019 1675138 1675282 "NAGC02" 1675519 T NAGC02 (NIL) -7 NIL NIL) (-725 1674079 1674636 1674676 "NAALG" 1674755 NIL NAALG (NIL T) -9 NIL 1674816) (-724 1673914 1673943 1674033 "NAALG-" 1674038 NIL NAALG- (NIL T T) -8 NIL NIL) (-723 1667864 1668972 1670159 "MULTSQFR" 1672810 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-722 1667183 1667258 1667442 "MULTFACT" 1667776 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-721 1660406 1664271 1664324 "MTSCAT" 1665394 NIL MTSCAT (NIL T T) -9 NIL 1665908) (-720 1660118 1660172 1660264 "MTHING" 1660346 NIL MTHING (NIL T) -7 NIL NIL) (-719 1659910 1659943 1660003 "MSYSCMD" 1660078 T MSYSCMD (NIL) -7 NIL NIL) (-718 1657005 1659471 1659512 "MSETAGG" 1659517 NIL MSETAGG (NIL T) -9 NIL 1659551) (-717 1653117 1655760 1656080 "MSET" 1656718 NIL MSET (NIL T) -8 NIL NIL) (-716 1649002 1650496 1651241 "MRING" 1652417 NIL MRING (NIL T T) -8 NIL NIL) (-715 1648568 1648635 1648766 "MRF2" 1648929 NIL MRF2 (NIL T T T) -7 NIL NIL) (-714 1648186 1648221 1648365 "MRATFAC" 1648527 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-713 1645798 1646093 1646524 "MPRFF" 1647891 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-712 1639884 1645652 1645749 "MPOLY" 1645754 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-711 1639374 1639409 1639617 "MPCPF" 1639843 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-710 1638888 1638931 1639115 "MPC3" 1639325 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-709 1638083 1638164 1638385 "MPC2" 1638803 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-708 1636384 1636721 1637111 "MONOTOOL" 1637743 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-707 1635635 1635926 1635954 "MONOID" 1636173 T MONOID (NIL) -9 NIL 1636320) (-706 1635181 1635300 1635481 "MONOID-" 1635486 NIL MONOID- (NIL T) -8 NIL NIL) (-705 1626240 1632137 1632196 "MONOGEN" 1632870 NIL MONOGEN (NIL T T) -9 NIL 1633326) (-704 1623479 1624207 1625200 "MONOGEN-" 1625319 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-703 1622338 1622758 1622786 "MONADWU" 1623178 T MONADWU (NIL) -9 NIL 1623416) (-702 1621710 1621869 1622117 "MONADWU-" 1622122 NIL MONADWU- (NIL T) -8 NIL NIL) (-701 1621095 1621313 1621341 "MONAD" 1621548 T MONAD (NIL) -9 NIL 1621660) (-700 1620780 1620858 1620990 "MONAD-" 1620995 NIL MONAD- (NIL T) -8 NIL NIL) (-699 1619096 1619693 1619972 "MOEBIUS" 1620533 NIL MOEBIUS (NIL T) -8 NIL NIL) (-698 1618488 1618866 1618906 "MODULE" 1618911 NIL MODULE (NIL T) -9 NIL 1618937) (-697 1618056 1618152 1618342 "MODULE-" 1618347 NIL MODULE- (NIL T T) -8 NIL NIL) (-696 1615815 1616464 1616791 "MODRING" 1617880 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-695 1612803 1613920 1614441 "MODOP" 1615344 NIL MODOP (NIL T T) -8 NIL NIL) (-694 1610990 1611442 1611783 "MODMONOM" 1612602 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-693 1600738 1609182 1609605 "MODMON" 1610618 NIL MODMON (NIL T T) -8 NIL NIL) (-692 1597955 1599606 1599882 "MODFIELD" 1600613 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-691 1596959 1597236 1597426 "MMLFORM" 1597785 T MMLFORM (NIL) -8 NIL NIL) (-690 1596485 1596528 1596707 "MMAP" 1596910 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-689 1594754 1595487 1595528 "MLO" 1595951 NIL MLO (NIL T) -9 NIL 1596193) (-688 1592121 1592636 1593238 "MLIFT" 1594235 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-687 1591512 1591596 1591750 "MKUCFUNC" 1592032 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-686 1591111 1591181 1591304 "MKRECORD" 1591435 NIL MKRECORD (NIL T T) -7 NIL NIL) (-685 1590159 1590320 1590548 "MKFUNC" 1590922 NIL MKFUNC (NIL T) -7 NIL NIL) (-684 1589547 1589651 1589807 "MKFLCFN" 1590042 NIL MKFLCFN (NIL T) -7 NIL NIL) (-683 1588973 1589340 1589429 "MKCHSET" 1589491 NIL MKCHSET (NIL T) -8 NIL NIL) (-682 1588250 1588352 1588537 "MKBCFUNC" 1588866 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-681 1584994 1587804 1587940 "MINT" 1588134 T MINT (NIL) -8 NIL NIL) (-680 1583806 1584049 1584326 "MHROWRED" 1584749 NIL MHROWRED (NIL T) -7 NIL NIL) (-679 1579241 1582341 1582746 "MFLOAT" 1583421 T MFLOAT (NIL) -8 NIL NIL) (-678 1578598 1578674 1578845 "MFINFACT" 1579153 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-677 1574933 1575776 1576655 "MESH" 1577739 T MESH (NIL) -7 NIL NIL) (-676 1573323 1573635 1573988 "MDDFACT" 1574620 NIL MDDFACT (NIL T) -7 NIL NIL) (-675 1570165 1572482 1572523 "MDAGG" 1572778 NIL MDAGG (NIL T) -9 NIL 1572921) (-674 1559963 1569458 1569665 "MCMPLX" 1569978 T MCMPLX (NIL) -8 NIL NIL) (-673 1559104 1559250 1559450 "MCDEN" 1559812 NIL MCDEN (NIL T T) -7 NIL NIL) (-672 1556994 1557264 1557644 "MCALCFN" 1558834 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-671 1555905 1556078 1556319 "MAYBE" 1556792 NIL MAYBE (NIL T) -8 NIL NIL) (-670 1553517 1554040 1554602 "MATSTOR" 1555376 NIL MATSTOR (NIL T) -7 NIL NIL) (-669 1549522 1552889 1553137 "MATRIX" 1553302 NIL MATRIX (NIL T) -8 NIL NIL) (-668 1545291 1545995 1546731 "MATLIN" 1548879 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-667 1543885 1544038 1544371 "MATCAT2" 1545126 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-666 1534033 1537174 1537251 "MATCAT" 1542134 NIL MATCAT (NIL T T T) -9 NIL 1543551) (-665 1530397 1531410 1532766 "MATCAT-" 1532771 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-664 1528509 1528833 1529217 "MAPPKG3" 1530072 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-663 1527490 1527663 1527885 "MAPPKG2" 1528333 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-662 1525989 1526273 1526600 "MAPPKG1" 1527196 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-661 1525095 1525395 1525572 "MAPPAST" 1525832 T MAPPAST (NIL) -8 NIL NIL) (-660 1524706 1524764 1524887 "MAPHACK3" 1525031 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-659 1524298 1524359 1524473 "MAPHACK2" 1524638 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-658 1523736 1523839 1523981 "MAPHACK1" 1524189 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-657 1521842 1522436 1522740 "MAGMA" 1523464 NIL MAGMA (NIL T) -8 NIL NIL) (-656 1521348 1521566 1521657 "MACROAST" 1521771 T MACROAST (NIL) -8 NIL NIL) (-655 1517815 1519587 1520048 "M3D" 1520920 NIL M3D (NIL T) -8 NIL NIL) (-654 1511972 1516185 1516226 "LZSTAGG" 1517008 NIL LZSTAGG (NIL T) -9 NIL 1517303) (-653 1507945 1509103 1510560 "LZSTAGG-" 1510565 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-652 1505059 1505836 1506323 "LWORD" 1507490 NIL LWORD (NIL T) -8 NIL NIL) (-651 1504662 1504863 1504938 "LSTAST" 1505004 T LSTAST (NIL) -8 NIL NIL) (-650 1497894 1504433 1504567 "LSQM" 1504572 NIL LSQM (NIL NIL T) -8 NIL NIL) (-649 1497118 1497257 1497485 "LSPP" 1497749 NIL LSPP (NIL T T T T) -7 NIL NIL) (-648 1493960 1494617 1495330 "LSMP1" 1496437 NIL LSMP1 (NIL T) -7 NIL NIL) (-647 1491795 1492089 1492538 "LSMP" 1493656 NIL LSMP (NIL T T T T) -7 NIL NIL) (-646 1485723 1490963 1491004 "LSAGG" 1491066 NIL LSAGG (NIL T) -9 NIL 1491144) (-645 1482418 1483342 1484555 "LSAGG-" 1484560 NIL LSAGG- (NIL T T) -8 NIL NIL) (-644 1480044 1481562 1481811 "LPOLY" 1482213 NIL LPOLY (NIL T T) -8 NIL NIL) (-643 1479626 1479711 1479834 "LPEFRAC" 1479953 NIL LPEFRAC (NIL T) -7 NIL NIL) (-642 1479278 1479390 1479418 "LOGIC" 1479529 T LOGIC (NIL) -9 NIL 1479610) (-641 1479140 1479163 1479234 "LOGIC-" 1479239 NIL LOGIC- (NIL T) -8 NIL NIL) (-640 1478333 1478473 1478666 "LODOOPS" 1478996 NIL LODOOPS (NIL T T) -7 NIL NIL) (-639 1476871 1477106 1477459 "LODOF" 1478080 NIL LODOF (NIL T T) -7 NIL NIL) (-638 1473328 1475711 1475752 "LODOCAT" 1476190 NIL LODOCAT (NIL T) -9 NIL 1476401) (-637 1473061 1473119 1473246 "LODOCAT-" 1473251 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-636 1470430 1472902 1473020 "LODO2" 1473025 NIL LODO2 (NIL T T) -8 NIL NIL) (-635 1467914 1470367 1470412 "LODO1" 1470417 NIL LODO1 (NIL T) -8 NIL NIL) (-634 1465386 1467830 1467896 "LODO" 1467901 NIL LODO (NIL T NIL) -8 NIL NIL) (-633 1464246 1464411 1464723 "LODEEF" 1465209 NIL LODEEF (NIL T T T) -7 NIL NIL) (-632 1462593 1463340 1463593 "LO" 1464078 NIL LO (NIL T T T) -8 NIL NIL) (-631 1457879 1460723 1460764 "LNAGG" 1461711 NIL LNAGG (NIL T) -9 NIL 1462155) (-630 1457026 1457240 1457582 "LNAGG-" 1457587 NIL LNAGG- (NIL T T) -8 NIL NIL) (-629 1453189 1453951 1454590 "LMOPS" 1456441 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-628 1452584 1452946 1452987 "LMODULE" 1453048 NIL LMODULE (NIL T) -9 NIL 1453090) (-627 1449830 1452229 1452352 "LMDICT" 1452494 NIL LMDICT (NIL T) -8 NIL NIL) (-626 1449556 1449738 1449798 "LITERAL" 1449803 NIL LITERAL (NIL T) -8 NIL NIL) (-625 1449081 1449155 1449294 "LIST3" 1449476 NIL LIST3 (NIL T T T) -7 NIL NIL) (-624 1447215 1447527 1447926 "LIST2MAP" 1448728 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-623 1446222 1446400 1446628 "LIST2" 1447033 NIL LIST2 (NIL T T) -7 NIL NIL) (-622 1439451 1445168 1445466 "LIST" 1445957 NIL LIST (NIL T) -8 NIL NIL) (-621 1438201 1438837 1438878 "LINEXP" 1439133 NIL LINEXP (NIL T) -9 NIL 1439282) (-620 1436848 1437108 1437405 "LINDEP" 1437953 NIL LINDEP (NIL T T) -7 NIL NIL) (-619 1433686 1434386 1435144 "LIMITRF" 1436122 NIL LIMITRF (NIL T) -7 NIL NIL) (-618 1431985 1432273 1432682 "LIMITPS" 1433388 NIL LIMITPS (NIL T T) -7 NIL NIL) (-617 1431034 1431477 1431517 "LIECAT" 1431657 NIL LIECAT (NIL T) -9 NIL 1431808) (-616 1430875 1430902 1430990 "LIECAT-" 1430995 NIL LIECAT- (NIL T T) -8 NIL NIL) (-615 1425362 1430386 1430614 "LIE" 1430696 NIL LIE (NIL T T) -8 NIL NIL) (-614 1417976 1424811 1424976 "LIB" 1425217 T LIB (NIL) -8 NIL NIL) (-613 1413613 1414494 1415429 "LGROBP" 1417093 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-612 1412453 1413145 1413173 "LFCAT" 1413380 T LFCAT (NIL) -9 NIL 1413519) (-611 1410319 1410593 1410955 "LF" 1412174 NIL LF (NIL T T) -7 NIL NIL) (-610 1407223 1407851 1408539 "LEXTRIPK" 1409683 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-609 1403994 1404793 1405296 "LEXP" 1406803 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-608 1403497 1403715 1403807 "LETAST" 1403922 T LETAST (NIL) -8 NIL NIL) (-607 1401895 1402208 1402609 "LEADCDET" 1403179 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-606 1401085 1401159 1401388 "LAZM3PK" 1401816 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-605 1396055 1399162 1399700 "LAUPOL" 1400597 NIL LAUPOL (NIL T T) -8 NIL NIL) (-604 1395620 1395664 1395832 "LAPLACE" 1396005 NIL LAPLACE (NIL T T) -7 NIL NIL) (-603 1394721 1395271 1395312 "LALG" 1395374 NIL LALG (NIL T) -9 NIL 1395433) (-602 1394435 1394494 1394630 "LALG-" 1394635 NIL LALG- (NIL T T) -8 NIL NIL) (-601 1392409 1393536 1393787 "LA" 1394268 NIL LA (NIL T T T) -8 NIL NIL) (-600 1391209 1391626 1391855 "KTVLOGIC" 1392200 T KTVLOGIC (NIL) -8 NIL NIL) (-599 1390113 1390300 1390599 "KOVACIC" 1391009 NIL KOVACIC (NIL T T) -7 NIL NIL) (-598 1389948 1389972 1390013 "KONVERT" 1390075 NIL KONVERT (NIL T) -9 NIL NIL) (-597 1389783 1389807 1389848 "KOERCE" 1389910 NIL KOERCE (NIL T) -9 NIL NIL) (-596 1389285 1389366 1389496 "KERNEL2" 1389697 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-595 1387019 1387779 1388172 "KERNEL" 1388924 NIL KERNEL (NIL T) -8 NIL NIL) (-594 1380870 1385558 1385612 "KDAGG" 1385989 NIL KDAGG (NIL T T) -9 NIL 1386195) (-593 1380399 1380523 1380728 "KDAGG-" 1380733 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-592 1373576 1380060 1380215 "KAFILE" 1380277 NIL KAFILE (NIL T) -8 NIL NIL) (-591 1368063 1373087 1373315 "JORDAN" 1373397 NIL JORDAN (NIL T T) -8 NIL NIL) (-590 1367469 1367712 1367833 "JOINAST" 1367962 T JOINAST (NIL) -8 NIL NIL) (-589 1367198 1367257 1367344 "JAVACODE" 1367402 T JAVACODE (NIL) -8 NIL NIL) (-588 1363497 1365403 1365457 "IXAGG" 1366386 NIL IXAGG (NIL T T) -9 NIL 1366845) (-587 1362416 1362722 1363141 "IXAGG-" 1363146 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-586 1357996 1362338 1362397 "IVECTOR" 1362402 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-585 1356762 1356999 1357265 "ITUPLE" 1357763 NIL ITUPLE (NIL T) -8 NIL NIL) (-584 1355198 1355375 1355681 "ITRIGMNP" 1356584 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-583 1353943 1354147 1354430 "ITFUN3" 1354974 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-582 1353575 1353632 1353741 "ITFUN2" 1353880 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-581 1351412 1352437 1352736 "ITAYLOR" 1353309 NIL ITAYLOR (NIL T) -8 NIL NIL) (-580 1340394 1345549 1346712 "ISUPS" 1350282 NIL ISUPS (NIL T) -8 NIL NIL) (-579 1339498 1339638 1339874 "ISUMP" 1340241 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-578 1334762 1339299 1339378 "ISTRING" 1339451 NIL ISTRING (NIL NIL) -8 NIL NIL) (-577 1334265 1334483 1334575 "ISAST" 1334690 T ISAST (NIL) -8 NIL NIL) (-576 1333475 1333556 1333772 "IRURPK" 1334179 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-575 1332411 1332612 1332852 "IRSN" 1333255 T IRSN (NIL) -7 NIL NIL) (-574 1330440 1330795 1331231 "IRRF2F" 1332049 NIL IRRF2F (NIL T) -7 NIL NIL) (-573 1330187 1330225 1330301 "IRREDFFX" 1330396 NIL IRREDFFX (NIL T) -7 NIL NIL) (-572 1328802 1329061 1329360 "IROOT" 1329920 NIL IROOT (NIL T) -7 NIL NIL) (-571 1327874 1327987 1328208 "IR2F" 1328685 NIL IR2F (NIL T T) -7 NIL NIL) (-570 1325487 1325982 1326548 "IR2" 1327352 NIL IR2 (NIL T T) -7 NIL NIL) (-569 1322119 1323171 1323863 "IR" 1324827 NIL IR (NIL T) -8 NIL NIL) (-568 1321910 1321944 1322004 "IPRNTPK" 1322079 T IPRNTPK (NIL) -7 NIL NIL) (-567 1318531 1321799 1321868 "IPF" 1321873 NIL IPF (NIL NIL) -8 NIL NIL) (-566 1316896 1318456 1318513 "IPADIC" 1318518 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-565 1316396 1316600 1316710 "IOMODE" 1316806 T IOMODE (NIL) -8 NIL NIL) (-564 1316160 1316300 1316328 "IOBCON" 1316333 T IOBCON (NIL) -9 NIL 1316354) (-563 1315657 1315715 1315905 "INVLAPLA" 1316096 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-562 1305354 1307695 1310069 "INTTR" 1313333 NIL INTTR (NIL T T) -7 NIL NIL) (-561 1301698 1302440 1303304 "INTTOOLS" 1304539 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-560 1301284 1301375 1301492 "INTSLPE" 1301601 T INTSLPE (NIL) -7 NIL NIL) (-559 1299279 1301207 1301266 "INTRVL" 1301271 NIL INTRVL (NIL T) -8 NIL NIL) (-558 1296881 1297393 1297968 "INTRF" 1298764 NIL INTRF (NIL T) -7 NIL NIL) (-557 1296292 1296389 1296531 "INTRET" 1296779 NIL INTRET (NIL T) -7 NIL NIL) (-556 1294289 1294678 1295148 "INTRAT" 1295900 NIL INTRAT (NIL T T) -7 NIL NIL) (-555 1291517 1292100 1292726 "INTPM" 1293774 NIL INTPM (NIL T T) -7 NIL NIL) (-554 1288243 1288835 1289573 "INTPAF" 1290910 NIL INTPAF (NIL T T T) -7 NIL NIL) (-553 1283422 1284384 1285435 "INTPACK" 1287212 T INTPACK (NIL) -7 NIL NIL) (-552 1282674 1282826 1283034 "INTHERTR" 1283264 NIL INTHERTR (NIL T T) -7 NIL NIL) (-551 1282113 1282193 1282381 "INTHERAL" 1282588 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-550 1279959 1280402 1280859 "INTHEORY" 1281676 T INTHEORY (NIL) -7 NIL NIL) (-549 1271325 1272928 1274689 "INTG0" 1278329 NIL INTG0 (NIL T T T) -7 NIL NIL) (-548 1257598 1260963 1264348 "INTFTBL" 1267960 T INTFTBL (NIL) -8 NIL NIL) (-547 1256847 1256985 1257158 "INTFACT" 1257457 NIL INTFACT (NIL T) -7 NIL NIL) (-546 1254238 1254682 1255244 "INTEF" 1256403 NIL INTEF (NIL T T) -7 NIL NIL) (-545 1252740 1253445 1253473 "INTDOM" 1253774 T INTDOM (NIL) -9 NIL 1253981) (-544 1252109 1252283 1252525 "INTDOM-" 1252530 NIL INTDOM- (NIL T) -8 NIL NIL) (-543 1248642 1250528 1250582 "INTCAT" 1251381 NIL INTCAT (NIL T) -9 NIL 1251701) (-542 1248115 1248217 1248345 "INTBIT" 1248534 T INTBIT (NIL) -7 NIL NIL) (-541 1246786 1246940 1247254 "INTALG" 1247960 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-540 1246243 1246333 1246503 "INTAF" 1246690 NIL INTAF (NIL T T) -7 NIL NIL) (-539 1239699 1246053 1246193 "INTABL" 1246198 NIL INTABL (NIL T T T) -8 NIL NIL) (-538 1236613 1239428 1239555 "INT" 1239592 T INT (NIL) -8 NIL NIL) (-537 1231670 1234339 1234367 "INS" 1235301 T INS (NIL) -9 NIL 1235965) (-536 1228910 1229681 1230655 "INS-" 1230728 NIL INS- (NIL T) -8 NIL NIL) (-535 1227758 1227963 1228239 "INPSIGN" 1228685 NIL INPSIGN (NIL T T) -7 NIL NIL) (-534 1226876 1226993 1227190 "INPRODPF" 1227638 NIL INPRODPF (NIL T T) -7 NIL NIL) (-533 1225770 1225887 1226124 "INPRODFF" 1226756 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-532 1224770 1224922 1225182 "INNMFACT" 1225606 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-531 1223967 1224064 1224252 "INMODGCD" 1224669 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-530 1222476 1222720 1223044 "INFSP" 1223712 NIL INFSP (NIL T T T) -7 NIL NIL) (-529 1221660 1221777 1221960 "INFPROD0" 1222356 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-528 1221270 1221330 1221428 "INFORM1" 1221595 NIL INFORM1 (NIL T) -7 NIL NIL) (-527 1218152 1219335 1219850 "INFORM" 1220763 T INFORM (NIL) -8 NIL NIL) (-526 1217675 1217764 1217878 "INFINITY" 1218058 T INFINITY (NIL) -7 NIL NIL) (-525 1216292 1216541 1216862 "INEP" 1217423 NIL INEP (NIL T T T) -7 NIL NIL) (-524 1215568 1216189 1216254 "INDE" 1216259 NIL INDE (NIL T) -8 NIL NIL) (-523 1215132 1215200 1215317 "INCRMAPS" 1215495 NIL INCRMAPS (NIL T) -7 NIL NIL) (-522 1214435 1214628 1214778 "INBFILE" 1215002 T INBFILE (NIL) -8 NIL NIL) (-521 1209746 1210671 1211615 "INBFF" 1213523 NIL INBFF (NIL T) -7 NIL NIL) (-520 1209415 1209491 1209519 "INBCON" 1209652 T INBCON (NIL) -9 NIL 1209730) (-519 1209255 1209290 1209366 "INBCON-" 1209371 NIL INBCON- (NIL T) -8 NIL NIL) (-518 1208757 1208976 1209068 "INAST" 1209183 T INAST (NIL) -8 NIL NIL) (-517 1208211 1208436 1208542 "IMPTAST" 1208671 T IMPTAST (NIL) -8 NIL NIL) (-516 1204704 1208055 1208159 "IMATRIX" 1208164 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-515 1203416 1203539 1203854 "IMATQF" 1204560 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-514 1201636 1201863 1202200 "IMATLIN" 1203172 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-513 1196264 1201560 1201618 "ILIST" 1201623 NIL ILIST (NIL T NIL) -8 NIL NIL) (-512 1194217 1196124 1196237 "IIARRAY2" 1196242 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-511 1189652 1194128 1194192 "IFF" 1194197 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-510 1189026 1189269 1189385 "IFAST" 1189556 T IFAST (NIL) -8 NIL NIL) (-509 1184069 1188318 1188506 "IFARRAY" 1188883 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-508 1183276 1183973 1184046 "IFAMON" 1184051 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-507 1182860 1182925 1182979 "IEVALAB" 1183186 NIL IEVALAB (NIL T T) -9 NIL NIL) (-506 1182535 1182603 1182763 "IEVALAB-" 1182768 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-505 1181812 1182424 1182499 "IDPOAMS" 1182504 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-504 1181146 1181701 1181776 "IDPOAM" 1181781 NIL IDPOAM (NIL T T) -8 NIL NIL) (-503 1180804 1181060 1181123 "IDPO" 1181128 NIL IDPO (NIL T T) -8 NIL NIL) (-502 1179889 1180139 1180192 "IDPC" 1180605 NIL IDPC (NIL T T) -9 NIL 1180754) (-501 1179385 1179781 1179854 "IDPAM" 1179859 NIL IDPAM (NIL T T) -8 NIL NIL) (-500 1178788 1179277 1179350 "IDPAG" 1179355 NIL IDPAG (NIL T T) -8 NIL NIL) (-499 1178518 1178703 1178753 "IDENT" 1178758 T IDENT (NIL) -8 NIL NIL) (-498 1174773 1175621 1176516 "IDECOMP" 1177675 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-497 1167646 1168696 1169743 "IDEAL" 1173809 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-496 1166810 1166922 1167121 "ICDEN" 1167530 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-495 1165909 1166290 1166437 "ICARD" 1166683 T ICARD (NIL) -8 NIL NIL) (-494 1163969 1164282 1164687 "IBPTOOLS" 1165586 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-493 1159603 1163589 1163702 "IBITS" 1163888 NIL IBITS (NIL NIL) -8 NIL NIL) (-492 1156326 1156902 1157597 "IBATOOL" 1159020 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-491 1154106 1154567 1155100 "IBACHIN" 1155861 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-490 1151983 1153952 1154055 "IARRAY2" 1154060 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-489 1148136 1151909 1151966 "IARRAY1" 1151971 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-488 1142140 1146550 1147030 "IAN" 1147676 T IAN (NIL) -8 NIL NIL) (-487 1141651 1141708 1141881 "IALGFACT" 1142077 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-486 1141179 1141292 1141320 "HYPCAT" 1141527 T HYPCAT (NIL) -9 NIL NIL) (-485 1140717 1140834 1141020 "HYPCAT-" 1141025 NIL HYPCAT- (NIL T) -8 NIL NIL) (-484 1140339 1140512 1140595 "HOSTNAME" 1140654 T HOSTNAME (NIL) -8 NIL NIL) (-483 1137018 1138349 1138390 "HOAGG" 1139371 NIL HOAGG (NIL T) -9 NIL 1140050) (-482 1135612 1136011 1136537 "HOAGG-" 1136542 NIL HOAGG- (NIL T T) -8 NIL NIL) (-481 1129521 1135053 1135219 "HEXADEC" 1135466 T HEXADEC (NIL) -8 NIL NIL) (-480 1128269 1128491 1128754 "HEUGCD" 1129298 NIL HEUGCD (NIL T) -7 NIL NIL) (-479 1127372 1128106 1128236 "HELLFDIV" 1128241 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-478 1125600 1127149 1127237 "HEAP" 1127316 NIL HEAP (NIL T) -8 NIL NIL) (-477 1124891 1125152 1125286 "HEADAST" 1125486 T HEADAST (NIL) -8 NIL NIL) (-476 1118818 1124806 1124868 "HDP" 1124873 NIL HDP (NIL NIL T) -8 NIL NIL) (-475 1112600 1118453 1118605 "HDMP" 1118719 NIL HDMP (NIL NIL T) -8 NIL NIL) (-474 1111925 1112064 1112228 "HB" 1112456 T HB (NIL) -7 NIL NIL) (-473 1105424 1111771 1111875 "HASHTBL" 1111880 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-472 1104927 1105145 1105237 "HASAST" 1105352 T HASAST (NIL) -8 NIL NIL) (-471 1102745 1104551 1104732 "HACKPI" 1104766 T HACKPI (NIL) -8 NIL NIL) (-470 1098467 1102598 1102711 "GTSET" 1102716 NIL GTSET (NIL T T T T) -8 NIL NIL) (-469 1091995 1098345 1098443 "GSTBL" 1098448 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-468 1084310 1091026 1091291 "GSERIES" 1091786 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-467 1083477 1083868 1083896 "GROUP" 1084099 T GROUP (NIL) -9 NIL 1084233) (-466 1082843 1083002 1083253 "GROUP-" 1083258 NIL GROUP- (NIL T) -8 NIL NIL) (-465 1081212 1081531 1081918 "GROEBSOL" 1082520 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-464 1080152 1080414 1080465 "GRMOD" 1080994 NIL GRMOD (NIL T T) -9 NIL 1081162) (-463 1079920 1079956 1080084 "GRMOD-" 1080089 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-462 1075245 1076274 1077274 "GRIMAGE" 1078940 T GRIMAGE (NIL) -8 NIL NIL) (-461 1073712 1073972 1074296 "GRDEF" 1074941 T GRDEF (NIL) -7 NIL NIL) (-460 1073156 1073272 1073413 "GRAY" 1073591 T GRAY (NIL) -7 NIL NIL) (-459 1072387 1072767 1072818 "GRALG" 1072971 NIL GRALG (NIL T T) -9 NIL 1073064) (-458 1072048 1072121 1072284 "GRALG-" 1072289 NIL GRALG- (NIL T T T) -8 NIL NIL) (-457 1068852 1071633 1071811 "GPOLSET" 1071955 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-456 1068206 1068263 1068521 "GOSPER" 1068789 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-455 1063965 1064644 1065170 "GMODPOL" 1067905 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-454 1062970 1063154 1063392 "GHENSEL" 1063777 NIL GHENSEL (NIL T T) -7 NIL NIL) (-453 1057021 1057864 1058891 "GENUPS" 1062054 NIL GENUPS (NIL T T) -7 NIL NIL) (-452 1056718 1056769 1056858 "GENUFACT" 1056964 NIL GENUFACT (NIL T) -7 NIL NIL) (-451 1056130 1056207 1056372 "GENPGCD" 1056636 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-450 1055604 1055639 1055852 "GENMFACT" 1056089 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-449 1054172 1054427 1054734 "GENEEZ" 1055347 NIL GENEEZ (NIL T T) -7 NIL NIL) (-448 1048116 1053783 1053945 "GDMP" 1054095 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-447 1037515 1041887 1042993 "GCNAALG" 1047099 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-446 1035977 1036805 1036833 "GCDDOM" 1037088 T GCDDOM (NIL) -9 NIL 1037245) (-445 1035447 1035574 1035789 "GCDDOM-" 1035794 NIL GCDDOM- (NIL T) -8 NIL NIL) (-444 1024067 1026393 1028785 "GBINTERN" 1033138 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-443 1021904 1022196 1022617 "GBF" 1023742 NIL GBF (NIL T T T T) -7 NIL NIL) (-442 1020685 1020850 1021117 "GBEUCLID" 1021720 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-441 1019357 1019542 1019846 "GB" 1020464 NIL GB (NIL T T T T) -7 NIL NIL) (-440 1018706 1018831 1018980 "GAUSSFAC" 1019228 T GAUSSFAC (NIL) -7 NIL NIL) (-439 1017073 1017375 1017689 "GALUTIL" 1018425 NIL GALUTIL (NIL T) -7 NIL NIL) (-438 1015381 1015655 1015979 "GALPOLYU" 1016800 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-437 1012746 1013036 1013443 "GALFACTU" 1015078 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-436 1004552 1006051 1007659 "GALFACT" 1011178 NIL GALFACT (NIL T) -7 NIL NIL) (-435 1001940 1002598 1002626 "FVFUN" 1003782 T FVFUN (NIL) -9 NIL 1004502) (-434 1001206 1001388 1001416 "FVC" 1001707 T FVC (NIL) -9 NIL 1001890) (-433 1000848 1001003 1001084 "FUNCTION" 1001158 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-432 999666 1000149 1000352 "FTEM" 1000665 T FTEM (NIL) -8 NIL NIL) (-431 997348 997896 998382 "FT" 999200 T FT (NIL) -8 NIL NIL) (-430 995604 995893 996297 "FSUPFACT" 997039 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-429 994001 994290 994622 "FST" 995292 T FST (NIL) -8 NIL NIL) (-428 993172 993278 993473 "FSRED" 993883 NIL FSRED (NIL T T) -7 NIL NIL) (-427 991851 992106 992460 "FSPRMELT" 992887 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-426 988936 989374 989873 "FSPECF" 991414 NIL FSPECF (NIL T T) -7 NIL NIL) (-425 988450 988504 988681 "FSINT" 988877 NIL FSINT (NIL T T) -7 NIL NIL) (-424 986777 987443 987746 "FSERIES" 988229 NIL FSERIES (NIL T T) -8 NIL NIL) (-423 985791 985907 986138 "FSCINT" 986657 NIL FSCINT (NIL T T) -7 NIL NIL) (-422 984833 984976 985203 "FSAGG2" 985644 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-421 981067 983777 983818 "FSAGG" 984188 NIL FSAGG (NIL T) -9 NIL 984447) (-420 978829 979430 980226 "FSAGG-" 980321 NIL FSAGG- (NIL T T) -8 NIL NIL) (-419 976484 976763 977317 "FS2UPS" 978547 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-418 975341 975512 975821 "FS2EXPXP" 976309 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-417 974923 974966 975121 "FS2" 975292 NIL FS2 (NIL T T T T) -7 NIL NIL) (-416 957394 965807 965847 "FS" 969695 NIL FS (NIL T) -9 NIL 971984) (-415 946125 949088 953117 "FS-" 953414 NIL FS- (NIL T T) -8 NIL NIL) (-414 945551 945666 945818 "FRUTIL" 946005 NIL FRUTIL (NIL T) -7 NIL NIL) (-413 940658 943269 943309 "FRNAALG" 944705 NIL FRNAALG (NIL T) -9 NIL 945312) (-412 936387 937441 938699 "FRNAALG-" 939449 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-411 936025 936068 936195 "FRNAAF2" 936338 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-410 934432 934879 935174 "FRMOD" 935837 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-409 933627 933714 934003 "FRIDEAL2" 934339 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-408 931406 932010 932327 "FRIDEAL" 933418 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-407 930655 931062 931103 "FRETRCT" 931108 NIL FRETRCT (NIL T) -9 NIL 931284) (-406 929788 930012 930356 "FRETRCT-" 930361 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-405 927038 928214 928273 "FRAMALG" 929155 NIL FRAMALG (NIL T T) -9 NIL 929447) (-404 925172 925627 926257 "FRAMALG-" 926480 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-403 924808 924865 924972 "FRAC2" 925109 NIL FRAC2 (NIL T T) -7 NIL NIL) (-402 918789 924283 924559 "FRAC" 924564 NIL FRAC (NIL T) -8 NIL NIL) (-401 918425 918482 918589 "FR2" 918726 NIL FR2 (NIL T T) -7 NIL NIL) (-400 910001 914005 915334 "FR" 917128 NIL FR (NIL T) -8 NIL NIL) (-399 904735 907579 907607 "FPS" 908726 T FPS (NIL) -9 NIL 909283) (-398 904184 904293 904457 "FPS-" 904603 NIL FPS- (NIL T) -8 NIL NIL) (-397 901692 903325 903353 "FPC" 903578 T FPC (NIL) -9 NIL 903720) (-396 901485 901525 901622 "FPC-" 901627 NIL FPC- (NIL T) -8 NIL NIL) (-395 900363 900973 901014 "FPATMAB" 901019 NIL FPATMAB (NIL T) -9 NIL 901171) (-394 898063 898539 898965 "FPARFRAC" 900000 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-393 893495 893994 894676 "FORTRAN" 897495 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-392 891171 891733 891761 "FORTFN" 892821 T FORTFN (NIL) -9 NIL 893445) (-391 890935 890985 891013 "FORTCAT" 891072 T FORTCAT (NIL) -9 NIL 891134) (-390 888651 889151 889690 "FORT" 890416 T FORT (NIL) -7 NIL NIL) (-389 888439 888469 888538 "FORMULA1" 888615 NIL FORMULA1 (NIL T) -7 NIL NIL) (-388 886499 886982 887381 "FORMULA" 888060 T FORMULA (NIL) -8 NIL NIL) (-387 886022 886074 886247 "FORDER" 886441 NIL FORDER (NIL T T T T) -7 NIL NIL) (-386 885118 885282 885475 "FOP" 885849 T FOP (NIL) -7 NIL NIL) (-385 883726 884398 884572 "FNLA" 885000 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-384 882394 882783 882811 "FNCAT" 883383 T FNCAT (NIL) -9 NIL 883676) (-383 881960 882353 882381 "FNAME" 882386 T FNAME (NIL) -8 NIL NIL) (-382 880658 881587 881615 "FMTC" 881620 T FMTC (NIL) -9 NIL 881656) (-381 877020 878181 878810 "FMONOID" 880062 NIL FMONOID (NIL T) -8 NIL NIL) (-380 874444 875090 875118 "FMFUN" 876262 T FMFUN (NIL) -9 NIL 876970) (-379 871656 872490 872544 "FMCAT" 873739 NIL FMCAT (NIL T T) -9 NIL 874234) (-378 870925 871106 871134 "FMC" 871424 T FMC (NIL) -9 NIL 871606) (-377 869818 870691 870791 "FM1" 870870 NIL FM1 (NIL T T) -8 NIL NIL) (-376 869037 869560 869709 "FM" 869714 NIL FM (NIL T T) -8 NIL NIL) (-375 866811 867227 867721 "FLOATRP" 868588 NIL FLOATRP (NIL T) -7 NIL NIL) (-374 864249 864749 865327 "FLOATCP" 866278 NIL FLOATCP (NIL T) -7 NIL NIL) (-373 857804 861905 862535 "FLOAT" 863639 T FLOAT (NIL) -8 NIL NIL) (-372 856633 857437 857478 "FLINEXP" 857483 NIL FLINEXP (NIL T) -9 NIL 857576) (-371 855787 856022 856350 "FLINEXP-" 856355 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-370 854863 855007 855231 "FLASORT" 855639 NIL FLASORT (NIL T T) -7 NIL NIL) (-369 852080 852922 852974 "FLALG" 854201 NIL FLALG (NIL T T) -9 NIL 854668) (-368 851122 851265 851492 "FLAGG2" 851933 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-367 844906 848608 848649 "FLAGG" 849911 NIL FLAGG (NIL T) -9 NIL 850563) (-366 843632 843971 844461 "FLAGG-" 844466 NIL FLAGG- (NIL T T) -8 NIL NIL) (-365 840645 841619 841678 "FINRALG" 842806 NIL FINRALG (NIL T T) -9 NIL 843314) (-364 839805 840034 840373 "FINRALG-" 840378 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-363 839211 839424 839452 "FINITE" 839648 T FINITE (NIL) -9 NIL 839755) (-362 831669 833830 833870 "FINAALG" 837537 NIL FINAALG (NIL T) -9 NIL 838990) (-361 827010 828051 829195 "FINAALG-" 830574 NIL FINAALG- (NIL T T) -8 NIL NIL) (-360 825694 826006 826060 "FILECAT" 826744 NIL FILECAT (NIL T T) -9 NIL 826960) (-359 825089 825449 825552 "FILE" 825624 NIL FILE (NIL T) -8 NIL NIL) (-358 823011 824503 824531 "FIELD" 824571 T FIELD (NIL) -9 NIL 824651) (-357 821631 822016 822527 "FIELD-" 822532 NIL FIELD- (NIL T) -8 NIL NIL) (-356 819509 820266 820613 "FGROUP" 821317 NIL FGROUP (NIL T) -8 NIL NIL) (-355 818599 818763 818983 "FGLMICPK" 819341 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-354 814468 818524 818581 "FFX" 818586 NIL FFX (NIL T NIL) -8 NIL NIL) (-353 814069 814130 814265 "FFSLPE" 814401 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-352 813573 813609 813818 "FFPOLY2" 814027 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-351 809566 810345 811141 "FFPOLY" 812809 NIL FFPOLY (NIL T) -7 NIL NIL) (-350 805454 809485 809548 "FFP" 809553 NIL FFP (NIL T NIL) -8 NIL NIL) (-349 800617 804797 804987 "FFNBX" 805308 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-348 795593 799752 800010 "FFNBP" 800471 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-347 790263 794877 795088 "FFNB" 795426 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-346 789095 789293 789608 "FFINTBAS" 790060 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-345 785381 787554 787582 "FFIELDC" 788202 T FFIELDC (NIL) -9 NIL 788578) (-344 784044 784414 784911 "FFIELDC-" 784916 NIL FFIELDC- (NIL T) -8 NIL NIL) (-343 783614 783659 783783 "FFHOM" 783986 NIL FFHOM (NIL T T T) -7 NIL NIL) (-342 781312 781796 782313 "FFF" 783129 NIL FFF (NIL T) -7 NIL NIL) (-341 776967 781054 781155 "FFCGX" 781255 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-340 772636 776699 776806 "FFCGP" 776910 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-339 767856 772363 772471 "FFCG" 772572 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-338 767267 767310 767545 "FFCAT2" 767807 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-337 749334 758361 758447 "FFCAT" 763612 NIL FFCAT (NIL T T T) -9 NIL 765063) (-336 744532 745579 746893 "FFCAT-" 748123 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-335 739967 744443 744507 "FF" 744512 NIL FF (NIL NIL NIL) -8 NIL NIL) (-334 729181 732939 734159 "FEXPR" 738819 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-333 728181 728616 728657 "FEVALAB" 728741 NIL FEVALAB (NIL T) -9 NIL 729002) (-332 727340 727550 727888 "FEVALAB-" 727893 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-331 724406 725121 725236 "FDIVCAT" 726804 NIL FDIVCAT (NIL T T T T) -9 NIL 727241) (-330 724168 724195 724365 "FDIVCAT-" 724370 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-329 723388 723475 723752 "FDIV2" 724075 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-328 721981 722771 722974 "FDIV" 723287 NIL FDIV (NIL T T T T) -8 NIL NIL) (-327 720667 720926 721215 "FCPAK1" 721712 T FCPAK1 (NIL) -7 NIL NIL) (-326 719795 720167 720308 "FCOMP" 720558 NIL FCOMP (NIL T) -8 NIL NIL) (-325 703430 706844 710405 "FC" 716254 T FC (NIL) -8 NIL NIL) (-324 696085 700064 700104 "FAXF" 701906 NIL FAXF (NIL T) -9 NIL 702598) (-323 693364 694019 694844 "FAXF-" 695309 NIL FAXF- (NIL T T) -8 NIL NIL) (-322 688464 692740 692916 "FARRAY" 693221 NIL FARRAY (NIL T) -8 NIL NIL) (-321 683878 685903 685956 "FAMR" 686979 NIL FAMR (NIL T T) -9 NIL 687439) (-320 682768 683070 683505 "FAMR-" 683510 NIL FAMR- (NIL T T T) -8 NIL NIL) (-319 681964 682690 682743 "FAMONOID" 682748 NIL FAMONOID (NIL T) -8 NIL NIL) (-318 679794 680478 680531 "FAMONC" 681472 NIL FAMONC (NIL T T) -9 NIL 681858) (-317 678486 679548 679685 "FAGROUP" 679690 NIL FAGROUP (NIL T) -8 NIL NIL) (-316 676281 676600 677003 "FACUTIL" 678167 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-315 675380 675565 675787 "FACTFUNC" 676091 NIL FACTFUNC (NIL T) -7 NIL NIL) (-314 667787 674631 674843 "EXPUPXS" 675236 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-313 665270 665810 666396 "EXPRTUBE" 667221 T EXPRTUBE (NIL) -7 NIL NIL) (-312 661464 662056 662793 "EXPRODE" 664609 NIL EXPRODE (NIL T T) -7 NIL NIL) (-311 655871 656458 657271 "EXPR2UPS" 660762 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-310 655507 655564 655671 "EXPR2" 655808 NIL EXPR2 (NIL T T) -7 NIL NIL) (-309 640942 654162 654590 "EXPR" 655111 NIL EXPR (NIL T) -8 NIL NIL) (-308 632375 640074 640371 "EXPEXPAN" 640779 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-307 631882 632099 632190 "EXITAST" 632304 T EXITAST (NIL) -8 NIL NIL) (-306 631709 631839 631868 "EXIT" 631873 T EXIT (NIL) -8 NIL NIL) (-305 631336 631398 631511 "EVALCYC" 631641 NIL EVALCYC (NIL T) -7 NIL NIL) (-304 630877 630995 631036 "EVALAB" 631206 NIL EVALAB (NIL T) -9 NIL 631310) (-303 630358 630480 630701 "EVALAB-" 630706 NIL EVALAB- (NIL T T) -8 NIL NIL) (-302 627861 629129 629157 "EUCDOM" 629712 T EUCDOM (NIL) -9 NIL 630062) (-301 626266 626708 627298 "EUCDOM-" 627303 NIL EUCDOM- (NIL T) -8 NIL NIL) (-300 625898 625955 626064 "ESTOOLS2" 626203 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-299 625649 625691 625771 "ESTOOLS1" 625850 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-298 613189 615947 618697 "ESTOOLS" 622919 T ESTOOLS (NIL) -7 NIL NIL) (-297 612934 612966 613048 "ESCONT1" 613151 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-296 609309 610069 610849 "ESCONT" 612174 T ESCONT (NIL) -7 NIL NIL) (-295 608984 609034 609134 "ES2" 609253 NIL ES2 (NIL T T) -7 NIL NIL) (-294 608614 608672 608781 "ES1" 608920 NIL ES1 (NIL T T) -7 NIL NIL) (-293 602539 604267 604295 "ES" 607063 T ES (NIL) -9 NIL 608472) (-292 597486 598773 600590 "ES-" 600754 NIL ES- (NIL T) -8 NIL NIL) (-291 596702 596831 597007 "ERROR" 597330 T ERROR (NIL) -7 NIL NIL) (-290 590207 596561 596652 "EQTBL" 596657 NIL EQTBL (NIL T T) -8 NIL NIL) (-289 589839 589896 590005 "EQ2" 590144 NIL EQ2 (NIL T T) -7 NIL NIL) (-288 582396 585153 586602 "EQ" 588423 NIL -3890 (NIL T) -8 NIL NIL) (-287 577688 578734 579827 "EP" 581335 NIL EP (NIL T) -7 NIL NIL) (-286 576270 576571 576888 "ENV" 577391 T ENV (NIL) -8 NIL NIL) (-285 575469 575989 576017 "ENTIRER" 576022 T ENTIRER (NIL) -9 NIL 576068) (-284 572027 573478 573848 "EMR" 575268 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-283 571171 571356 571410 "ELTAGG" 571790 NIL ELTAGG (NIL T T) -9 NIL 572001) (-282 570890 570952 571093 "ELTAGG-" 571098 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-281 570679 570708 570762 "ELTAB" 570846 NIL ELTAB (NIL T T) -9 NIL NIL) (-280 569805 569951 570150 "ELFUTS" 570530 NIL ELFUTS (NIL T T) -7 NIL NIL) (-279 569547 569603 569631 "ELEMFUN" 569736 T ELEMFUN (NIL) -9 NIL NIL) (-278 569417 569438 569506 "ELEMFUN-" 569511 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-277 564308 567517 567558 "ELAGG" 568498 NIL ELAGG (NIL T) -9 NIL 568961) (-276 562593 563027 563690 "ELAGG-" 563695 NIL ELAGG- (NIL T T) -8 NIL NIL) (-275 561250 561530 561825 "ELABEXPR" 562318 T ELABEXPR (NIL) -8 NIL NIL) (-274 554243 555917 556744 "EFUPXS" 560526 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-273 547820 549494 550304 "EFULS" 553519 NIL EFULS (NIL T T T) -8 NIL NIL) (-272 545242 545600 546079 "EFSTRUC" 547452 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-271 534314 535879 537439 "EF" 543757 NIL EF (NIL T T) -7 NIL NIL) (-270 533415 533799 533948 "EAB" 534185 T EAB (NIL) -8 NIL NIL) (-269 532624 533374 533402 "E04UCFA" 533407 T E04UCFA (NIL) -8 NIL NIL) (-268 531833 532583 532611 "E04NAFA" 532616 T E04NAFA (NIL) -8 NIL NIL) (-267 531042 531792 531820 "E04MBFA" 531825 T E04MBFA (NIL) -8 NIL NIL) (-266 530251 531001 531029 "E04JAFA" 531034 T E04JAFA (NIL) -8 NIL NIL) (-265 529462 530210 530238 "E04GCFA" 530243 T E04GCFA (NIL) -8 NIL NIL) (-264 528673 529421 529449 "E04FDFA" 529454 T E04FDFA (NIL) -8 NIL NIL) (-263 527882 528632 528660 "E04DGFA" 528665 T E04DGFA (NIL) -8 NIL NIL) (-262 522060 523407 524771 "E04AGNT" 526538 T E04AGNT (NIL) -7 NIL NIL) (-261 520784 521264 521304 "DVARCAT" 521779 NIL DVARCAT (NIL T) -9 NIL 521978) (-260 519988 520200 520514 "DVARCAT-" 520519 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-259 512929 519787 519916 "DSMP" 519921 NIL DSMP (NIL T T T) -8 NIL NIL) (-258 512594 512653 512751 "DROPT1" 512864 NIL DROPT1 (NIL T) -7 NIL NIL) (-257 507709 508835 509972 "DROPT0" 511477 T DROPT0 (NIL) -7 NIL NIL) (-256 502519 503654 504722 "DROPT" 506661 T DROPT (NIL) -8 NIL NIL) (-255 500864 501189 501575 "DRAWPT" 502153 T DRAWPT (NIL) -7 NIL NIL) (-254 500497 500550 500668 "DRAWHACK" 500805 NIL DRAWHACK (NIL T) -7 NIL NIL) (-253 499228 499497 499788 "DRAWCX" 500226 T DRAWCX (NIL) -7 NIL NIL) (-252 498744 498812 498963 "DRAWCURV" 499154 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-251 489215 491174 493289 "DRAWCFUN" 496649 T DRAWCFUN (NIL) -7 NIL NIL) (-250 483802 484725 485804 "DRAW" 488189 NIL DRAW (NIL T) -7 NIL NIL) (-249 480615 482497 482538 "DQAGG" 483167 NIL DQAGG (NIL T) -9 NIL 483440) (-248 469170 475831 475914 "DPOLCAT" 477766 NIL DPOLCAT (NIL T T T T) -9 NIL 478311) (-247 464060 465389 467330 "DPOLCAT-" 467335 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-246 457222 463921 464019 "DPMO" 464024 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-245 450287 457002 457169 "DPMM" 457174 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-244 449707 449910 450024 "DOMAIN" 450193 T DOMAIN (NIL) -8 NIL NIL) (-243 443489 449342 449494 "DMP" 449608 NIL DMP (NIL NIL T) -8 NIL NIL) (-242 443089 443145 443289 "DLP" 443427 NIL DLP (NIL T) -7 NIL NIL) (-241 436735 442190 442417 "DLIST" 442894 NIL DLIST (NIL T) -8 NIL NIL) (-240 433582 435590 435631 "DLAGG" 436181 NIL DLAGG (NIL T) -9 NIL 436410) (-239 432432 433062 433090 "DIVRING" 433182 T DIVRING (NIL) -9 NIL 433265) (-238 431669 431859 432159 "DIVRING-" 432164 NIL DIVRING- (NIL T) -8 NIL NIL) (-237 429771 430128 430534 "DISPLAY" 431283 T DISPLAY (NIL) -7 NIL NIL) (-236 428619 428822 429087 "DIRPROD2" 429564 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-235 422568 428533 428596 "DIRPROD" 428601 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-234 412113 418058 418111 "DIRPCAT" 418521 NIL DIRPCAT (NIL NIL T) -9 NIL 419361) (-233 409439 410081 410962 "DIRPCAT-" 411299 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-232 408726 408886 409072 "DIOSP" 409273 T DIOSP (NIL) -7 NIL NIL) (-231 405428 407638 407679 "DIOPS" 408113 NIL DIOPS (NIL T) -9 NIL 408342) (-230 404977 405091 405282 "DIOPS-" 405287 NIL DIOPS- (NIL T T) -8 NIL NIL) (-229 403889 404483 404511 "DIFRING" 404698 T DIFRING (NIL) -9 NIL 404808) (-228 403535 403612 403764 "DIFRING-" 403769 NIL DIFRING- (NIL T) -8 NIL NIL) (-227 401360 402598 402639 "DIFEXT" 403002 NIL DIFEXT (NIL T) -9 NIL 403296) (-226 399645 400073 400739 "DIFEXT-" 400744 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-225 396967 399177 399218 "DIAGG" 399223 NIL DIAGG (NIL T) -9 NIL 399243) (-224 396351 396508 396760 "DIAGG-" 396765 NIL DIAGG- (NIL T T) -8 NIL NIL) (-223 391815 395310 395587 "DHMATRIX" 396120 NIL DHMATRIX (NIL T) -8 NIL NIL) (-222 387427 388336 389346 "DFSFUN" 390825 T DFSFUN (NIL) -7 NIL NIL) (-221 382547 386358 386670 "DFLOAT" 387135 T DFLOAT (NIL) -8 NIL NIL) (-220 380775 381056 381452 "DFINTTLS" 382255 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-219 377840 378796 379196 "DERHAM" 380441 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-218 375689 377615 377704 "DEQUEUE" 377784 NIL DEQUEUE (NIL T) -8 NIL NIL) (-217 374904 375037 375233 "DEGRED" 375551 NIL DEGRED (NIL T T) -7 NIL NIL) (-216 371479 372179 372987 "DEFINTRF" 374177 NIL DEFINTRF (NIL T) -7 NIL NIL) (-215 369118 369559 370130 "DEFINTEF" 371026 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-214 368495 368738 368853 "DEFAST" 369023 T DEFAST (NIL) -8 NIL NIL) (-213 362404 367936 368102 "DECIMAL" 368349 T DECIMAL (NIL) -8 NIL NIL) (-212 359916 360374 360880 "DDFACT" 361948 NIL DDFACT (NIL T T) -7 NIL NIL) (-211 359512 359555 359706 "DBLRESP" 359867 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-210 357222 357556 357925 "DBASE" 359270 NIL DBASE (NIL T) -8 NIL NIL) (-209 356491 356702 356848 "DATABUF" 357121 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-208 355624 356450 356478 "D03FAFA" 356483 T D03FAFA (NIL) -8 NIL NIL) (-207 354758 355583 355611 "D03EEFA" 355616 T D03EEFA (NIL) -8 NIL NIL) (-206 352708 353174 353663 "D03AGNT" 354289 T D03AGNT (NIL) -7 NIL NIL) (-205 352024 352667 352695 "D02EJFA" 352700 T D02EJFA (NIL) -8 NIL NIL) (-204 351340 351983 352011 "D02CJFA" 352016 T D02CJFA (NIL) -8 NIL NIL) (-203 350656 351299 351327 "D02BHFA" 351332 T D02BHFA (NIL) -8 NIL NIL) (-202 349972 350615 350643 "D02BBFA" 350648 T D02BBFA (NIL) -8 NIL NIL) (-201 343170 344758 346364 "D02AGNT" 348386 T D02AGNT (NIL) -7 NIL NIL) (-200 340939 341461 342007 "D01WGTS" 342644 T D01WGTS (NIL) -7 NIL NIL) (-199 340034 340898 340926 "D01TRNS" 340931 T D01TRNS (NIL) -8 NIL NIL) (-198 339129 339993 340021 "D01GBFA" 340026 T D01GBFA (NIL) -8 NIL NIL) (-197 338224 339088 339116 "D01FCFA" 339121 T D01FCFA (NIL) -8 NIL NIL) (-196 337319 338183 338211 "D01ASFA" 338216 T D01ASFA (NIL) -8 NIL NIL) (-195 336414 337278 337306 "D01AQFA" 337311 T D01AQFA (NIL) -8 NIL NIL) (-194 335509 336373 336401 "D01APFA" 336406 T D01APFA (NIL) -8 NIL NIL) (-193 334604 335468 335496 "D01ANFA" 335501 T D01ANFA (NIL) -8 NIL NIL) (-192 333699 334563 334591 "D01AMFA" 334596 T D01AMFA (NIL) -8 NIL NIL) (-191 332794 333658 333686 "D01ALFA" 333691 T D01ALFA (NIL) -8 NIL NIL) (-190 331889 332753 332781 "D01AKFA" 332786 T D01AKFA (NIL) -8 NIL NIL) (-189 330984 331848 331876 "D01AJFA" 331881 T D01AJFA (NIL) -8 NIL NIL) (-188 324281 325832 327393 "D01AGNT" 329443 T D01AGNT (NIL) -7 NIL NIL) (-187 323618 323746 323898 "CYCLOTOM" 324149 T CYCLOTOM (NIL) -7 NIL NIL) (-186 320353 321066 321793 "CYCLES" 322911 T CYCLES (NIL) -7 NIL NIL) (-185 319665 319799 319970 "CVMP" 320214 NIL CVMP (NIL T) -7 NIL NIL) (-184 317436 317694 318070 "CTRIGMNP" 319393 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-183 316972 317167 317268 "CTORKIND" 317355 T CTORKIND (NIL) -8 NIL NIL) (-182 316483 316672 316771 "CTORCALL" 316893 T CTORCALL (NIL) -8 NIL NIL) (-181 315898 316106 316220 "CTOR" 316389 T CTOR (NIL) -8 NIL NIL) (-180 315272 315371 315524 "CSTTOOLS" 315795 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-179 311071 311728 312486 "CRFP" 314584 NIL CRFP (NIL T T) -7 NIL NIL) (-178 310573 310792 310884 "CRCEAST" 310999 T CRCEAST (NIL) -8 NIL NIL) (-177 309620 309805 310033 "CRAPACK" 310377 NIL CRAPACK (NIL T) -7 NIL NIL) (-176 309004 309105 309309 "CPMATCH" 309496 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-175 308729 308757 308863 "CPIMA" 308970 NIL CPIMA (NIL T T T) -7 NIL NIL) (-174 305093 305765 306483 "COORDSYS" 308064 NIL COORDSYS (NIL T) -7 NIL NIL) (-173 304477 304606 304756 "CONTOUR" 304963 T CONTOUR (NIL) -8 NIL NIL) (-172 300405 302480 302972 "CONTFRAC" 304017 NIL CONTFRAC (NIL T) -8 NIL NIL) (-171 300285 300306 300334 "CONDUIT" 300371 T CONDUIT (NIL) -9 NIL NIL) (-170 299478 299998 300026 "COMRING" 300031 T COMRING (NIL) -9 NIL 300083) (-169 298559 298836 299020 "COMPPROP" 299314 T COMPPROP (NIL) -8 NIL NIL) (-168 298220 298255 298383 "COMPLPAT" 298518 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-167 297856 297913 298020 "COMPLEX2" 298157 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-166 287933 297665 297774 "COMPLEX" 297779 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 287651 287686 287784 "COMPFACT" 287892 NIL COMPFACT (NIL T T) -7 NIL NIL) (-164 272058 282265 282305 "COMPCAT" 283309 NIL COMPCAT (NIL T) -9 NIL 284704) (-163 261594 264511 268131 "COMPCAT-" 268487 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-162 261323 261351 261454 "COMMUPC" 261560 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-161 261118 261151 261210 "COMMONOP" 261284 T COMMONOP (NIL) -7 NIL NIL) (-160 260722 260922 260997 "COMMAAST" 261063 T COMMAAST (NIL) -8 NIL NIL) (-159 260305 260473 260560 "COMM" 260655 T COMM (NIL) -8 NIL NIL) (-158 259554 259748 259776 "COMBOPC" 260114 T COMBOPC (NIL) -9 NIL 260289) (-157 258450 258660 258902 "COMBINAT" 259344 NIL COMBINAT (NIL T) -7 NIL NIL) (-156 254648 255221 255861 "COMBF" 257872 NIL COMBF (NIL T T) -7 NIL NIL) (-155 253434 253764 253999 "COLOR" 254433 T COLOR (NIL) -8 NIL NIL) (-154 252937 253155 253247 "COLONAST" 253362 T COLONAST (NIL) -8 NIL NIL) (-153 252577 252624 252749 "CMPLXRT" 252884 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-152 252052 252277 252376 "CLLCTAST" 252498 T CLLCTAST (NIL) -8 NIL NIL) (-151 247554 248582 249662 "CLIP" 250992 T CLIP (NIL) -7 NIL NIL) (-150 245936 246660 246899 "CLIF" 247381 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-149 242158 244082 244123 "CLAGG" 245052 NIL CLAGG (NIL T) -9 NIL 245588) (-148 240580 241037 241620 "CLAGG-" 241625 NIL CLAGG- (NIL T T) -8 NIL NIL) (-147 240124 240209 240349 "CINTSLPE" 240489 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-146 237625 238096 238644 "CHVAR" 239652 NIL CHVAR (NIL T T T) -7 NIL NIL) (-145 236888 237408 237436 "CHARZ" 237441 T CHARZ (NIL) -9 NIL 237456) (-144 236642 236682 236760 "CHARPOL" 236842 NIL CHARPOL (NIL T) -7 NIL NIL) (-143 235789 236342 236370 "CHARNZ" 236417 T CHARNZ (NIL) -9 NIL 236473) (-142 233814 234479 234814 "CHAR" 235474 T CHAR (NIL) -8 NIL NIL) (-141 233540 233601 233629 "CFCAT" 233740 T CFCAT (NIL) -9 NIL NIL) (-140 232785 232896 233078 "CDEN" 233424 NIL CDEN (NIL T T T) -7 NIL NIL) (-139 228777 231938 232218 "CCLASS" 232525 T CCLASS (NIL) -8 NIL NIL) (-138 228696 228722 228757 "CATEGORY" 228762 T -10 (NIL) -8 NIL NIL) (-137 228170 228396 228495 "CATAST" 228617 T CATAST (NIL) -8 NIL NIL) (-136 227673 227891 227983 "CASEAST" 228098 T CASEAST (NIL) -8 NIL NIL) (-135 226781 226929 227150 "CARTEN2" 227520 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-134 221833 222810 223563 "CARTEN" 226084 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-133 220175 220983 221240 "CARD" 221596 T CARD (NIL) -8 NIL NIL) (-132 219778 219979 220054 "CAPSLAST" 220120 T CAPSLAST (NIL) -8 NIL NIL) (-131 219150 219478 219506 "CACHSET" 219638 T CACHSET (NIL) -9 NIL 219715) (-130 218646 218942 218970 "CABMON" 219020 T CABMON (NIL) -9 NIL 219076) (-129 214594 218593 218627 "BYTEARY" 218632 T BYTEARY (NIL) -8 NIL NIL) (-128 213521 213949 214145 "BYTE" 214418 T BYTE (NIL) -8 NIL NIL) (-127 211080 213213 213320 "BTREE" 213447 NIL BTREE (NIL T) -8 NIL NIL) (-126 208580 210728 210850 "BTOURN" 210990 NIL BTOURN (NIL T) -8 NIL NIL) (-125 206000 208051 208092 "BTCAT" 208160 NIL BTCAT (NIL T) -9 NIL 208237) (-124 205667 205747 205896 "BTCAT-" 205901 NIL BTCAT- (NIL T T) -8 NIL NIL) (-123 200959 204810 204838 "BTAGG" 205060 T BTAGG (NIL) -9 NIL 205221) (-122 200449 200574 200780 "BTAGG-" 200785 NIL BTAGG- (NIL T) -8 NIL NIL) (-121 197495 199727 199942 "BSTREE" 200266 NIL BSTREE (NIL T) -8 NIL NIL) (-120 196633 196759 196943 "BRILL" 197351 NIL BRILL (NIL T) -7 NIL NIL) (-119 193335 195361 195402 "BRAGG" 196051 NIL BRAGG (NIL T) -9 NIL 196308) (-118 191867 192272 192826 "BRAGG-" 192831 NIL BRAGG- (NIL T T) -8 NIL NIL) (-117 185154 191213 191397 "BPADICRT" 191715 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-116 183506 185091 185136 "BPADIC" 185141 NIL BPADIC (NIL NIL) -8 NIL NIL) (-115 183204 183234 183348 "BOUNDZRO" 183470 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-114 180825 181269 181789 "BOP1" 182717 NIL BOP1 (NIL T) -7 NIL NIL) (-113 176340 177431 178298 "BOP" 179978 T BOP (NIL) -8 NIL NIL) (-112 175078 175764 175957 "BOOLEAN" 176167 T BOOLEAN (NIL) -8 NIL NIL) (-111 174440 174818 174872 "BMODULE" 174877 NIL BMODULE (NIL T T) -9 NIL 174942) (-110 170270 174238 174311 "BITS" 174387 T BITS (NIL) -8 NIL NIL) (-109 169367 169802 169954 "BINFILE" 170138 T BINFILE (NIL) -8 NIL NIL) (-108 168779 168901 169043 "BINDING" 169245 T BINDING (NIL) -8 NIL NIL) (-107 162692 168223 168388 "BINARY" 168634 T BINARY (NIL) -8 NIL NIL) (-106 160519 161947 161988 "BGAGG" 162248 NIL BGAGG (NIL T) -9 NIL 162385) (-105 160350 160382 160473 "BGAGG-" 160478 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 159448 159734 159939 "BFUNCT" 160165 T BFUNCT (NIL) -8 NIL NIL) (-103 158132 158313 158601 "BEZOUT" 159272 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 154651 156984 157314 "BBTREE" 157835 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154385 154438 154466 "BASTYPE" 154585 T BASTYPE (NIL) -9 NIL NIL) (-100 154237 154266 154339 "BASTYPE-" 154344 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 153675 153751 153901 "BALFACT" 154148 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 152558 153090 153276 "AUTOMOR" 153520 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152284 152289 152315 "ATTREG" 152320 T ATTREG (NIL) -9 NIL NIL) (-96 150563 150981 151333 "ATTRBUT" 151950 T ATTRBUT (NIL) -8 NIL NIL) (-95 150198 150391 150457 "ATTRAST" 150515 T ATTRAST (NIL) -8 NIL NIL) (-94 149734 149847 149873 "ATRIG" 150074 T ATRIG (NIL) -9 NIL NIL) (-93 149543 149584 149671 "ATRIG-" 149676 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149165 149325 149351 "ASTCAT" 149409 T ASTCAT (NIL) -9 NIL 149472) (-91 148892 148951 149070 "ASTCAT-" 149075 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147089 148668 148756 "ASTACK" 148835 NIL ASTACK (NIL T) -8 NIL NIL) (-89 145594 145891 146256 "ASSOCEQ" 146771 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 144648 145253 145377 "ASP9" 145501 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 143539 144253 144395 "ASP80" 144537 NIL ASP80 (NIL NIL) -8 NIL NIL) (-86 143303 143487 143526 "ASP8" 143531 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 142279 142980 143098 "ASP78" 143216 NIL ASP78 (NIL NIL) -8 NIL NIL) (-84 141270 141959 142076 "ASP77" 142193 NIL ASP77 (NIL NIL) -8 NIL NIL) (-83 140204 140908 141039 "ASP74" 141170 NIL ASP74 (NIL NIL) -8 NIL NIL) (-82 139126 139839 139971 "ASP73" 140103 NIL ASP73 (NIL NIL) -8 NIL NIL) (-81 138047 138761 138893 "ASP7" 139025 NIL ASP7 (NIL NIL) -8 NIL NIL) (-80 137024 137724 137842 "ASP6" 137960 NIL ASP6 (NIL NIL) -8 NIL NIL) (-79 135994 136701 136819 "ASP55" 136937 NIL ASP55 (NIL NIL) -8 NIL NIL) (-78 134966 135668 135787 "ASP50" 135906 NIL ASP50 (NIL NIL) -8 NIL NIL) (-77 134076 134667 134777 "ASP49" 134887 NIL ASP49 (NIL NIL) -8 NIL NIL) (-76 132883 133615 133783 "ASP42" 133965 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-75 131682 132416 132586 "ASP41" 132770 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-74 130792 131383 131493 "ASP4" 131603 NIL ASP4 (NIL NIL) -8 NIL NIL) (-73 129764 130469 130587 "ASP35" 130705 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 129529 129712 129751 "ASP34" 129756 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129266 129333 129409 "ASP33" 129484 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128183 128901 129033 "ASP31" 129165 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 127948 128131 128170 "ASP30" 128175 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 127683 127752 127828 "ASP29" 127903 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127448 127631 127670 "ASP28" 127675 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127213 127396 127435 "ASP27" 127440 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126319 126911 127022 "ASP24" 127133 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125257 125960 126090 "ASP20" 126220 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 124223 124931 125050 "ASP19" 125169 NIL ASP19 (NIL NIL) -8 NIL NIL) (-62 123960 124027 124103 "ASP12" 124178 NIL ASP12 (NIL NIL) -8 NIL NIL) (-61 122834 123559 123703 "ASP10" 123847 NIL ASP10 (NIL NIL) -8 NIL NIL) (-60 121944 122535 122645 "ASP1" 122755 NIL ASP1 (NIL NIL) -8 NIL NIL) (-59 119843 121788 121879 "ARRAY2" 121884 NIL ARRAY2 (NIL T) -8 NIL NIL) (-58 118875 119048 119269 "ARRAY12" 119666 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-57 114691 118523 118637 "ARRAY1" 118792 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 109050 110921 110996 "ARR2CAT" 113626 NIL ARR2CAT (NIL T T T) -9 NIL 114384) (-55 106484 107228 108182 "ARR2CAT-" 108187 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-54 105232 105384 105690 "APPRULE" 106320 NIL APPRULE (NIL T T T) -7 NIL NIL) (-53 104883 104931 105050 "APPLYORE" 105178 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-52 104161 104284 104441 "ANY1" 104757 NIL ANY1 (NIL T) -7 NIL NIL) (-51 103135 103426 103621 "ANY" 103984 T ANY (NIL) -8 NIL NIL) (-50 100700 101572 101899 "ANTISYM" 102859 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-49 100215 100404 100501 "ANON" 100621 T ANON (NIL) -8 NIL NIL) (-48 94358 98756 99209 "AN" 99780 T AN (NIL) -8 NIL NIL) (-47 90739 92093 92144 "AMR" 92892 NIL AMR (NIL T T) -9 NIL 93492) (-46 89851 90072 90435 "AMR-" 90440 NIL AMR- (NIL T T T) -8 NIL NIL) (-45 74407 89768 89829 "ALIST" 89834 NIL ALIST (NIL T T) -8 NIL NIL) (-44 71276 74001 74170 "ALGSC" 74325 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-43 67832 68386 68993 "ALGPKG" 70716 NIL ALGPKG (NIL T T) -7 NIL NIL) (-42 67109 67210 67394 "ALGMFACT" 67718 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 62848 63533 64188 "ALGMANIP" 66632 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54265 62474 62624 "ALGFF" 62781 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-39 53461 53592 53771 "ALGFACT" 54123 NIL ALGFACT (NIL T) -7 NIL NIL) (-38 52491 53057 53095 "ALGEBRA" 53155 NIL ALGEBRA (NIL T) -9 NIL 53214) (-37 52209 52268 52400 "ALGEBRA-" 52405 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-36 34475 50212 50264 "ALAGG" 50400 NIL ALAGG (NIL T T) -9 NIL 50561) (-35 34011 34124 34150 "AHYP" 34351 T AHYP (NIL) -9 NIL NIL) (-34 32942 33190 33216 "AGG" 33715 T AGG (NIL) -9 NIL 33994) (-33 32376 32538 32752 "AGG-" 32757 NIL AGG- (NIL T) -8 NIL NIL) (-32 30053 30475 30893 "AF" 32018 NIL AF (NIL T T) -7 NIL NIL) (-31 29560 29778 29868 "ADDAST" 29981 T ADDAST (NIL) -8 NIL NIL) (-30 28829 29087 29243 "ACPLOT" 29422 T ACPLOT (NIL) -8 NIL NIL) (-29 18356 26221 26272 "ACFS" 26983 NIL ACFS (NIL T) -9 NIL 27222) (-28 16370 16860 17635 "ACFS-" 17640 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14589 14615 "ACF" 15494 T ACF (NIL) -9 NIL 15906) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL)) \ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index c684054d..b3ed780e 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,3962 +1,3962 @@
-(730437 . 3432414587)
+(730693 . 3432506633)
(((*1 *2 *3 *4)
- (|partial| -12 (-5 *3 (-1229 *4)) (-4 *4 (-619 (-536)))
- (-5 *2 (-1229 (-400 (-536)))) (-5 *1 (-1257 *4)))))
+ (|partial| -12 (-5 *3 (-1231 *4)) (-4 *4 (-621 (-538)))
+ (-5 *2 (-1231 (-402 (-538)))) (-5 *1 (-1259 *4)))))
(((*1 *2 *3)
- (|partial| -12 (-5 *3 (-1229 *4)) (-4 *4 (-619 (-536)))
- (-5 *2 (-1229 (-536))) (-5 *1 (-1257 *4)))))
+ (|partial| -12 (-5 *3 (-1231 *4)) (-4 *4 (-621 (-538)))
+ (-5 *2 (-1231 (-538))) (-5 *1 (-1259 *4)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-1229 *4)) (-4 *4 (-619 (-536))) (-5 *2 (-112))
- (-5 *1 (-1257 *4)))))
+ (-12 (-5 *3 (-1231 *4)) (-4 *4 (-621 (-538))) (-5 *2 (-112))
+ (-5 *1 (-1259 *4)))))
(((*1 *2 *3)
- (-12 (-4 *5 (-13 (-596 *2) (-170))) (-5 *2 (-864 *4)) (-5 *1 (-168 *4 *5 *3))
- (-4 *4 (-1072)) (-4 *3 (-164 *5))))
+ (-12 (-4 *5 (-13 (-598 *2) (-170))) (-5 *2 (-866 *4)) (-5 *1 (-168 *4 *5 *3))
+ (-4 *4 (-1074)) (-4 *3 (-164 *5))))
((*1 *2 *3)
- (-12 (-5 *3 (-620 (-1060 (-817 (-371)))))
- (-5 *2 (-620 (-1060 (-817 (-219))))) (-5 *1 (-296))))
- ((*1 *1 *2) (-12 (-5 *2 (-219)) (-5 *1 (-371))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-838)) (-5 *3 (-536)) (-5 *1 (-386))))
+ (-12 (-5 *3 (-622 (-1062 (-819 (-373)))))
+ (-5 *2 (-622 (-1062 (-819 (-221))))) (-5 *1 (-298))))
+ ((*1 *1 *2) (-12 (-5 *2 (-221)) (-5 *1 (-373))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-840)) (-5 *3 (-538)) (-5 *1 (-388))))
((*1 *1 *2)
- (-12 (-5 *2 (-1229 *3)) (-4 *3 (-170)) (-4 *1 (-403 *3 *4))
- (-4 *4 (-1205 *3))))
+ (-12 (-5 *2 (-1231 *3)) (-4 *3 (-170)) (-4 *1 (-405 *3 *4))
+ (-4 *4 (-1207 *3))))
((*1 *2 *1)
- (-12 (-4 *1 (-403 *3 *4)) (-4 *3 (-170)) (-4 *4 (-1205 *3))
- (-5 *2 (-1229 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1229 *3)) (-4 *3 (-170)) (-4 *1 (-411 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-411 *3)) (-4 *3 (-170)) (-5 *2 (-1229 *3))))
+ (-12 (-4 *1 (-405 *3 *4)) (-4 *3 (-170)) (-4 *4 (-1207 *3))
+ (-5 *2 (-1231 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1231 *3)) (-4 *3 (-170)) (-4 *1 (-413 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-413 *3)) (-4 *3 (-170)) (-5 *2 (-1231 *3))))
((*1 *1 *2)
- (-12 (-5 *2 (-398 *1)) (-4 *1 (-414 *3)) (-4 *3 (-543)) (-4 *3 (-825))))
+ (-12 (-5 *2 (-400 *1)) (-4 *1 (-416 *3)) (-4 *3 (-545)) (-4 *3 (-827))))
((*1 *1 *2)
- (-12 (-5 *2 (-620 *6)) (-4 *6 (-1037 *3 *4 *5)) (-4 *3 (-1023))
- (-4 *4 (-771)) (-4 *5 (-825)) (-5 *1 (-455 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-525))))
- ((*1 *2 *1) (-12 (-4 *1 (-596 *2)) (-4 *2 (-1183))))
- ((*1 *1 *2) (-12 (-4 *3 (-170)) (-4 *1 (-703 *3 *2)) (-4 *2 (-1205 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-620 (-864 *3))) (-5 *1 (-864 *3)) (-4 *3 (-1072))))
- ((*1 *1 *2) (-12 (-5 *2 (-620 *3)) (-4 *3 (-1023)) (-4 *1 (-954 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1147)) (-5 *1 (-1034))))
+ (-12 (-5 *2 (-622 *6)) (-4 *6 (-1039 *3 *4 *5)) (-4 *3 (-1025))
+ (-4 *4 (-773)) (-4 *5 (-827)) (-5 *1 (-457 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1076)) (-5 *1 (-527))))
+ ((*1 *2 *1) (-12 (-4 *1 (-598 *2)) (-4 *2 (-1185))))
+ ((*1 *1 *2) (-12 (-4 *3 (-170)) (-4 *1 (-705 *3 *2)) (-4 *2 (-1207 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-622 (-866 *3))) (-5 *1 (-866 *3)) (-4 *3 (-1074))))
+ ((*1 *1 *2) (-12 (-5 *2 (-622 *3)) (-4 *3 (-1025)) (-4 *1 (-956 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1149)) (-5 *1 (-1036))))
((*1 *1 *2)
- (-12 (-5 *2 (-920 *3)) (-4 *3 (-1023)) (-4 *1 (-1037 *3 *4 *5))
- (-4 *5 (-596 (-1147))) (-4 *4 (-771)) (-4 *5 (-825))))
+ (-12 (-5 *2 (-922 *3)) (-4 *3 (-1025)) (-4 *1 (-1039 *3 *4 *5))
+ (-4 *5 (-598 (-1149))) (-4 *4 (-773)) (-4 *5 (-827))))
((*1 *1 *2)
- (-3886
- (-12 (-5 *2 (-920 (-536))) (-4 *1 (-1037 *3 *4 *5))
- (-12 (-3671 (-4 *3 (-38 (-400 (-536))))) (-4 *3 (-38 (-536)))
- (-4 *5 (-596 (-1147))))
- (-4 *3 (-1023)) (-4 *4 (-771)) (-4 *5 (-825)))
- (-12 (-5 *2 (-920 (-536))) (-4 *1 (-1037 *3 *4 *5))
- (-12 (-4 *3 (-38 (-400 (-536)))) (-4 *5 (-596 (-1147)))) (-4 *3 (-1023))
- (-4 *4 (-771)) (-4 *5 (-825)))))
+ (-3891
+ (-12 (-5 *2 (-922 (-538))) (-4 *1 (-1039 *3 *4 *5))
+ (-12 (-3676 (-4 *3 (-38 (-402 (-538))))) (-4 *3 (-38 (-538)))
+ (-4 *5 (-598 (-1149))))
+ (-4 *3 (-1025)) (-4 *4 (-773)) (-4 *5 (-827)))
+ (-12 (-5 *2 (-922 (-538))) (-4 *1 (-1039 *3 *4 *5))
+ (-12 (-4 *3 (-38 (-402 (-538)))) (-4 *5 (-598 (-1149)))) (-4 *3 (-1025))
+ (-4 *4 (-773)) (-4 *5 (-827)))))
((*1 *1 *2)
- (-12 (-5 *2 (-920 (-400 (-536)))) (-4 *1 (-1037 *3 *4 *5))
- (-4 *3 (-38 (-400 (-536)))) (-4 *5 (-596 (-1147))) (-4 *3 (-1023))
- (-4 *4 (-771)) (-4 *5 (-825))))
+ (-12 (-5 *2 (-922 (-402 (-538)))) (-4 *1 (-1039 *3 *4 *5))
+ (-4 *3 (-38 (-402 (-538)))) (-4 *5 (-598 (-1149))) (-4 *3 (-1025))
+ (-4 *4 (-773)) (-4 *5 (-827))))
((*1 *2 *3)
- (-12 (-5 *3 (-2 (|:| |val| (-620 *7)) (|:| -1655 *8)))
- (-4 *7 (-1037 *4 *5 *6)) (-4 *8 (-1043 *4 *5 *6 *7)) (-4 *4 (-444))
- (-4 *5 (-771)) (-4 *6 (-825)) (-5 *2 (-1129))
- (-5 *1 (-1041 *4 *5 *6 *7 *8))))
- ((*1 *2 *1) (-12 (-5 *2 (-1147)) (-5 *1 (-1053))))
- ((*1 *1 *2) (-12 (-4 *1 (-1065 *2)) (-4 *2 (-1183))))
+ (-12 (-5 *3 (-2 (|:| |val| (-622 *7)) (|:| -1660 *8)))
+ (-4 *7 (-1039 *4 *5 *6)) (-4 *8 (-1045 *4 *5 *6 *7)) (-4 *4 (-446))
+ (-4 *5 (-773)) (-4 *6 (-827)) (-5 *2 (-1131))
+ (-5 *1 (-1043 *4 *5 *6 *7 *8))))
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((*1 *2 *1)
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(-4 *3
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((*1 *1 *2)
(-12
(-5 *2
(-2
- (|:| -4215
- (-2 (|:| |var| (-1147)) (|:| |fn| (-307 (-219)))
- (|:| -1556 (-1060 (-817 (-219)))) (|:| |abserr| (-219))
- (|:| |relerr| (-219))))
- (|:| -2186
+ (|:| -4220
+ (-2 (|:| |var| (-1149)) (|:| |fn| (-309 (-221)))
+ (|:| -1561 (-1062 (-819 (-221)))) (|:| |abserr| (-221))
+ (|:| |relerr| (-221))))
+ (|:| -2191
(-2
(|:| |endPointContinuity|
(-3 (|:| |continuous| "Continuous at the end points")
@@ -3969,8025 +3969,8026 @@
(|:| |notEvaluated|
"End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1124 (-219)))
+ (-3 (|:| |str| (-1126 (-221)))
(|:| |notEvaluated|
"Internal singularities not yet evaluated")))
- (|:| -1556
+ (|:| -1561
(-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 (-546))))
- ((*1 *1 *2 *1 *3) (-12 (-5 *3 (-749)) (-4 *1 (-673 *2)) (-4 *2 (-1072))))
+ (-5 *1 (-548))))
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((*1 *1 *2)
(-12
(-5 *2
(-2
- (|:| -4215
- (-2 (|:| |xinit| (-219)) (|:| |xend| (-219))
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- (|:| |intvals| (-620 (-219))) (|:| |g| (-307 (-219)))
- (|:| |abserr| (-219)) (|:| |relerr| (-219))))
- (|:| -2186
- (-2 (|:| |stiffness| (-371)) (|:| |stability| (-371))
- (|:| |expense| (-371)) (|:| |accuracy| (-371))
- (|:| |intermediateResults| (-371))))))
- (-5 *1 (-781))))
- ((*1 *2 *3 *4)
- (-12 (-5 *2 (-1235)) (-5 *1 (-1161 *3 *4)) (-4 *3 (-1072)) (-4 *4 (-1072)))))
-(((*1 *2 *3)
- (|partial| -12 (-4 *2 (-1072)) (-5 *1 (-1161 *3 *2)) (-4 *3 (-1072)))))
+ (|:| -4220
+ (-2 (|:| |xinit| (-221)) (|:| |xend| (-221))
+ (|:| |fn| (-1231 (-309 (-221)))) (|:| |yinit| (-622 (-221)))
+ (|:| |intvals| (-622 (-221))) (|:| |g| (-309 (-221)))
+ (|:| |abserr| (-221)) (|:| |relerr| (-221))))
+ (|:| -2191
+ (-2 (|:| |stiffness| (-373)) (|:| |stability| (-373))
+ (|:| |expense| (-373)) (|:| |accuracy| (-373))
+ (|:| |intermediateResults| (-373))))))
+ (-5 *1 (-783))))
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+ (|partial| -12 (-4 *2 (-1074)) (-5 *1 (-1163 *3 *2)) (-4 *3 (-1074)))))
(((*1 *2)
- (-12 (-5 *2 (-112)) (-5 *1 (-1161 *3 *4)) (-4 *3 (-1072)) (-4 *4 (-1072)))))
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(((*1 *2)
- (-12 (-5 *2 (-112)) (-5 *1 (-1161 *3 *4)) (-4 *3 (-1072)) (-4 *4 (-1072)))))
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(((*1 *2)
- (-12 (-5 *2 (-112)) (-5 *1 (-1161 *3 *4)) (-4 *3 (-1072)) (-4 *4 (-1072)))))
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(((*1 *2)
- (-12 (-5 *2 (-1235)) (-5 *1 (-1161 *3 *4)) (-4 *3 (-1072)) (-4 *4 (-1072)))))
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(((*1 *2)
- (-12 (-5 *2 (-1235)) (-5 *1 (-1161 *3 *4)) (-4 *3 (-1072)) (-4 *4 (-1072)))))
+ (-12 (-5 *2 (-1237)) (-5 *1 (-1163 *3 *4)) (-4 *3 (-1074)) (-4 *4 (-1074)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-1129)) (-5 *2 (-1235)) (-5 *1 (-1161 *4 *5)) (-4 *4 (-1072))
- (-4 *5 (-1072)))))
+ (-12 (-5 *3 (-1131)) (-5 *2 (-1237)) (-5 *1 (-1163 *4 *5)) (-4 *4 (-1074))
+ (-4 *5 (-1074)))))
(((*1 *2 *3 *3)
- (-12 (-5 *3 (-1129)) (-5 *2 (-1235)) (-5 *1 (-1161 *4 *5)) (-4 *4 (-1072))
- (-4 *5 (-1072)))))
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+ (-4 *5 (-1074)))))
(((*1 *2)
- (-12 (-5 *2 (-1235)) (-5 *1 (-1161 *3 *4)) (-4 *3 (-1072)) (-4 *4 (-1072)))))
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(((*1 *1 *2)
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+ (-12 (-5 *2 (-1 (-221) (-221))) (-5 *3 (-1062 (-221))) (-5 *1 (-903))))
((*1 *1 *2 *2 *2 *2 *3)
- (-12 (-5 *2 (-1 (-219) (-219))) (-5 *3 (-1060 (-219))) (-5 *1 (-901)))))
-(((*1 *2 *1) (-12 (-5 *2 (-1060 (-219))) (-5 *1 (-899))))
- ((*1 *2 *1) (-12 (-5 *2 (-1060 (-219))) (-5 *1 (-901)))))
-(((*1 *2 *1) (-12 (-5 *2 (-620 (-620 (-219)))) (-5 *1 (-901)))))
-(((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-901)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-901)))))
-(((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-901)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-901)))))
-(((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-901)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-901)))))
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+(((*1 *2 *1) (-12 (-5 *2 (-1062 (-221))) (-5 *1 (-901))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1062 (-221))) (-5 *1 (-903)))))
+(((*1 *2 *1) (-12 (-5 *2 (-622 (-622 (-221)))) (-5 *1 (-903)))))
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+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-903)))))
+(((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-903)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-903)))))
+(((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-903)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-903)))))
+(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-903)))))
+(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-903)))))
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+(((*1 *1 *2) (-12 (-5 *2 (-1 (-221) (-221))) (-5 *1 (-901))))
+ ((*1 *1 *2 *3)
+ (-12 (-5 *2 (-1 (-221) (-221))) (-5 *3 (-1062 (-221))) (-5 *1 (-901))))
+ ((*1 *2 *3 *4 *5)
+ (-12 (-5 *4 (-1149)) (-5 *5 (-1062 (-221))) (-5 *2 (-901)) (-5 *1 (-902 *3))
+ (-4 *3 (-598 (-527)))))
+ ((*1 *2 *3 *4)
+ (-12 (-5 *4 (-1149)) (-5 *2 (-901)) (-5 *1 (-902 *3)) (-4 *3 (-598 (-527))))))
+(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-901)))))
+(((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-461))))
+ ((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-461))))
+ ((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-901)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-901)))))
+(((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-461))))
+ ((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-461))))
+ ((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-901)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-901)))))
+(((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-461))))
+ ((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-461))))
+ ((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-901)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-901)))))
(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-901)))))
(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-901)))))
-(((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-901)))))
+(((*1 *2) (-12 (-5 *2 (-538)) (-5 *1 (-901)))))
(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-901)))))
-(((*1 *1 *2) (-12 (-5 *2 (-1 (-219) (-219))) (-5 *1 (-899))))
- ((*1 *1 *2 *3)
- (-12 (-5 *2 (-1 (-219) (-219))) (-5 *3 (-1060 (-219))) (-5 *1 (-899))))
- ((*1 *2 *3 *4 *5)
- (-12 (-5 *4 (-1147)) (-5 *5 (-1060 (-219))) (-5 *2 (-899)) (-5 *1 (-900 *3))
- (-4 *3 (-596 (-525)))))
- ((*1 *2 *3 *4)
- (-12 (-5 *4 (-1147)) (-5 *2 (-899)) (-5 *1 (-900 *3)) (-4 *3 (-596 (-525))))))
-(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-899)))))
-(((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-459))))
- ((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-459))))
- ((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-899)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-899)))))
-(((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-459))))
- ((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-459))))
- ((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-899)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-899)))))
-(((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-459))))
- ((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-459))))
- ((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-899)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-899)))))
-(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-899)))))
-(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-899)))))
-(((*1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-899)))))
-(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-899)))))
-(((*1 *2 *3)
- (-12 (-5 *3 (-620 *7)) (-4 *7 (-924 *4 *6 *5)) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771)) (-5 *2 (-112))
- (-5 *1 (-898 *4 *5 *6 *7))))
+(((*1 *2 *3)
+ (-12 (-5 *3 (-622 *7)) (-4 *7 (-926 *4 *6 *5)) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773)) (-5 *2 (-112))
+ (-5 *1 (-900 *4 *5 *6 *7))))
((*1 *2 *3)
- (-12 (-5 *3 (-620 (-920 *4))) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771)) (-5 *2 (-112))
- (-5 *1 (-898 *4 *5 *6 *7)) (-4 *7 (-924 *4 *6 *5)))))
+ (-12 (-5 *3 (-622 (-922 *4))) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773)) (-5 *2 (-112))
+ (-5 *1 (-900 *4 *5 *6 *7)) (-4 *7 (-926 *4 *6 *5)))))
(((*1 *2 *2)
- (-12 (-4 *3 (-13 (-300) (-145))) (-4 *4 (-13 (-825) (-596 (-1147))))
- (-4 *5 (-771)) (-5 *1 (-898 *3 *4 *5 *2)) (-4 *2 (-924 *3 *5 *4)))))
+ (-12 (-4 *3 (-13 (-302) (-145))) (-4 *4 (-13 (-827) (-598 (-1149))))
+ (-4 *5 (-773)) (-5 *1 (-900 *3 *4 *5 *2)) (-4 *2 (-926 *3 *5 *4)))))
(((*1 *2 *3 *4 *5 *6 *7 *7 *8)
(-12
(-5 *3
- (-2 (|:| |det| *12) (|:| |rows| (-620 (-536))) (|:| |cols| (-620 (-536)))))
- (-5 *4 (-667 *12)) (-5 *5 (-620 (-400 (-920 *9)))) (-5 *6 (-620 (-620 *12)))
- (-5 *7 (-749)) (-5 *8 (-536)) (-4 *9 (-13 (-300) (-145)))
- (-4 *12 (-924 *9 *11 *10)) (-4 *10 (-13 (-825) (-596 (-1147))))
- (-4 *11 (-771))
+ (-2 (|:| |det| *12) (|:| |rows| (-622 (-538))) (|:| |cols| (-622 (-538)))))
+ (-5 *4 (-669 *12)) (-5 *5 (-622 (-402 (-922 *9)))) (-5 *6 (-622 (-622 *12)))
+ (-5 *7 (-751)) (-5 *8 (-538)) (-4 *9 (-13 (-302) (-145)))
+ (-4 *12 (-926 *9 *11 *10)) (-4 *10 (-13 (-827) (-598 (-1149))))
+ (-4 *11 (-773))
(-5 *2
- (-2 (|:| |eqzro| (-620 *12)) (|:| |neqzro| (-620 *12))
- (|:| |wcond| (-620 (-920 *9)))
+ (-2 (|:| |eqzro| (-622 *12)) (|:| |neqzro| (-622 *12))
+ (|:| |wcond| (-622 (-922 *9)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *9))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *9)))))))))
- (-5 *1 (-898 *9 *10 *11 *12)))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *9))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *9)))))))))
+ (-5 *1 (-900 *9 *10 *11 *12)))))
(((*1 *2 *2 *3)
- (-12 (-5 *2 (-667 *7)) (-5 *3 (-620 *7)) (-4 *7 (-924 *4 *6 *5))
- (-4 *4 (-13 (-300) (-145))) (-4 *5 (-13 (-825) (-596 (-1147))))
- (-4 *6 (-771)) (-5 *1 (-898 *4 *5 *6 *7)))))
+ (-12 (-5 *2 (-669 *7)) (-5 *3 (-622 *7)) (-4 *7 (-926 *4 *6 *5))
+ (-4 *4 (-13 (-302) (-145))) (-4 *5 (-13 (-827) (-598 (-1149))))
+ (-4 *6 (-773)) (-5 *1 (-900 *4 *5 *6 *7)))))
(((*1 *2 *3 *4)
- (-12 (-5 *3 (-667 *8)) (-5 *4 (-749)) (-4 *8 (-924 *5 *7 *6))
- (-4 *5 (-13 (-300) (-145))) (-4 *6 (-13 (-825) (-596 (-1147))))
- (-4 *7 (-771))
+ (-12 (-5 *3 (-669 *8)) (-5 *4 (-751)) (-4 *8 (-926 *5 *7 *6))
+ (-4 *5 (-13 (-302) (-145))) (-4 *6 (-13 (-827) (-598 (-1149))))
+ (-4 *7 (-773))
(-5 *2
- (-620
- (-2 (|:| |det| *8) (|:| |rows| (-620 (-536)))
- (|:| |cols| (-620 (-536))))))
- (-5 *1 (-898 *5 *6 *7 *8)))))
+ (-622
+ (-2 (|:| |det| *8) (|:| |rows| (-622 (-538)))
+ (|:| |cols| (-622 (-538))))))
+ (-5 *1 (-900 *5 *6 *7 *8)))))
(((*1 *2 *3 *4)
- (-12 (-5 *4 (-620 (-620 *8))) (-5 *3 (-620 *8)) (-4 *8 (-924 *5 *7 *6))
- (-4 *5 (-13 (-300) (-145))) (-4 *6 (-13 (-825) (-596 (-1147))))
- (-4 *7 (-771)) (-5 *2 (-112)) (-5 *1 (-898 *5 *6 *7 *8)))))
+ (-12 (-5 *4 (-622 (-622 *8))) (-5 *3 (-622 *8)) (-4 *8 (-926 *5 *7 *6))
+ (-4 *5 (-13 (-302) (-145))) (-4 *6 (-13 (-827) (-598 (-1149))))
+ (-4 *7 (-773)) (-5 *2 (-112)) (-5 *1 (-900 *5 *6 *7 *8)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-13 (-300) (-145))) (-4 *5 (-13 (-825) (-596 (-1147))))
- (-4 *6 (-771)) (-5 *2 (-620 (-620 (-536)))) (-5 *1 (-898 *4 *5 *6 *7))
- (-5 *3 (-536)) (-4 *7 (-924 *4 *6 *5)))))
+ (-12 (-4 *4 (-13 (-302) (-145))) (-4 *5 (-13 (-827) (-598 (-1149))))
+ (-4 *6 (-773)) (-5 *2 (-622 (-622 (-538)))) (-5 *1 (-900 *4 *5 *6 *7))
+ (-5 *3 (-538)) (-4 *7 (-926 *4 *6 *5)))))
(((*1 *2 *2)
- (-12 (-5 *2 (-620 (-620 *6))) (-4 *6 (-924 *3 *5 *4))
- (-4 *3 (-13 (-300) (-145))) (-4 *4 (-13 (-825) (-596 (-1147))))
- (-4 *5 (-771)) (-5 *1 (-898 *3 *4 *5 *6)))))
+ (-12 (-5 *2 (-622 (-622 *6))) (-4 *6 (-926 *3 *5 *4))
+ (-4 *3 (-13 (-302) (-145))) (-4 *4 (-13 (-827) (-598 (-1149))))
+ (-4 *5 (-773)) (-5 *1 (-900 *3 *4 *5 *6)))))
(((*1 *2 *3)
(-12
(-5 *3
- (-620
- (-2 (|:| -3439 (-749))
+ (-622
+ (-2 (|:| -3444 (-751))
(|:| |eqns|
- (-620
- (-2 (|:| |det| *7) (|:| |rows| (-620 (-536)))
- (|:| |cols| (-620 (-536))))))
- (|:| |fgb| (-620 *7)))))
- (-4 *7 (-924 *4 *6 *5)) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771)) (-5 *2 (-749))
- (-5 *1 (-898 *4 *5 *6 *7)))))
+ (-622
+ (-2 (|:| |det| *7) (|:| |rows| (-622 (-538)))
+ (|:| |cols| (-622 (-538))))))
+ (|:| |fgb| (-622 *7)))))
+ (-4 *7 (-926 *4 *6 *5)) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773)) (-5 *2 (-751))
+ (-5 *1 (-900 *4 *5 *6 *7)))))
(((*1 *2 *3)
(-12
(-5 *3
- (-620
- (-2 (|:| -3439 (-749))
+ (-622
+ (-2 (|:| -3444 (-751))
(|:| |eqns|
- (-620
- (-2 (|:| |det| *7) (|:| |rows| (-620 (-536)))
- (|:| |cols| (-620 (-536))))))
- (|:| |fgb| (-620 *7)))))
- (-4 *7 (-924 *4 *6 *5)) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771)) (-5 *2 (-749))
- (-5 *1 (-898 *4 *5 *6 *7)))))
-(((*1 *2 *3)
- (-12 (-4 *4 (-13 (-300) (-145))) (-4 *5 (-13 (-825) (-596 (-1147))))
- (-4 *6 (-771)) (-5 *2 (-620 *3)) (-5 *1 (-898 *4 *5 *6 *3))
- (-4 *3 (-924 *4 *6 *5)))))
+ (-622
+ (-2 (|:| |det| *7) (|:| |rows| (-622 (-538)))
+ (|:| |cols| (-622 (-538))))))
+ (|:| |fgb| (-622 *7)))))
+ (-4 *7 (-926 *4 *6 *5)) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773)) (-5 *2 (-751))
+ (-5 *1 (-900 *4 *5 *6 *7)))))
+(((*1 *2 *3)
+ (-12 (-4 *4 (-13 (-302) (-145))) (-4 *5 (-13 (-827) (-598 (-1149))))
+ (-4 *6 (-773)) (-5 *2 (-622 *3)) (-5 *1 (-900 *4 *5 *6 *3))
+ (-4 *3 (-926 *4 *6 *5)))))
(((*1 *2 *3)
(-12
(-5 *3
- (-2 (|:| -1695 (-667 (-400 (-920 *4)))) (|:| |vec| (-620 (-400 (-920 *4))))
- (|:| -3439 (-749)) (|:| |rows| (-620 (-536))) (|:| |cols| (-620 (-536)))))
- (-4 *4 (-13 (-300) (-145))) (-4 *5 (-13 (-825) (-596 (-1147))))
- (-4 *6 (-771))
+ (-2 (|:| -1700 (-669 (-402 (-922 *4)))) (|:| |vec| (-622 (-402 (-922 *4))))
+ (|:| -3444 (-751)) (|:| |rows| (-622 (-538))) (|:| |cols| (-622 (-538)))))
+ (-4 *4 (-13 (-302) (-145))) (-4 *5 (-13 (-827) (-598 (-1149))))
+ (-4 *6 (-773))
(-5 *2
- (-2 (|:| |partsol| (-1229 (-400 (-920 *4))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *4)))))))
- (-5 *1 (-898 *4 *5 *6 *7)) (-4 *7 (-924 *4 *6 *5)))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *4))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *4)))))))
+ (-5 *1 (-900 *4 *5 *6 *7)) (-4 *7 (-926 *4 *6 *5)))))
(((*1 *2 *2 *3)
(-12
(-5 *2
- (-2 (|:| |partsol| (-1229 (-400 (-920 *4))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *4)))))))
- (-5 *3 (-620 *7)) (-4 *4 (-13 (-300) (-145))) (-4 *7 (-924 *4 *6 *5))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771))
- (-5 *1 (-898 *4 *5 *6 *7)))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *4))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *4)))))))
+ (-5 *3 (-622 *7)) (-4 *4 (-13 (-302) (-145))) (-4 *7 (-926 *4 *6 *5))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773))
+ (-5 *1 (-900 *4 *5 *6 *7)))))
(((*1 *2 *3 *4)
- (-12 (-5 *3 (-667 *8)) (-4 *8 (-924 *5 *7 *6)) (-4 *5 (-13 (-300) (-145)))
- (-4 *6 (-13 (-825) (-596 (-1147)))) (-4 *7 (-771))
+ (-12 (-5 *3 (-669 *8)) (-4 *8 (-926 *5 *7 *6)) (-4 *5 (-13 (-302) (-145)))
+ (-4 *6 (-13 (-827) (-598 (-1149)))) (-4 *7 (-773))
(-5 *2
- (-620
- (-2 (|:| -3439 (-749))
+ (-622
+ (-2 (|:| -3444 (-751))
(|:| |eqns|
- (-620
- (-2 (|:| |det| *8) (|:| |rows| (-620 (-536)))
- (|:| |cols| (-620 (-536))))))
- (|:| |fgb| (-620 *8)))))
- (-5 *1 (-898 *5 *6 *7 *8)) (-5 *4 (-749)))))
+ (-622
+ (-2 (|:| |det| *8) (|:| |rows| (-622 (-538)))
+ (|:| |cols| (-622 (-538))))))
+ (|:| |fgb| (-622 *8)))))
+ (-5 *1 (-900 *5 *6 *7 *8)) (-5 *4 (-751)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-13 (-300) (-145))) (-4 *5 (-13 (-825) (-596 (-1147))))
- (-4 *6 (-771)) (-4 *7 (-924 *4 *6 *5))
- (-5 *2 (-2 (|:| |sysok| (-112)) (|:| |z0| (-620 *7)) (|:| |n0| (-620 *7))))
- (-5 *1 (-898 *4 *5 *6 *7)) (-5 *3 (-620 *7)))))
-(((*1 *2 *3)
- (-12 (-5 *3 (-920 *4)) (-4 *4 (-13 (-300) (-145))) (-4 *2 (-924 *4 *6 *5))
- (-5 *1 (-898 *4 *5 *6 *2)) (-4 *5 (-13 (-825) (-596 (-1147))))
- (-4 *6 (-771)))))
-(((*1 *2 *3)
- (-12 (-5 *3 (-620 (-1147))) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771))
- (-5 *2 (-620 (-400 (-920 *4)))) (-5 *1 (-898 *4 *5 *6 *7))
- (-4 *7 (-924 *4 *6 *5)))))
-(((*1 *2 *3)
- (-12 (-4 *4 (-13 (-300) (-145))) (-4 *5 (-13 (-825) (-596 (-1147))))
- (-4 *6 (-771)) (-5 *2 (-400 (-920 *4))) (-5 *1 (-898 *4 *5 *6 *3))
- (-4 *3 (-924 *4 *6 *5))))
+ (-12 (-4 *4 (-13 (-302) (-145))) (-4 *5 (-13 (-827) (-598 (-1149))))
+ (-4 *6 (-773)) (-4 *7 (-926 *4 *6 *5))
+ (-5 *2 (-2 (|:| |sysok| (-112)) (|:| |z0| (-622 *7)) (|:| |n0| (-622 *7))))
+ (-5 *1 (-900 *4 *5 *6 *7)) (-5 *3 (-622 *7)))))
+(((*1 *2 *3)
+ (-12 (-5 *3 (-922 *4)) (-4 *4 (-13 (-302) (-145))) (-4 *2 (-926 *4 *6 *5))
+ (-5 *1 (-900 *4 *5 *6 *2)) (-4 *5 (-13 (-827) (-598 (-1149))))
+ (-4 *6 (-773)))))
+(((*1 *2 *3)
+ (-12 (-5 *3 (-622 (-1149))) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773))
+ (-5 *2 (-622 (-402 (-922 *4)))) (-5 *1 (-900 *4 *5 *6 *7))
+ (-4 *7 (-926 *4 *6 *5)))))
+(((*1 *2 *3)
+ (-12 (-4 *4 (-13 (-302) (-145))) (-4 *5 (-13 (-827) (-598 (-1149))))
+ (-4 *6 (-773)) (-5 *2 (-402 (-922 *4))) (-5 *1 (-900 *4 *5 *6 *3))
+ (-4 *3 (-926 *4 *6 *5))))
((*1 *2 *3)
- (-12 (-5 *3 (-667 *7)) (-4 *7 (-924 *4 *6 *5)) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771))
- (-5 *2 (-667 (-400 (-920 *4)))) (-5 *1 (-898 *4 *5 *6 *7))))
+ (-12 (-5 *3 (-669 *7)) (-4 *7 (-926 *4 *6 *5)) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773))
+ (-5 *2 (-669 (-402 (-922 *4)))) (-5 *1 (-900 *4 *5 *6 *7))))
((*1 *2 *3)
- (-12 (-5 *3 (-620 *7)) (-4 *7 (-924 *4 *6 *5)) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771))
- (-5 *2 (-620 (-400 (-920 *4)))) (-5 *1 (-898 *4 *5 *6 *7)))))
+ (-12 (-5 *3 (-622 *7)) (-4 *7 (-926 *4 *6 *5)) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773))
+ (-5 *2 (-622 (-402 (-922 *4)))) (-5 *1 (-900 *4 *5 *6 *7)))))
(((*1 *2 *3 *4 *5 *6 *7)
- (-12 (-5 *3 (-667 *11)) (-5 *4 (-620 (-400 (-920 *8)))) (-5 *5 (-749))
- (-5 *6 (-1129)) (-4 *8 (-13 (-300) (-145))) (-4 *11 (-924 *8 *10 *9))
- (-4 *9 (-13 (-825) (-596 (-1147)))) (-4 *10 (-771))
+ (-12 (-5 *3 (-669 *11)) (-5 *4 (-622 (-402 (-922 *8)))) (-5 *5 (-751))
+ (-5 *6 (-1131)) (-4 *8 (-13 (-302) (-145))) (-4 *11 (-926 *8 *10 *9))
+ (-4 *9 (-13 (-827) (-598 (-1149)))) (-4 *10 (-773))
(-5 *2
(-2
(|:| |rgl|
- (-620
- (-2 (|:| |eqzro| (-620 *11)) (|:| |neqzro| (-620 *11))
- (|:| |wcond| (-620 (-920 *8)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *11)) (|:| |neqzro| (-622 *11))
+ (|:| |wcond| (-622 (-922 *8)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *8))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *8))))))))))
- (|:| |rgsz| (-536))))
- (-5 *1 (-898 *8 *9 *10 *11)) (-5 *7 (-536)))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *8))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *8))))))))))
+ (|:| |rgsz| (-538))))
+ (-5 *1 (-900 *8 *9 *10 *11)) (-5 *7 (-538)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-1129)) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771))
+ (-12 (-5 *3 (-1131)) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773))
(-5 *2
- (-620
- (-2 (|:| |eqzro| (-620 *7)) (|:| |neqzro| (-620 *7))
- (|:| |wcond| (-620 (-920 *4)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *7)) (|:| |neqzro| (-622 *7))
+ (|:| |wcond| (-622 (-922 *4)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *4))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *4))))))))))
- (-5 *1 (-898 *4 *5 *6 *7)) (-4 *7 (-924 *4 *6 *5)))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *4))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *4))))))))))
+ (-5 *1 (-900 *4 *5 *6 *7)) (-4 *7 (-926 *4 *6 *5)))))
(((*1 *2 *3 *4)
(-12
(-5 *3
- (-620
- (-2 (|:| |eqzro| (-620 *8)) (|:| |neqzro| (-620 *8))
- (|:| |wcond| (-620 (-920 *5)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *8)) (|:| |neqzro| (-622 *8))
+ (|:| |wcond| (-622 (-922 *5)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *5))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *5))))))))))
- (-5 *4 (-1129)) (-4 *5 (-13 (-300) (-145))) (-4 *8 (-924 *5 *7 *6))
- (-4 *6 (-13 (-825) (-596 (-1147)))) (-4 *7 (-771)) (-5 *2 (-536))
- (-5 *1 (-898 *5 *6 *7 *8)))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *5))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *5))))))))))
+ (-5 *4 (-1131)) (-4 *5 (-13 (-302) (-145))) (-4 *8 (-926 *5 *7 *6))
+ (-4 *6 (-13 (-827) (-598 (-1149)))) (-4 *7 (-773)) (-5 *2 (-538))
+ (-5 *1 (-900 *5 *6 *7 *8)))))
(((*1 *2 *3 *4)
- (-12 (-5 *3 (-667 *8)) (-4 *8 (-924 *5 *7 *6)) (-4 *5 (-13 (-300) (-145)))
- (-4 *6 (-13 (-825) (-596 (-1147)))) (-4 *7 (-771))
+ (-12 (-5 *3 (-669 *8)) (-4 *8 (-926 *5 *7 *6)) (-4 *5 (-13 (-302) (-145)))
+ (-4 *6 (-13 (-827) (-598 (-1149)))) (-4 *7 (-773))
(-5 *2
- (-620
- (-2 (|:| |eqzro| (-620 *8)) (|:| |neqzro| (-620 *8))
- (|:| |wcond| (-620 (-920 *5)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *8)) (|:| |neqzro| (-622 *8))
+ (|:| |wcond| (-622 (-922 *5)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *5))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *5))))))))))
- (-5 *1 (-898 *5 *6 *7 *8)) (-5 *4 (-620 *8))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *5))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *5))))))))))
+ (-5 *1 (-900 *5 *6 *7 *8)) (-5 *4 (-622 *8))))
((*1 *2 *3 *4)
- (-12 (-5 *3 (-667 *8)) (-5 *4 (-620 (-1147))) (-4 *8 (-924 *5 *7 *6))
- (-4 *5 (-13 (-300) (-145))) (-4 *6 (-13 (-825) (-596 (-1147))))
- (-4 *7 (-771))
+ (-12 (-5 *3 (-669 *8)) (-5 *4 (-622 (-1149))) (-4 *8 (-926 *5 *7 *6))
+ (-4 *5 (-13 (-302) (-145))) (-4 *6 (-13 (-827) (-598 (-1149))))
+ (-4 *7 (-773))
(-5 *2
- (-620
- (-2 (|:| |eqzro| (-620 *8)) (|:| |neqzro| (-620 *8))
- (|:| |wcond| (-620 (-920 *5)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *8)) (|:| |neqzro| (-622 *8))
+ (|:| |wcond| (-622 (-922 *5)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *5))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *5))))))))))
- (-5 *1 (-898 *5 *6 *7 *8))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *5))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *5))))))))))
+ (-5 *1 (-900 *5 *6 *7 *8))))
((*1 *2 *3)
- (-12 (-5 *3 (-667 *7)) (-4 *7 (-924 *4 *6 *5)) (-4 *4 (-13 (-300) (-145)))
- (-4 *5 (-13 (-825) (-596 (-1147)))) (-4 *6 (-771))
+ (-12 (-5 *3 (-669 *7)) (-4 *7 (-926 *4 *6 *5)) (-4 *4 (-13 (-302) (-145)))
+ (-4 *5 (-13 (-827) (-598 (-1149)))) (-4 *6 (-773))
(-5 *2
- (-620
- (-2 (|:| |eqzro| (-620 *7)) (|:| |neqzro| (-620 *7))
- (|:| |wcond| (-620 (-920 *4)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *7)) (|:| |neqzro| (-622 *7))
+ (|:| |wcond| (-622 (-922 *4)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *4))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *4))))))))))
- (-5 *1 (-898 *4 *5 *6 *7))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *4))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *4))))))))))
+ (-5 *1 (-900 *4 *5 *6 *7))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *3 (-667 *9)) (-5 *5 (-893)) (-4 *9 (-924 *6 *8 *7))
- (-4 *6 (-13 (-300) (-145))) (-4 *7 (-13 (-825) (-596 (-1147))))
- (-4 *8 (-771))
+ (-12 (-5 *3 (-669 *9)) (-5 *5 (-895)) (-4 *9 (-926 *6 *8 *7))
+ (-4 *6 (-13 (-302) (-145))) (-4 *7 (-13 (-827) (-598 (-1149))))
+ (-4 *8 (-773))
(-5 *2
- (-620
- (-2 (|:| |eqzro| (-620 *9)) (|:| |neqzro| (-620 *9))
- (|:| |wcond| (-620 (-920 *6)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *9)) (|:| |neqzro| (-622 *9))
+ (|:| |wcond| (-622 (-922 *6)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *6))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *6))))))))))
- (-5 *1 (-898 *6 *7 *8 *9)) (-5 *4 (-620 *9))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *6))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *6))))))))))
+ (-5 *1 (-900 *6 *7 *8 *9)) (-5 *4 (-622 *9))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *3 (-667 *9)) (-5 *4 (-620 (-1147))) (-5 *5 (-893))
- (-4 *9 (-924 *6 *8 *7)) (-4 *6 (-13 (-300) (-145)))
- (-4 *7 (-13 (-825) (-596 (-1147)))) (-4 *8 (-771))
+ (-12 (-5 *3 (-669 *9)) (-5 *4 (-622 (-1149))) (-5 *5 (-895))
+ (-4 *9 (-926 *6 *8 *7)) (-4 *6 (-13 (-302) (-145)))
+ (-4 *7 (-13 (-827) (-598 (-1149)))) (-4 *8 (-773))
(-5 *2
- (-620
- (-2 (|:| |eqzro| (-620 *9)) (|:| |neqzro| (-620 *9))
- (|:| |wcond| (-620 (-920 *6)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *9)) (|:| |neqzro| (-622 *9))
+ (|:| |wcond| (-622 (-922 *6)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *6))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *6))))))))))
- (-5 *1 (-898 *6 *7 *8 *9))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *6))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *6))))))))))
+ (-5 *1 (-900 *6 *7 *8 *9))))
((*1 *2 *3 *4)
- (-12 (-5 *3 (-667 *8)) (-5 *4 (-893)) (-4 *8 (-924 *5 *7 *6))
- (-4 *5 (-13 (-300) (-145))) (-4 *6 (-13 (-825) (-596 (-1147))))
- (-4 *7 (-771))
+ (-12 (-5 *3 (-669 *8)) (-5 *4 (-895)) (-4 *8 (-926 *5 *7 *6))
+ (-4 *5 (-13 (-302) (-145))) (-4 *6 (-13 (-827) (-598 (-1149))))
+ (-4 *7 (-773))
(-5 *2
- (-620
- (-2 (|:| |eqzro| (-620 *8)) (|:| |neqzro| (-620 *8))
- (|:| |wcond| (-620 (-920 *5)))
+ (-622
+ (-2 (|:| |eqzro| (-622 *8)) (|:| |neqzro| (-622 *8))
+ (|:| |wcond| (-622 (-922 *5)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1229 (-400 (-920 *5))))
- (|:| -2123 (-620 (-1229 (-400 (-920 *5))))))))))
- (-5 *1 (-898 *5 *6 *7 *8))))
+ (-2 (|:| |partsol| (-1231 (-402 (-922 *5))))
+ (|:| -2128 (-622 (-1231 (-402 (-922 *5))))))))))
+ (-5 *1 (-900 *5 *6 *7 *8))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *3 (-667 *9)) (-5 *4 (-620 *9)) (-5 *5 (-1129))
- (-4 *9 (-924 *6 *8 *7)) (-4 *6 (-13 (-300) (-145)))
- (-4 *7 (-13 (-825) (-596 (-1147)))) (-4 *8 (-771)) (-5 *2 (-536))
- (-5 *1 (-898 *6 *7 *8 *9))))
+ (-12 (-5 *3 (-669 *9)) (-5 *4 (-622 *9)) (-5 *5 (-1131))
+ (-4 *9 (-926 *6 *8 *7)) (-4 *6 (-13 (-302) (-145)))
+ (-4 *7 (-13 (-827) (-598 (-1149)))) (-4 *8 (-773)) (-5 *2 (-538))
+ (-5 *1 (-900 *6 *7 *8 *9))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *3 (-667 *9)) (-5 *4 (-620 (-1147))) (-5 *5 (-1129))
- (-4 *9 (-924 *6 *8 *7)) (-4 *6 (-13 (-300) (-145)))
- (-4 *7 (-13 (-825) (-596 (-1147)))) (-4 *8 (-771)) (-5 *2 (-536))
- (-5 *1 (-898 *6 *7 *8 *9))))
- ((*1 *2 *3 *4)
- (-12 (-5 *3 (-667 *8)) (-5 *4 (-1129)) (-4 *8 (-924 *5 *7 *6))
- (-4 *5 (-13 (-300) (-145))) (-4 *6 (-13 (-825) (-596 (-1147))))
- (-4 *7 (-771)) (-5 *2 (-536)) (-5 *1 (-898 *5 *6 *7 *8))))
+ (-12 (-5 *3 (-669 *9)) (-5 *4 (-622 (-1149))) (-5 *5 (-1131))
+ (-4 *9 (-926 *6 *8 *7)) (-4 *6 (-13 (-302) (-145)))
+ (-4 *7 (-13 (-827) (-598 (-1149)))) (-4 *8 (-773)) (-5 *2 (-538))
+ (-5 *1 (-900 *6 *7 *8 *9))))
+ ((*1 *2 *3 *4)
+ (-12 (-5 *3 (-669 *8)) (-5 *4 (-1131)) (-4 *8 (-926 *5 *7 *6))
+ (-4 *5 (-13 (-302) (-145))) (-4 *6 (-13 (-827) (-598 (-1149))))
+ (-4 *7 (-773)) (-5 *2 (-538)) (-5 *1 (-900 *5 *6 *7 *8))))
((*1 *2 *3 *4 *5 *6)
- (-12 (-5 *3 (-667 *10)) (-5 *4 (-620 *10)) (-5 *5 (-893)) (-5 *6 (-1129))
- (-4 *10 (-924 *7 *9 *8)) (-4 *7 (-13 (-300) (-145)))
- (-4 *8 (-13 (-825) (-596 (-1147)))) (-4 *9 (-771)) (-5 *2 (-536))
- (-5 *1 (-898 *7 *8 *9 *10))))
+ (-12 (-5 *3 (-669 *10)) (-5 *4 (-622 *10)) (-5 *5 (-895)) (-5 *6 (-1131))
+ (-4 *10 (-926 *7 *9 *8)) (-4 *7 (-13 (-302) (-145)))
+ (-4 *8 (-13 (-827) (-598 (-1149)))) (-4 *9 (-773)) (-5 *2 (-538))
+ (-5 *1 (-900 *7 *8 *9 *10))))
((*1 *2 *3 *4 *5 *6)
- (-12 (-5 *3 (-667 *10)) (-5 *4 (-620 (-1147))) (-5 *5 (-893)) (-5 *6 (-1129))
- (-4 *10 (-924 *7 *9 *8)) (-4 *7 (-13 (-300) (-145)))
- (-4 *8 (-13 (-825) (-596 (-1147)))) (-4 *9 (-771)) (-5 *2 (-536))
- (-5 *1 (-898 *7 *8 *9 *10))))
+ (-12 (-5 *3 (-669 *10)) (-5 *4 (-622 (-1149))) (-5 *5 (-895)) (-5 *6 (-1131))
+ (-4 *10 (-926 *7 *9 *8)) (-4 *7 (-13 (-302) (-145)))
+ (-4 *8 (-13 (-827) (-598 (-1149)))) (-4 *9 (-773)) (-5 *2 (-538))
+ (-5 *1 (-900 *7 *8 *9 *10))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *3 (-667 *9)) (-5 *4 (-893)) (-5 *5 (-1129)) (-4 *9 (-924 *6 *8 *7))
- (-4 *6 (-13 (-300) (-145))) (-4 *7 (-13 (-825) (-596 (-1147))))
- (-4 *8 (-771)) (-5 *2 (-536)) (-5 *1 (-898 *6 *7 *8 *9)))))
+ (-12 (-5 *3 (-669 *9)) (-5 *4 (-895)) (-5 *5 (-1131)) (-4 *9 (-926 *6 *8 *7))
+ (-4 *6 (-13 (-302) (-145))) (-4 *7 (-13 (-827) (-598 (-1149))))
+ (-4 *8 (-773)) (-5 *2 (-538)) (-5 *1 (-900 *6 *7 *8 *9)))))
(((*1 *2 *3 *3)
- (-12 (-5 *3 (-620 *4)) (-4 *4 (-356)) (-4 *2 (-1205 *4))
- (-5 *1 (-897 *4 *2)))))
+ (-12 (-5 *3 (-622 *4)) (-4 *4 (-358)) (-4 *2 (-1207 *4))
+ (-5 *1 (-899 *4 *2)))))
(((*1 *2 *3)
- (-12 (-4 *1 (-895)) (-5 *2 (-2 (|:| -4308 (-620 *1)) (|:| -2496 *1)))
- (-5 *3 (-620 *1)))))
-(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-620 *1)) (-4 *1 (-895)))))
+ (-12 (-4 *1 (-897)) (-5 *2 (-2 (|:| -4313 (-622 *1)) (|:| -2501 *1)))
+ (-5 *3 (-622 *1)))))
+(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-622 *1)) (-4 *1 (-897)))))
(((*1 *2 *2 *3)
- (-12 (-5 *2 (-620 (-920 *4))) (-5 *3 (-620 (-1147))) (-4 *4 (-444))
- (-5 *1 (-892 *4)))))
+ (-12 (-5 *2 (-622 (-922 *4))) (-5 *3 (-622 (-1149))) (-4 *4 (-446))
+ (-5 *1 (-894 *4)))))
(((*1 *2 *2 *3)
- (-12 (-5 *2 (-620 (-920 *4))) (-5 *3 (-620 (-1147))) (-4 *4 (-444))
- (-5 *1 (-892 *4)))))
-(((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2 *3) (-12 (-5 *3 (-945)) (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2) (-12 (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2) (-12 (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2) (-12 (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2) (-12 (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2) (-12 (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2) (-12 (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2) (-12 (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-893)) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-893)) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-620 (-893))) (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-893)) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
-(((*1 *2 *3) (-12 (-5 *3 (-893)) (-5 *2 (-879 (-536))) (-5 *1 (-891))))
- ((*1 *2 *3) (-12 (-5 *3 (-620 (-536))) (-5 *2 (-879 (-536))) (-5 *1 (-891)))))
+ (-12 (-5 *2 (-622 (-922 *4))) (-5 *3 (-622 (-1149))) (-4 *4 (-446))
+ (-5 *1 (-894 *4)))))
+(((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2 *3) (-12 (-5 *3 (-947)) (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2) (-12 (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2) (-12 (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2) (-12 (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2) (-12 (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2) (-12 (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2) (-12 (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2) (-12 (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-895)) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-895)) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-622 (-895))) (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-895)) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
+(((*1 *2 *3) (-12 (-5 *3 (-895)) (-5 *2 (-881 (-538))) (-5 *1 (-893))))
+ ((*1 *2 *3) (-12 (-5 *3 (-622 (-538))) (-5 *2 (-881 (-538))) (-5 *1 (-893)))))
(((*1 *2 *2 *2)
- (-12 (-4 *3 (-771)) (-4 *4 (-825)) (-4 *5 (-300)) (-5 *1 (-890 *3 *4 *5 *2))
- (-4 *2 (-924 *5 *3 *4))))
+ (-12 (-4 *3 (-773)) (-4 *4 (-827)) (-4 *5 (-302)) (-5 *1 (-892 *3 *4 *5 *2))
+ (-4 *2 (-926 *5 *3 *4))))
((*1 *2 *2 *2)
- (-12 (-5 *2 (-1141 *6)) (-4 *6 (-924 *5 *3 *4)) (-4 *3 (-771)) (-4 *4 (-825))
- (-4 *5 (-300)) (-5 *1 (-890 *3 *4 *5 *6))))
+ (-12 (-5 *2 (-1143 *6)) (-4 *6 (-926 *5 *3 *4)) (-4 *3 (-773)) (-4 *4 (-827))
+ (-4 *5 (-302)) (-5 *1 (-892 *3 *4 *5 *6))))
((*1 *2 *3)
- (-12 (-5 *3 (-620 *2)) (-4 *2 (-924 *6 *4 *5)) (-5 *1 (-890 *4 *5 *6 *2))
- (-4 *4 (-771)) (-4 *5 (-825)) (-4 *6 (-300)))))
-(((*1 *1 *2 *3) (-12 (-5 *3 (-398 *2)) (-4 *2 (-300)) (-5 *1 (-888 *2))))
+ (-12 (-5 *3 (-622 *2)) (-4 *2 (-926 *6 *4 *5)) (-5 *1 (-892 *4 *5 *6 *2))
+ (-4 *4 (-773)) (-4 *5 (-827)) (-4 *6 (-302)))))
+(((*1 *1 *2 *3) (-12 (-5 *3 (-400 *2)) (-4 *2 (-302)) (-5 *1 (-890 *2))))
((*1 *2 *3 *4)
- (-12 (-5 *3 (-400 (-920 *5))) (-5 *4 (-1147)) (-4 *5 (-13 (-300) (-145)))
- (-5 *2 (-51)) (-5 *1 (-889 *5))))
+ (-12 (-5 *3 (-402 (-922 *5))) (-5 *4 (-1149)) (-4 *5 (-13 (-302) (-145)))
+ (-5 *2 (-51)) (-5 *1 (-891 *5))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *4 (-398 (-920 *6))) (-5 *5 (-1147)) (-5 *3 (-920 *6))
- (-4 *6 (-13 (-300) (-145))) (-5 *2 (-51)) (-5 *1 (-889 *6)))))
-(((*1 *1 *1) (-12 (-5 *1 (-888 *2)) (-4 *2 (-300)))))
-(((*1 *2 *1) (-12 (-5 *2 (-398 *3)) (-5 *1 (-888 *3)) (-4 *3 (-300)))))
-(((*1 *2 *1) (-12 (-5 *1 (-888 *2)) (-4 *2 (-300)))))
-(((*1 *1 *1 *2) (-12 (-5 *2 (-536)) (-5 *1 (-888 *3)) (-4 *3 (-300)))))
-(((*1 *2 *1) (-12 (-5 *2 (-536)) (-5 *1 (-888 *3)) (-4 *3 (-300)))))
-(((*1 *2 *3 *3) (-12 (-5 *2 (-1141 *3)) (-5 *1 (-888 *3)) (-4 *3 (-300)))))
-(((*1 *1 *1) (-12 (-5 *1 (-888 *2)) (-4 *2 (-300)))))
+ (-12 (-5 *4 (-400 (-922 *6))) (-5 *5 (-1149)) (-5 *3 (-922 *6))
+ (-4 *6 (-13 (-302) (-145))) (-5 *2 (-51)) (-5 *1 (-891 *6)))))
+(((*1 *1 *1) (-12 (-5 *1 (-890 *2)) (-4 *2 (-302)))))
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(((*1 *2 *1)
(-12
(-5 *2
- (-620
+ (-622
(-2
- (|:| -4215
- (-2 (|:| |var| (-1147)) (|:| |fn| (-307 (-219)))
- (|:| -1556 (-1060 (-817 (-219)))) (|:| |abserr| (-219))
- (|:| |relerr| (-219))))
- (|:| -2186
+ (|:| -4220
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+ (|:| -2191
(-2
(|:| |endPointContinuity|
(-3 (|:| |continuous| "Continuous at the end points")
@@ -12000,502 +12001,502 @@
(|:| |notEvaluated|
"End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1124 (-219)))
+ (-3 (|:| |str| (-1126 (-221)))
(|:| |notEvaluated|
"Internal singularities not yet evaluated")))
- (|:| -1556
+ (|:| -1561
(-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 *1 *2 *3 *4)
(-12
(-5 *3
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+ (-12 (-5 *4 (-1149)) (-4 *5 (-13 (-827) (-1014 (-538)) (-446) (-621 (-538))))
+ (-5 *2 (-2 (|:| -2419 *3) (|:| |nconst| *3))) (-5 *1 (-555 *5 *3))
+ (-4 *3 (-13 (-27) (-1171) (-416 *5))))))
(((*1 *2 *3 *4 *5 *5 *6)
- (-12 (-5 *5 (-593 *4)) (-5 *6 (-1147)) (-4 *4 (-13 (-414 *7) (-27) (-1169)))
- (-4 *7 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2123 (-620 *4))))
- (-5 *1 (-552 *7 *4 *3)) (-4 *3 (-636 *4)) (-4 *3 (-1072)))))
+ (-12 (-5 *5 (-595 *4)) (-5 *6 (-1149)) (-4 *4 (-13 (-416 *7) (-27) (-1171)))
+ (-4 *7 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2128 (-622 *4))))
+ (-5 *1 (-554 *7 *4 *3)) (-4 *3 (-638 *4)) (-4 *3 (-1074)))))
(((*1 *2 *2 *2 *2 *3 *3 *4)
- (|partial| -12 (-5 *3 (-593 *2)) (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1147)))
- (-4 *2 (-13 (-414 *5) (-27) (-1169)))
- (-4 *5 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *1 (-552 *5 *2 *6)) (-4 *6 (-1072)))))
+ (|partial| -12 (-5 *3 (-595 *2)) (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1149)))
+ (-4 *2 (-13 (-416 *5) (-27) (-1171)))
+ (-4 *5 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *1 (-554 *5 *2 *6)) (-4 *6 (-1074)))))
(((*1 *2 *3 *4 *4 *5)
- (|partial| -12 (-5 *4 (-593 *3)) (-5 *5 (-620 *3))
- (-4 *3 (-13 (-414 *6) (-27) (-1169)))
- (-4 *6 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
+ (|partial| -12 (-5 *4 (-595 *3)) (-5 *5 (-622 *3))
+ (-4 *3 (-13 (-416 *6) (-27) (-1171)))
+ (-4 *6 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
(-5 *2
(-2 (|:| |mainpart| *3)
- (|:| |limitedlogs| (-620 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
- (-5 *1 (-552 *6 *3 *7)) (-4 *7 (-1072)))))
+ (|:| |limitedlogs| (-622 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
+ (-5 *1 (-554 *6 *3 *7)) (-4 *7 (-1074)))))
(((*1 *2 *3 *4 *4 *3)
- (|partial| -12 (-5 *4 (-593 *3)) (-4 *3 (-13 (-414 *5) (-27) (-1169)))
- (-4 *5 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-2 (|:| -2246 *3) (|:| |coeff| *3))) (-5 *1 (-552 *5 *3 *6))
- (-4 *6 (-1072)))))
+ (|partial| -12 (-5 *4 (-595 *3)) (-4 *3 (-13 (-416 *5) (-27) (-1171)))
+ (-4 *5 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-2 (|:| -2251 *3) (|:| |coeff| *3))) (-5 *1 (-554 *5 *3 *6))
+ (-4 *6 (-1074)))))
(((*1 *2 *3 *4 *4)
- (-12 (-5 *4 (-593 *3)) (-4 *3 (-13 (-414 *5) (-27) (-1169)))
- (-4 *5 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-567 *3)) (-5 *1 (-552 *5 *3 *6)) (-4 *6 (-1072)))))
+ (-12 (-5 *4 (-595 *3)) (-4 *3 (-13 (-416 *5) (-27) (-1171)))
+ (-4 *5 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-569 *3)) (-5 *1 (-554 *5 *3 *6)) (-4 *6 (-1074)))))
(((*1 *2 *3 *4)
- (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1205 *5)) (-4 *5 (-356))
- (-4 *7 (-1205 (-400 *6))) (-5 *2 (-2 (|:| |answer| *3) (|:| -2245 *3)))
- (-5 *1 (-549 *5 *6 *7 *3)) (-4 *3 (-335 *5 *6 *7))))
+ (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1207 *5)) (-4 *5 (-358))
+ (-4 *7 (-1207 (-402 *6))) (-5 *2 (-2 (|:| |answer| *3) (|:| -2250 *3)))
+ (-5 *1 (-551 *5 *6 *7 *3)) (-4 *3 (-337 *5 *6 *7))))
((*1 *2 *3 *4)
- (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1205 *5)) (-4 *5 (-356))
+ (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1207 *5)) (-4 *5 (-358))
(-5 *2
- (-2 (|:| |answer| (-400 *6)) (|:| -2245 (-400 *6))
- (|:| |specpart| (-400 *6)) (|:| |polypart| *6)))
- (-5 *1 (-550 *5 *6)) (-5 *3 (-400 *6)))))
-(((*1 *2 *2 *3) (-12 (-5 *2 (-536)) (-5 *3 (-749)) (-5 *1 (-548)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-548)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-548)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-548)))))
-(((*1 *2 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-548)))))
-(((*1 *2 *3) (-12 (-5 *2 (-400 (-536))) (-5 *1 (-548)) (-5 *3 (-536)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-548)))))
-(((*1 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-548)))))
-(((*1 *2 *3) (-12 (-5 *2 (-620 (-536))) (-5 *1 (-548)) (-5 *3 (-536)))))
-(((*1 *2 *3 *3) (-12 (-5 *3 (-620 *2)) (-5 *1 (-177 *2)) (-4 *2 (-300))))
+ (-2 (|:| |answer| (-402 *6)) (|:| -2250 (-402 *6))
+ (|:| |specpart| (-402 *6)) (|:| |polypart| *6)))
+ (-5 *1 (-552 *5 *6)) (-5 *3 (-402 *6)))))
+(((*1 *2 *2 *3) (-12 (-5 *2 (-538)) (-5 *3 (-751)) (-5 *1 (-550)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-550)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-550)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-550)))))
+(((*1 *2 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-550)))))
+(((*1 *2 *3) (-12 (-5 *2 (-402 (-538))) (-5 *1 (-550)) (-5 *3 (-538)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-550)))))
+(((*1 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-550)))))
+(((*1 *2 *3) (-12 (-5 *2 (-622 (-538))) (-5 *1 (-550)) (-5 *3 (-538)))))
+(((*1 *2 *3 *3) (-12 (-5 *3 (-622 *2)) (-5 *1 (-177 *2)) (-4 *2 (-302))))
((*1 *2 *3 *2)
- (-12 (-5 *3 (-620 (-620 *4))) (-5 *2 (-620 *4)) (-4 *4 (-300))
+ (-12 (-5 *3 (-622 (-622 *4))) (-5 *2 (-622 *4)) (-4 *4 (-302))
(-5 *1 (-177 *4))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *3 (-620 *8))
+ (-12 (-5 *3 (-622 *8))
(-5 *4
- (-620
- (-2 (|:| -2123 (-667 *7)) (|:| |basisDen| *7)
- (|:| |basisInv| (-667 *7)))))
- (-5 *5 (-749)) (-4 *8 (-1205 *7)) (-4 *7 (-1205 *6)) (-4 *6 (-343))
+ (-622
+ (-2 (|:| -2128 (-669 *7)) (|:| |basisDen| *7)
+ (|:| |basisInv| (-669 *7)))))
+ (-5 *5 (-751)) (-4 *8 (-1207 *7)) (-4 *7 (-1207 *6)) (-4 *6 (-345))
(-5 *2
- (-2 (|:| -2123 (-667 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-667 *7))))
- (-5 *1 (-489 *6 *7 *8))))
- ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-536)) (-5 *1 (-548)))))
+ (-2 (|:| -2128 (-669 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-669 *7))))
+ (-5 *1 (-491 *6 *7 *8))))
+ ((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-538)) (-5 *1 (-550)))))
(((*1 *2 *3 *4 *5 *5 *4 *6)
- (-12 (-5 *5 (-593 *4)) (-5 *6 (-1141 *4))
- (-4 *4 (-13 (-414 *7) (-27) (-1169)))
- (-4 *7 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2123 (-620 *4))))
- (-5 *1 (-547 *7 *4 *3)) (-4 *3 (-636 *4)) (-4 *3 (-1072))))
+ (-12 (-5 *5 (-595 *4)) (-5 *6 (-1143 *4))
+ (-4 *4 (-13 (-416 *7) (-27) (-1171)))
+ (-4 *7 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2128 (-622 *4))))
+ (-5 *1 (-549 *7 *4 *3)) (-4 *3 (-638 *4)) (-4 *3 (-1074))))
((*1 *2 *3 *4 *5 *5 *5 *4 *6)
- (-12 (-5 *5 (-593 *4)) (-5 *6 (-400 (-1141 *4)))
- (-4 *4 (-13 (-414 *7) (-27) (-1169)))
- (-4 *7 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2123 (-620 *4))))
- (-5 *1 (-547 *7 *4 *3)) (-4 *3 (-636 *4)) (-4 *3 (-1072)))))
+ (-12 (-5 *5 (-595 *4)) (-5 *6 (-402 (-1143 *4)))
+ (-4 *4 (-13 (-416 *7) (-27) (-1171)))
+ (-4 *7 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2128 (-622 *4))))
+ (-5 *1 (-549 *7 *4 *3)) (-4 *3 (-638 *4)) (-4 *3 (-1074)))))
(((*1 *2 *2 *2 *3 *3 *4 *2 *5)
- (|partial| -12 (-5 *3 (-593 *2))
- (-5 *4 (-1 (-3 *2 #1="failed") *2 *2 (-1147))) (-5 *5 (-1141 *2))
- (-4 *2 (-13 (-414 *6) (-27) (-1169)))
- (-4 *6 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *1 (-547 *6 *2 *7)) (-4 *7 (-1072))))
+ (|partial| -12 (-5 *3 (-595 *2))
+ (-5 *4 (-1 (-3 *2 #1="failed") *2 *2 (-1149))) (-5 *5 (-1143 *2))
+ (-4 *2 (-13 (-416 *6) (-27) (-1171)))
+ (-4 *6 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *1 (-549 *6 *2 *7)) (-4 *7 (-1074))))
((*1 *2 *2 *2 *3 *3 *4 *3 *2 *5)
- (|partial| -12 (-5 *3 (-593 *2)) (-5 *4 (-1 (-3 *2 #1#) *2 *2 (-1147)))
- (-5 *5 (-400 (-1141 *2))) (-4 *2 (-13 (-414 *6) (-27) (-1169)))
- (-4 *6 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *1 (-547 *6 *2 *7)) (-4 *7 (-1072)))))
+ (|partial| -12 (-5 *3 (-595 *2)) (-5 *4 (-1 (-3 *2 #1#) *2 *2 (-1149)))
+ (-5 *5 (-402 (-1143 *2))) (-4 *2 (-13 (-416 *6) (-27) (-1171)))
+ (-4 *6 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *1 (-549 *6 *2 *7)) (-4 *7 (-1074)))))
(((*1 *2 *3 *4 *4 *5 *3 *6)
- (|partial| -12 (-5 *4 (-593 *3)) (-5 *5 (-620 *3)) (-5 *6 (-1141 *3))
- (-4 *3 (-13 (-414 *7) (-27) (-1169)))
- (-4 *7 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
+ (|partial| -12 (-5 *4 (-595 *3)) (-5 *5 (-622 *3)) (-5 *6 (-1143 *3))
+ (-4 *3 (-13 (-416 *7) (-27) (-1171)))
+ (-4 *7 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
(-5 *2
(-2 (|:| |mainpart| *3)
- (|:| |limitedlogs| (-620 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
- (-5 *1 (-547 *7 *3 *8)) (-4 *8 (-1072))))
+ (|:| |limitedlogs| (-622 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
+ (-5 *1 (-549 *7 *3 *8)) (-4 *8 (-1074))))
((*1 *2 *3 *4 *4 *5 *4 *3 *6)
- (|partial| -12 (-5 *4 (-593 *3)) (-5 *5 (-620 *3)) (-5 *6 (-400 (-1141 *3)))
- (-4 *3 (-13 (-414 *7) (-27) (-1169)))
- (-4 *7 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
+ (|partial| -12 (-5 *4 (-595 *3)) (-5 *5 (-622 *3)) (-5 *6 (-402 (-1143 *3)))
+ (-4 *3 (-13 (-416 *7) (-27) (-1171)))
+ (-4 *7 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
(-5 *2
(-2 (|:| |mainpart| *3)
- (|:| |limitedlogs| (-620 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
- (-5 *1 (-547 *7 *3 *8)) (-4 *8 (-1072)))))
+ (|:| |limitedlogs| (-622 (-2 (|:| |coeff| *3) (|:| |logand| *3))))))
+ (-5 *1 (-549 *7 *3 *8)) (-4 *8 (-1074)))))
(((*1 *2 *3 *4 *4 *3 *3 *5)
- (|partial| -12 (-5 *4 (-593 *3)) (-5 *5 (-1141 *3))
- (-4 *3 (-13 (-414 *6) (-27) (-1169)))
- (-4 *6 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-2 (|:| -2246 *3) (|:| |coeff| *3))) (-5 *1 (-547 *6 *3 *7))
- (-4 *7 (-1072))))
+ (|partial| -12 (-5 *4 (-595 *3)) (-5 *5 (-1143 *3))
+ (-4 *3 (-13 (-416 *6) (-27) (-1171)))
+ (-4 *6 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-2 (|:| -2251 *3) (|:| |coeff| *3))) (-5 *1 (-549 *6 *3 *7))
+ (-4 *7 (-1074))))
((*1 *2 *3 *4 *4 *3 *4 *3 *5)
- (|partial| -12 (-5 *4 (-593 *3)) (-5 *5 (-400 (-1141 *3)))
- (-4 *3 (-13 (-414 *6) (-27) (-1169)))
- (-4 *6 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-2 (|:| -2246 *3) (|:| |coeff| *3))) (-5 *1 (-547 *6 *3 *7))
- (-4 *7 (-1072)))))
+ (|partial| -12 (-5 *4 (-595 *3)) (-5 *5 (-402 (-1143 *3)))
+ (-4 *3 (-13 (-416 *6) (-27) (-1171)))
+ (-4 *6 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-2 (|:| -2251 *3) (|:| |coeff| *3))) (-5 *1 (-549 *6 *3 *7))
+ (-4 *7 (-1074)))))
(((*1 *2 *3 *4 *4 *3 *5)
- (-12 (-5 *4 (-593 *3)) (-5 *5 (-1141 *3))
- (-4 *3 (-13 (-414 *6) (-27) (-1169)))
- (-4 *6 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-567 *3)) (-5 *1 (-547 *6 *3 *7)) (-4 *7 (-1072))))
+ (-12 (-5 *4 (-595 *3)) (-5 *5 (-1143 *3))
+ (-4 *3 (-13 (-416 *6) (-27) (-1171)))
+ (-4 *6 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-569 *3)) (-5 *1 (-549 *6 *3 *7)) (-4 *7 (-1074))))
((*1 *2 *3 *4 *4 *4 *3 *5)
- (-12 (-5 *4 (-593 *3)) (-5 *5 (-400 (-1141 *3)))
- (-4 *3 (-13 (-414 *6) (-27) (-1169)))
- (-4 *6 (-13 (-444) (-1012 (-536)) (-825) (-145) (-619 (-536))))
- (-5 *2 (-567 *3)) (-5 *1 (-547 *6 *3 *7)) (-4 *7 (-1072)))))
+ (-12 (-5 *4 (-595 *3)) (-5 *5 (-402 (-1143 *3)))
+ (-4 *3 (-13 (-416 *6) (-27) (-1171)))
+ (-4 *6 (-13 (-446) (-1014 (-538)) (-827) (-145) (-621 (-538))))
+ (-5 *2 (-569 *3)) (-5 *1 (-549 *6 *3 *7)) (-4 *7 (-1074)))))
(((*1 *2 *3)
(-12
(-5 *3
- (-2 (|:| |var| (-1147)) (|:| |fn| (-307 (-219)))
- (|:| -1556 (-1060 (-817 (-219)))) (|:| |abserr| (-219))
- (|:| |relerr| (-219))))
+ (-2 (|:| |var| (-1149)) (|:| |fn| (-309 (-221)))
+ (|:| -1561 (-1062 (-819 (-221)))) (|:| |abserr| (-221))
+ (|:| |relerr| (-221))))
(-5 *2
(-2
(|:| |endPointContinuity|
@@ -12507,21 +12508,21 @@
(|:| |bothSingular| "There are singularities at both end points")
(|:| |notEvaluated| "End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1124 (-219)))
+ (-3 (|:| |str| (-1126 (-221)))
(|:| |notEvaluated| "Internal singularities not yet evaluated")))
- (|:| -1556
+ (|:| -1561
(-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 (-546)))))
+ (-5 *1 (-548)))))
(((*1 *2 *3)
(|partial| -12
(-5 *3
- (-2 (|:| |var| (-1147)) (|:| |fn| (-307 (-219)))
- (|:| -1556 (-1060 (-817 (-219)))) (|:| |abserr| (-219))
- (|:| |relerr| (-219))))
+ (-2 (|:| |var| (-1149)) (|:| |fn| (-309 (-221)))
+ (|:| -1561 (-1062 (-819 (-221)))) (|:| |abserr| (-221))
+ (|:| |relerr| (-221))))
(-5 *2
(-2
(|:| |endPointContinuity|
@@ -12533,25 +12534,25 @@
(|:| |bothSingular| "There are singularities at both end points")
(|:| |notEvaluated| "End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1124 (-219)))
+ (-3 (|:| |str| (-1126 (-221)))
(|:| |notEvaluated| "Internal singularities not yet evaluated")))
- (|:| -1556
+ (|:| -1561
(-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 (-546)))))
+ (-5 *1 (-548)))))
(((*1 *1 *2)
(-12
(-5 *2
- (-620
+ (-622
(-2
- (|:| -4215
- (-2 (|:| |var| (-1147)) (|:| |fn| (-307 (-219)))
- (|:| -1556 (-1060 (-817 (-219)))) (|:| |abserr| (-219))
- (|:| |relerr| (-219))))
- (|:| -2186
+ (|:| -4220
+ (-2 (|:| |var| (-1149)) (|:| |fn| (-309 (-221)))
+ (|:| -1561 (-1062 (-819 (-221)))) (|:| |abserr| (-221))
+ (|:| |relerr| (-221))))
+ (|:| -2191
(-2
(|:| |endPointContinuity|
(-3 (|:| |continuous| "Continuous at the end points")
@@ -12564,1652 +12565,1652 @@
(|:| |notEvaluated|
"End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1124 (-219)))
+ (-3 (|:| |str| (-1126 (-221)))
(|:| |notEvaluated|
"Internal singularities not yet evaluated")))
- (|:| -1556
+ (|:| -1561
(-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 (-546)))))
-(((*1 *2) (-12 (-5 *2 (-1235)) (-5 *1 (-546)))))
-(((*1 *1) (-5 *1 (-546))))
-(((*1 *2 *2) (|partial| -12 (-5 *1 (-545 *2)) (-4 *2 (-535)))))
-(((*1 *2 *3) (-12 (-5 *2 (-398 *3)) (-5 *1 (-545 *3)) (-4 *3 (-535)))))
+ (-5 *1 (-548)))))
+(((*1 *2) (-12 (-5 *2 (-1237)) (-5 *1 (-548)))))
+(((*1 *1) (-5 *1 (-548))))
+(((*1 *2 *2) (|partial| -12 (-5 *1 (-547 *2)) (-4 *2 (-537)))))
+(((*1 *2 *3) (-12 (-5 *2 (-400 *3)) (-5 *1 (-547 *3)) (-4 *3 (-537)))))
(((*1 *2 *3 *4 *5 *6)
- (|partial| -12 (-5 *4 (-1147)) (-5 *6 (-620 (-593 *3))) (-5 *5 (-593 *3))
- (-4 *3 (-13 (-27) (-1169) (-414 *7)))
- (-4 *7 (-13 (-444) (-825) (-145) (-1012 (-536)) (-619 (-536))))
- (-5 *2 (-2 (|:| -2246 *3) (|:| |coeff| *3))) (-5 *1 (-544 *7 *3)))))
+ (|partial| -12 (-5 *4 (-1149)) (-5 *6 (-622 (-595 *3))) (-5 *5 (-595 *3))
+ (-4 *3 (-13 (-27) (-1171) (-416 *7)))
+ (-4 *7 (-13 (-446) (-827) (-145) (-1014 (-538)) (-621 (-538))))
+ (-5 *2 (-2 (|:| -2251 *3) (|:| |coeff| *3))) (-5 *1 (-546 *7 *3)))))
(((*1 *2 *3 *4)
- (-12 (-5 *4 (-1147))
- (-4 *5 (-13 (-444) (-825) (-145) (-1012 (-536)) (-619 (-536))))
- (-5 *2 (-567 *3)) (-5 *1 (-544 *5 *3))
- (-4 *3 (-13 (-27) (-1169) (-414 *5))))))
+ (-12 (-5 *4 (-1149))
+ (-4 *5 (-13 (-446) (-827) (-145) (-1014 (-538)) (-621 (-538))))
+ (-5 *2 (-569 *3)) (-5 *1 (-546 *5 *3))
+ (-4 *3 (-13 (-27) (-1171) (-416 *5))))))
(((*1 *2 *2 *3)
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(-5 *2
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(-5 *2
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- ((*1 *1 *2) (-12 (-5 *2 (-307 (-677))) (-5 *1 (-323))))
- ((*1 *1) (-5 *1 (-323))))
-(((*1 *1 *2 *1 *1) (-12 (-5 *2 (-1146)) (-5 *1 (-323))))
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+ (-12 (-5 *2 (-1065 (-922 (-538)))) (-5 *3 (-922 (-538))) (-5 *1 (-325))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1065 (-922 (-538)))) (-5 *1 (-325)))))
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+ ((*1 *1 *2) (-12 (-5 *2 (-1131)) (-5 *1 (-325)))))
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+(((*1 *1 *2) (-12 (-5 *2 (-309 (-166 (-373)))) (-5 *1 (-325))))
+ ((*1 *1 *2) (-12 (-5 *2 (-309 (-538))) (-5 *1 (-325))))
+ ((*1 *1 *2) (-12 (-5 *2 (-309 (-373))) (-5 *1 (-325))))
+ ((*1 *1 *2) (-12 (-5 *2 (-309 (-674))) (-5 *1 (-325))))
+ ((*1 *1 *2) (-12 (-5 *2 (-309 (-681))) (-5 *1 (-325))))
+ ((*1 *1 *2) (-12 (-5 *2 (-309 (-679))) (-5 *1 (-325))))
+ ((*1 *1) (-5 *1 (-325))))
+(((*1 *1 *2 *1 *1) (-12 (-5 *2 (-1148)) (-5 *1 (-325))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1148)) (-5 *1 (-325)))))
+(((*1 *1 *2) (-12 (-5 *2 (-622 (-325))) (-5 *1 (-325)))))
+(((*1 *1) (-5 *1 (-325))))
+(((*1 *1) (-5 *1 (-325))))
+(((*1 *1 *2) (-12 (-5 *2 (-622 (-840))) (-5 *1 (-325)))))
+(((*1 *1 *2 *3) (-12 (-5 *3 (-622 (-1149))) (-5 *2 (-1149)) (-5 *1 (-325)))))
(((*1 *2 *1)
(-12
(-5 *2
@@ -14220,163 +14221,163 @@
(|:| |Goto| "goto") (|:| |Continue| "continue")
(|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save")
(|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")))
- (-5 *1 (-323)))))
+ (-5 *1 (-325)))))
(((*1 *2 *1)
(-12
(-5 *2
(-3 (|:| |nullBranch| "null")
(|:| |assignmentBranch|
- (-2 (|:| |var| (-1147)) (|:| |arrayIndex| (-620 (-920 (-536))))
- (|:| |rand| (-2 (|:| |ints2Floats?| (-112)) (|:| -3599 (-838))))))
+ (-2 (|:| |var| (-1149)) (|:| |arrayIndex| (-622 (-922 (-538))))
+ (|:| |rand| (-2 (|:| |ints2Floats?| (-112)) (|:| -3604 (-840))))))
(|:| |arrayAssignmentBranch|
- (-2 (|:| |var| (-1147)) (|:| |rand| (-838))
+ (-2 (|:| |var| (-1149)) (|:| |rand| (-840))
(|:| |ints2Floats?| (-112))))
(|:| |conditionalBranch|
- (-2 (|:| |switch| (-1146)) (|:| |thenClause| (-323))
- (|:| |elseClause| (-323))))
+ (-2 (|:| |switch| (-1148)) (|:| |thenClause| (-325))
+ (|:| |elseClause| (-325))))
(|:| |returnBranch|
- (-2 (|:| -3757 (-112))
- (|:| -3756 (-2 (|:| |ints2Floats?| (-112)) (|:| -3599 (-838))))))
- (|:| |blockBranch| (-620 (-323))) (|:| |commentBranch| (-620 (-1129)))
- (|:| |callBranch| (-1129))
+ (-2 (|:| -3762 (-112))
+ (|:| -3761 (-2 (|:| |ints2Floats?| (-112)) (|:| -3604 (-840))))))
+ (|:| |blockBranch| (-622 (-325))) (|:| |commentBranch| (-622 (-1131)))
+ (|:| |callBranch| (-1131))
(|:| |forBranch|
- (-2 (|:| -1556 (-1063 (-920 (-536)))) (|:| |span| (-920 (-536)))
- (|:| -3579 (-323))))
- (|:| |labelBranch| (-1091))
- (|:| |loopBranch| (-2 (|:| |switch| (-1146)) (|:| -3579 (-323))))
+ (-2 (|:| -1561 (-1065 (-922 (-538)))) (|:| |span| (-922 (-538)))
+ (|:| -3584 (-325))))
+ (|:| |labelBranch| (-1093))
+ (|:| |loopBranch| (-2 (|:| |switch| (-1148)) (|:| -3584 (-325))))
(|:| |commonBranch|
- (-2 (|:| -3900 (-1147)) (|:| |contents| (-620 (-1147)))))
- (|:| |printBranch| (-620 (-838)))))
- (-5 *1 (-323)))))
-(((*1 *2 *1) (-12 (-5 *2 (-1235)) (-5 *1 (-323)))))
-(((*1 *2 *1) (-12 (-5 *2 (-1074)) (-5 *1 (-323)))))
-(((*1 *2 *2) (-12 (-5 *2 (-1091)) (-5 *1 (-323)))))
-(((*1 *1) (-12 (-4 *1 (-322 *2)) (-4 *2 (-361)) (-4 *2 (-356)))))
+ (-2 (|:| -3905 (-1149)) (|:| |contents| (-622 (-1149)))))
+ (|:| |printBranch| (-622 (-840)))))
+ (-5 *1 (-325)))))
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+(((*1 *2 *2) (-12 (-5 *2 (-1093)) (-5 *1 (-325)))))
+(((*1 *1) (-12 (-4 *1 (-324 *2)) (-4 *2 (-363)) (-4 *2 (-358)))))
(((*1 *1 *1 *2)
- (-12 (-5 *2 (-1141 *3)) (-4 *3 (-361)) (-4 *1 (-322 *3)) (-4 *3 (-356)))))
+ (-12 (-5 *2 (-1143 *3)) (-4 *3 (-363)) (-4 *1 (-324 *3)) (-4 *3 (-358)))))
(((*1 *2 *1)
- (-12 (-4 *1 (-322 *3)) (-4 *3 (-356)) (-4 *3 (-361)) (-5 *2 (-1141 *3)))))
+ (-12 (-4 *1 (-324 *3)) (-4 *3 (-358)) (-4 *3 (-363)) (-5 *2 (-1143 *3)))))
(((*1 *2 *1 *1)
- (|partial| -12 (-4 *1 (-322 *3)) (-4 *3 (-356)) (-4 *3 (-361))
- (-5 *2 (-1141 *3))))
+ (|partial| -12 (-4 *1 (-324 *3)) (-4 *3 (-358)) (-4 *3 (-363))
+ (-5 *2 (-1143 *3))))
((*1 *2 *1)
- (-12 (-4 *1 (-322 *3)) (-4 *3 (-356)) (-4 *3 (-361)) (-5 *2 (-1141 *3)))))
+ (-12 (-4 *1 (-324 *3)) (-4 *3 (-358)) (-4 *3 (-363)) (-5 *2 (-1143 *3)))))
(((*1 *1 *2 *1)
- (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-319 *3 *4)) (-4 *3 (-1023)) (-4 *4 (-770)))))
+ (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-321 *3 *4)) (-4 *3 (-1025)) (-4 *4 (-772)))))
(((*1 *1 *1 *2 *3 *1)
- (-12 (-4 *1 (-319 *2 *3)) (-4 *2 (-1023)) (-4 *3 (-770)))))
+ (-12 (-4 *1 (-321 *2 *3)) (-4 *2 (-1025)) (-4 *3 (-772)))))
(((*1 *1 *1 *1 *2)
- (-12 (-5 *2 (-749)) (-4 *1 (-319 *3 *4)) (-4 *3 (-1023)) (-4 *4 (-770))
+ (-12 (-5 *2 (-751)) (-4 *1 (-321 *3 *4)) (-4 *3 (-1025)) (-4 *4 (-772))
(-4 *3 (-170)))))
(((*1 *2 *1 *3)
- (-12 (-5 *3 (-536)) (-4 *1 (-316 *4 *2)) (-4 *4 (-1072)) (-4 *2 (-130)))))
+ (-12 (-5 *3 (-538)) (-4 *1 (-318 *4 *2)) (-4 *4 (-1074)) (-4 *2 (-130)))))
(((*1 *1 *2 *1)
- (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-316 *3 *4)) (-4 *3 (-1072)) (-4 *4 (-130)))))
+ (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-318 *3 *4)) (-4 *3 (-1074)) (-4 *4 (-130)))))
(((*1 *1 *1 *1)
- (-12 (-4 *1 (-316 *2 *3)) (-4 *2 (-1072)) (-4 *3 (-130)) (-4 *3 (-770)))))
+ (-12 (-4 *1 (-318 *2 *3)) (-4 *2 (-1074)) (-4 *3 (-130)) (-4 *3 (-772)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-536)) (-4 *4 (-771)) (-4 *5 (-825)) (-4 *2 (-1023))
- (-5 *1 (-314 *4 *5 *2 *6)) (-4 *6 (-924 *2 *4 *5)))))
+ (-12 (-5 *3 (-538)) (-4 *4 (-773)) (-4 *5 (-827)) (-4 *2 (-1025))
+ (-5 *1 (-316 *4 *5 *2 *6)) (-4 *6 (-926 *2 *4 *5)))))
(((*1 *2 *2 *3)
- (-12 (-5 *2 (-1141 *7)) (-5 *3 (-536)) (-4 *7 (-924 *6 *4 *5)) (-4 *4 (-771))
- (-4 *5 (-825)) (-4 *6 (-1023)) (-5 *1 (-314 *4 *5 *6 *7)))))
+ (-12 (-5 *2 (-1143 *7)) (-5 *3 (-538)) (-4 *7 (-926 *6 *4 *5)) (-4 *4 (-773))
+ (-4 *5 (-827)) (-4 *6 (-1025)) (-5 *1 (-316 *4 *5 *6 *7)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-1141 *6)) (-4 *6 (-1023)) (-4 *4 (-771)) (-4 *5 (-825))
- (-5 *2 (-1141 *7)) (-5 *1 (-314 *4 *5 *6 *7)) (-4 *7 (-924 *6 *4 *5)))))
+ (-12 (-5 *3 (-1143 *6)) (-4 *6 (-1025)) (-4 *4 (-773)) (-4 *5 (-827))
+ (-5 *2 (-1143 *7)) (-5 *1 (-316 *4 *5 *6 *7)) (-4 *7 (-926 *6 *4 *5)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-1141 *7)) (-4 *7 (-924 *6 *4 *5)) (-4 *4 (-771)) (-4 *5 (-825))
- (-4 *6 (-1023)) (-5 *2 (-1141 *6)) (-5 *1 (-314 *4 *5 *6 *7)))))
+ (-12 (-5 *3 (-1143 *7)) (-4 *7 (-926 *6 *4 *5)) (-4 *4 (-773)) (-4 *5 (-827))
+ (-4 *6 (-1025)) (-5 *2 (-1143 *6)) (-5 *1 (-316 *4 *5 *6 *7)))))
(((*1 *2 *3 *4 *5)
- (-12 (-5 *3 (-1141 *9)) (-5 *4 (-620 *7)) (-5 *5 (-620 *8)) (-4 *7 (-825))
- (-4 *8 (-1023)) (-4 *9 (-924 *8 *6 *7)) (-4 *6 (-771)) (-5 *2 (-1141 *8))
- (-5 *1 (-314 *6 *7 *8 *9)))))
+ (-12 (-5 *3 (-1143 *9)) (-5 *4 (-622 *7)) (-5 *5 (-622 *8)) (-4 *7 (-827))
+ (-4 *8 (-1025)) (-4 *9 (-926 *8 *6 *7)) (-4 *6 (-773)) (-5 *2 (-1143 *8))
+ (-5 *1 (-316 *6 *7 *8 *9)))))
(((*1 *2 *1)
- (-12 (-5 *2 (-400 (-536))) (-5 *1 (-312 *3 *4 *5))
- (-4 *3 (-13 (-356) (-825))) (-14 *4 (-1147)) (-14 *5 *3))))
+ (-12 (-5 *2 (-402 (-538))) (-5 *1 (-314 *3 *4 *5))
+ (-4 *3 (-13 (-358) (-827))) (-14 *4 (-1149)) (-14 *5 *3))))
(((*1 *2 *3 *3 *3 *4 *5 *4 *6)
- (-12 (-5 *3 (-307 (-536))) (-5 *4 (-1 (-219) (-219))) (-5 *5 (-1060 (-219)))
- (-5 *6 (-536)) (-5 *2 (-1179 (-901))) (-5 *1 (-311))))
+ (-12 (-5 *3 (-309 (-538))) (-5 *4 (-1 (-221) (-221))) (-5 *5 (-1062 (-221)))
+ (-5 *6 (-538)) (-5 *2 (-1181 (-903))) (-5 *1 (-313))))
((*1 *2 *3 *3 *3 *4 *5 *4 *6 *7)
- (-12 (-5 *3 (-307 (-536))) (-5 *4 (-1 (-219) (-219))) (-5 *5 (-1060 (-219)))
- (-5 *6 (-536)) (-5 *7 (-1129)) (-5 *2 (-1179 (-901))) (-5 *1 (-311))))
+ (-12 (-5 *3 (-309 (-538))) (-5 *4 (-1 (-221) (-221))) (-5 *5 (-1062 (-221)))
+ (-5 *6 (-538)) (-5 *7 (-1131)) (-5 *2 (-1181 (-903))) (-5 *1 (-313))))
((*1 *2 *3 *3 *3 *4 *5 *6 *7)
- (-12 (-5 *3 (-307 (-536))) (-5 *4 (-1 (-219) (-219))) (-5 *5 (-1060 (-219)))
- (-5 *6 (-219)) (-5 *7 (-536)) (-5 *2 (-1179 (-901))) (-5 *1 (-311))))
+ (-12 (-5 *3 (-309 (-538))) (-5 *4 (-1 (-221) (-221))) (-5 *5 (-1062 (-221)))
+ (-5 *6 (-221)) (-5 *7 (-538)) (-5 *2 (-1181 (-903))) (-5 *1 (-313))))
((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
- (-12 (-5 *3 (-307 (-536))) (-5 *4 (-1 (-219) (-219))) (-5 *5 (-1060 (-219)))
- (-5 *6 (-219)) (-5 *7 (-536)) (-5 *8 (-1129)) (-5 *2 (-1179 (-901)))
- (-5 *1 (-311)))))
-(((*1 *2 *3) (-12 (-5 *2 (-1 (-219) (-219))) (-5 *1 (-311)) (-5 *3 (-219)))))
+ (-12 (-5 *3 (-309 (-538))) (-5 *4 (-1 (-221) (-221))) (-5 *5 (-1062 (-221)))
+ (-5 *6 (-221)) (-5 *7 (-538)) (-5 *8 (-1131)) (-5 *2 (-1181 (-903)))
+ (-5 *1 (-313)))))
+(((*1 *2 *3) (-12 (-5 *2 (-1 (-221) (-221))) (-5 *1 (-313)) (-5 *3 (-221)))))
(((*1 *2 *3 *4 *3 *3)
- (-12 (-5 *3 (-286 *6)) (-5 *4 (-113)) (-4 *6 (-414 *5))
- (-4 *5 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *5 *6))))
+ (-12 (-5 *3 (-288 *6)) (-5 *4 (-113)) (-4 *6 (-416 *5))
+ (-4 *5 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *5 *6))))
((*1 *2 *3 *4 *3 *5)
- (-12 (-5 *3 (-286 *7)) (-5 *4 (-113)) (-5 *5 (-620 *7)) (-4 *7 (-414 *6))
- (-4 *6 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *6 *7))))
+ (-12 (-5 *3 (-288 *7)) (-5 *4 (-113)) (-5 *5 (-622 *7)) (-4 *7 (-416 *6))
+ (-4 *6 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *6 *7))))
((*1 *2 *3 *4 *5 *3)
- (-12 (-5 *3 (-620 (-286 *7))) (-5 *4 (-620 (-113))) (-5 *5 (-286 *7))
- (-4 *7 (-414 *6)) (-4 *6 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *6 *7))))
+ (-12 (-5 *3 (-622 (-288 *7))) (-5 *4 (-622 (-113))) (-5 *5 (-288 *7))
+ (-4 *7 (-416 *6)) (-4 *6 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *6 *7))))
((*1 *2 *3 *4 *5 *6)
- (-12 (-5 *3 (-620 (-286 *8))) (-5 *4 (-620 (-113))) (-5 *5 (-286 *8))
- (-5 *6 (-620 *8)) (-4 *8 (-414 *7))
- (-4 *7 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *7 *8))))
+ (-12 (-5 *3 (-622 (-288 *8))) (-5 *4 (-622 (-113))) (-5 *5 (-288 *8))
+ (-5 *6 (-622 *8)) (-4 *8 (-416 *7))
+ (-4 *7 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *7 *8))))
((*1 *2 *3 *4 *5 *3)
- (-12 (-5 *3 (-620 *7)) (-5 *4 (-620 (-113))) (-5 *5 (-286 *7))
- (-4 *7 (-414 *6)) (-4 *6 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *6 *7))))
+ (-12 (-5 *3 (-622 *7)) (-5 *4 (-622 (-113))) (-5 *5 (-288 *7))
+ (-4 *7 (-416 *6)) (-4 *6 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *6 *7))))
((*1 *2 *3 *4 *5 *6)
- (-12 (-5 *3 (-620 *8)) (-5 *4 (-620 (-113))) (-5 *6 (-620 (-286 *8)))
- (-4 *8 (-414 *7)) (-5 *5 (-286 *8))
- (-4 *7 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *7 *8))))
+ (-12 (-5 *3 (-622 *8)) (-5 *4 (-622 (-113))) (-5 *6 (-622 (-288 *8)))
+ (-4 *8 (-416 *7)) (-5 *5 (-288 *8))
+ (-4 *7 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *7 *8))))
((*1 *2 *3 *4 *3 *5)
- (-12 (-5 *3 (-286 *5)) (-5 *4 (-113)) (-4 *5 (-414 *6))
- (-4 *6 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *6 *5))))
+ (-12 (-5 *3 (-288 *5)) (-5 *4 (-113)) (-4 *5 (-416 *6))
+ (-4 *6 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *6 *5))))
((*1 *2 *3 *4 *5 *3)
- (-12 (-5 *4 (-113)) (-5 *5 (-286 *3)) (-4 *3 (-414 *6))
- (-4 *6 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *6 *3))))
+ (-12 (-5 *4 (-113)) (-5 *5 (-288 *3)) (-4 *3 (-416 *6))
+ (-4 *6 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *6 *3))))
((*1 *2 *3 *4 *5 *5)
- (-12 (-5 *4 (-113)) (-5 *5 (-286 *3)) (-4 *3 (-414 *6))
- (-4 *6 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *6 *3))))
+ (-12 (-5 *4 (-113)) (-5 *5 (-288 *3)) (-4 *3 (-416 *6))
+ (-4 *6 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *6 *3))))
((*1 *2 *3 *4 *5 *6)
- (-12 (-5 *4 (-113)) (-5 *5 (-286 *3)) (-5 *6 (-620 *3)) (-4 *3 (-414 *7))
- (-4 *7 (-13 (-825) (-543) (-596 (-525)))) (-5 *2 (-51))
- (-5 *1 (-310 *7 *3)))))
+ (-12 (-5 *4 (-113)) (-5 *5 (-288 *3)) (-5 *6 (-622 *3)) (-4 *3 (-416 *7))
+ (-4 *7 (-13 (-827) (-545) (-598 (-527)))) (-5 *2 (-51))
+ (-5 *1 (-312 *7 *3)))))
(((*1 *2 *1)
- (-12 (-5 *2 (-112)) (-5 *1 (-307 *3)) (-4 *3 (-543)) (-4 *3 (-825)))))
+ (-12 (-5 *2 (-112)) (-5 *1 (-309 *3)) (-4 *3 (-545)) (-4 *3 (-827)))))
(((*1 *1 *1 *2)
- (-12 (-5 *2 (-536)) (-5 *1 (-307 *3)) (-4 *3 (-543)) (-4 *3 (-825)))))
-(((*1 *2 *1 *1) (-12 (-4 *1 (-300)) (-5 *2 (-112)))))
-(((*1 *2 *1) (-12 (-4 *1 (-300)) (-5 *2 (-749)))))
+ (-12 (-5 *2 (-538)) (-5 *1 (-309 *3)) (-4 *3 (-545)) (-4 *3 (-827)))))
+(((*1 *2 *1 *1) (-12 (-4 *1 (-302)) (-5 *2 (-112)))))
+(((*1 *2 *1) (-12 (-4 *1 (-302)) (-5 *2 (-751)))))
(((*1 *2 *1 *1 *1)
(|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1)))
- (-4 *1 (-300))))
+ (-4 *1 (-302))))
((*1 *2 *1 *1)
- (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2496 *1)))
- (-4 *1 (-300)))))
-(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-620 *1)) (-4 *1 (-300)))))
-(((*1 *2 *2) (-12 (-5 *2 (-620 *3)) (-4 *3 (-823)) (-5 *1 (-297 *3)))))
+ (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2501 *1)))
+ (-4 *1 (-302)))))
+(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-622 *1)) (-4 *1 (-302)))))
+(((*1 *2 *2) (-12 (-5 *2 (-622 *3)) (-4 *3 (-825)) (-5 *1 (-299 *3)))))
(((*1 *2 *3 *4)
- (-12 (-5 *3 (-620 (-219))) (-5 *4 (-749)) (-5 *2 (-667 (-219)))
- (-5 *1 (-296)))))
-(((*1 *2 *3) (-12 (-5 *3 (-400 (-536))) (-5 *2 (-219)) (-5 *1 (-296)))))
-(((*1 *2 *3) (-12 (-5 *3 (-219)) (-5 *2 (-307 (-371))) (-5 *1 (-296)))))
-(((*1 *2 *3) (-12 (-5 *3 (-920 (-219))) (-5 *2 (-219)) (-5 *1 (-296)))))
-(((*1 *2 *3) (-12 (-5 *3 (-920 (-219))) (-5 *2 (-307 (-371))) (-5 *1 (-296)))))
+ (-12 (-5 *3 (-622 (-221))) (-5 *4 (-751)) (-5 *2 (-669 (-221)))
+ (-5 *1 (-298)))))
+(((*1 *2 *3) (-12 (-5 *3 (-402 (-538))) (-5 *2 (-221)) (-5 *1 (-298)))))
+(((*1 *2 *3) (-12 (-5 *3 (-221)) (-5 *2 (-309 (-373))) (-5 *1 (-298)))))
+(((*1 *2 *3) (-12 (-5 *3 (-922 (-221))) (-5 *2 (-221)) (-5 *1 (-298)))))
+(((*1 *2 *3) (-12 (-5 *3 (-922 (-221))) (-5 *2 (-309 (-373))) (-5 *1 (-298)))))
(((*1 *2 *3)
(-12
(-5 *3
- (-2 (|:| |stiffness| (-371)) (|:| |stability| (-371))
- (|:| |expense| (-371)) (|:| |accuracy| (-371))
- (|:| |intermediateResults| (-371))))
- (-5 *2 (-1009)) (-5 *1 (-296)))))
+ (-2 (|:| |stiffness| (-373)) (|:| |stability| (-373))
+ (|:| |expense| (-373)) (|:| |accuracy| (-373))
+ (|:| |intermediateResults| (-373))))
+ (-5 *2 (-1011)) (-5 *1 (-298)))))
(((*1 *2 *3)
(-12
(-5 *3
@@ -14390,1070 +14391,1077 @@
(|:| |bothSingular| "There are singularities at both end points")
(|:| |notEvaluated| "End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1124 (-219)))
+ (-3 (|:| |str| (-1126 (-221)))
(|:| |notEvaluated| "Internal singularities not yet evaluated")))
- (|:| -1556
+ (|:| -1561
(-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 *1 (-29 *4))))
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- (|:| |abserr| (-219)) (|:| |relerr| (-219))))
- (-5 *2 (-371)) (-5 *1 (-199)))))
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(((*1 *2 *3)
(-12
(-5 *3
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- (|:| |abserr| (-219)) (|:| |relerr| (-219))))
- (-5 *2 (-371)) (-5 *1 (-199)))))
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(((*1 *2 *3)
(-12
(-5 *3
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- (|:| |abserr| (-219)) (|:| |relerr| (-219))))
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(((*1 *2 *3)
(-12
(-5 *3
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-(((*1 *2 *3)
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(((*1 *2 *3)
(-12
(-5 *3
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(((*1 *2 *3)
(|partial| -12
(-5 *3
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- (-5 *2 (-620 (-219))) (-5 *1 (-198)))))
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(((*1 *2 *3)
(|partial| -12
(-5 *3
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(((*1 *2 *3)
(-12
(-5 *3
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(((*1 *2 *3)
(-12
(-5 *3
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(-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 (-186)))))
+ (-5 *1 (-188)))))
(((*1 *2 *3)
(-12
(-5 *3
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(-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")))
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(((*1 *2 *3 *3)
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(((*1 *2 *3 *3)
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(((*1 *2 *2)
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(((*1 *2 *2)
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((*1 *2 *3)
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(((*1 *2 *3)
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(((*1 *2 *3)
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(((*1 *2 *3)
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(((*1 *2 *3)
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(((*1 *2 *2)
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(((*1 *2 *2)
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(((*1 *2 *2)
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(((*1 *1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-173)))))
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@@ -15461,1084 +15469,1083 @@
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generated by cgit v1.2.3 (git 2.39.1) at 2024-07-03 08:03:08 +0000